math anxiety research paper

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• Published: 25 February 2021

What impact does maths anxiety have on university students?

• Eihab Khasawneh   ORCID: orcid.org/0000-0002-9106-9008 1 , 2 ,
• Cameron Gosling 1 &
• Brett Williams 1  

BMC Psychology volume  9 , Article number:  37 ( 2021 ) Cite this article

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Maths anxiety is defined as a feeling of tension and apprehension that interferes with maths performance ability, the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations. Our aim was to identify the facilitators and barriers of maths anxiety in university students.

A scoping review methodology was used in this study. A search of databases including: Cumulative Index of Nursing and Allied Health Literature, Embase, Scopus, PsycInfo, Medline, Education Resources Information Centre, Google Scholar and grey literature. Articles were included if they addressed the maths anxiety concept, identified barriers and facilitators of maths anxiety, had a study population comprised of university students and were in Arabic or English languages.

Results and discussion

After duplicate removal and applying the inclusion criteria, 10 articles were included in this study. Maths anxiety is an issue that effects many disciplines across multiple countries and sectors. The following themes emerged from the included papers: gender, self-awareness, numerical ability, and learning difficulty. The pattern in which gender impacts maths anxiety differs across countries and disciplines. There was a significant positive relationship between students’ maths self-efficacy and maths performance and between maths self-efficacy, drug calculation self-efficacy and drug calculation performance.

Maths anxiety is an issue that effects many disciplines across multiple countries and sectors. Developing anxiety toward maths might be affected by gender; females are more prone to maths anxiety than males. Maths confidence, maths values and self-efficacy are related to self-awareness. Improving these concepts could end up with overcoming maths anxiety and improving performance.

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Introduction

Maths anxiety can be defined as a feeling of tension, apprehension and anxiety that interferes with maths performance ability the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations [ 1 ]. According to Olango [ 2 ] maths anxiety consists of an affective, behavioural and cognitive response to a perceived threat to self-esteem that occurs as a response to situations involving mathematics. Maths anxiety, which is rooted in emotional factors, can be differentiated from dyscalculia, which is characterized by a specific cognitive deficit in mathematics [ 3 ], in two ways. Firstly, maths anxiety can exist in people who have maths capability even though they may dislike maths. Secondly, maths anxiety has an emotional component which is not the case in dyscalculia [ 4 ].

Maths anxiety may occur in all levels of education from primary school to university education. Harari et al. [ 5 ] reported that negative reactions and numerical confidence are the most salient dimensions of maths anxiety in a sample of first-grade students. Similar findings were also observed at tertiary levels across multiple disciplines, including health care professions. For example, Roykenes and Larsen [ 6 ] studied 116 baccalaureate nursing students and found that there was a negative relationship between previous mathematic likes/dislikes and self-assessment of mathematic ability.

Many factors may contribute to or facilitate the maths anxiety. These factors or facilitators may include teachers, parents, peers and society. Negative experiences of maths learning in classroom or home can lead to maths anxiety [ 7 ]. Firstly, the teacher plays important role in making the class more attractive and reducing anxieties. Good maths teachers can create a learning environment in which students have a positive expectation about their learning [ 8 ]. Secondly, parents play an important part in developing or reducing the maths anxiety of their children. Parents' behaviours and relations with children are very important in this aspect [ 7 ]. By discussing the anxieties and the fears that their children might face, the parents are able to pinpoint any learning problem at early stage [ 8 ]. This might prevent the developing of any learning anxieties that the students might face later in life. Moreover, parents’ maths anxiety causes their children to learn less maths over the school year and to have more maths anxiety by the school year's end [ 9 ]. Thirdly, peers play important role in facilitating maths anxiety [ 7 ]. Peers at any stage of learning may have a negative impact on their colleagues, for example when students might feel inferior in front of their colleagues when they make mistakes [ 7 ]. Finally, society can contribute to the development of maths anxiety due to the misconception about mathematics, or maths myths [ 7 ].

Maths anxiety has negative impacts on individuals; many students who suffer from mathematics anxiety have little confidence in their ability to do mathematics and tend to take the minimum number of required mathematics courses, which greatly limits their career [ 10 ]. Fortunately, certain strategies can act as barriers, or prevent maths anxiety occurring. Uusimaki and Kidman [ 11 ] stated that whenever the persons become self-aware of maths anxiety and its consequences, their abilities to overcome it might increase [ 11 ]. On the other hand, activity-based learning and online/distance learning may reduce the fear of looking stupid in front of peers [ 12 ]. Another strategy is the use of untimed/unassessed (low stakes) tests to reduce the maths anxiety as well as to increase confidence [ 13 ]. Relevancy of studying maths can reduce maths anxiety; applying mathematics and statistics to real-life examples rather than pure maths can reduce maths anxiety [ 13 ].

Empirical investigations first began on maths anxiety in the 1950s, and Dreger and Alken [ 14 ] introduced the concept of maths anxiety to describe students’ attitudinal difficulty with maths. The aim of this study was to identify the facilitators and barriers of maths anxiety in university students using a scoping review methodology.

A scoping review methodology was used in conducting this study to allow for a greater breadth of literature to be investigated. Scoping reviews identify and map existing literature on a selected subject. This scoping review utilised the Arksey and O’Malley framework which includes six methodological steps: identifying the research question, identifying relevant studies, selecting studies, charting the data, collating, summarising and reporting the results and consulting experts [ 15 ]. The scoping approach systematically maps and reviews existing literature on a selected topic [ 16 ] including evidence from both peer-reviewed research and the non-peer reviewed literature.

Identify the research question

After several review iterations, the research team agreed on the question that guided this review: What are the barriers and facilitators of maths anxiety in university students? This question was broad so it could cover a wide literature in different disciplines that allowed a better summary of the available literature.

Identify relevant studies

A list of search terms was compiled from the available literature and previous research into maths anxiety and students. Suitable Medical Subject Headings (MeSH) terms and free text keywords were identified (Table 1 ). A search of databases included: Cumulative Index of Nursing and Allied Health Literature (CINHAL), Embase, Scopus, PsycInfo, Medline, ERIC, Trove, Google Scholar and Grey literature. The search involved any related studies from July-2018 backward. Studies in Arabic and English languages were filtered from the search yield and the abstracts scanned. The databases search were conducted by one of the researchers (EK). The search yield resulted in 656 records which were exported to EndNote17 referencing for screening.

Duplicates and irrelevant studies were removed by one of the researchers (EK) and potentially relevant abstracts were complied. The selection process was conducted at two levels: a title and abstract review and full-text review. The title and abstract of the retrieved studies were independently screened (EK and BW) for inclusion based on predetermined criteria. In the second stage, the selected studies full text of potentially eligible studies were assessed and inclusion confirmed by two of the authors (EK and BW). After removing the duplicates, (EK and BW) conducted the title and abstract review of 656 articles. After applying the inclusion criteria 20 articles resulted. These 20 articles were reviewed by (EK and BW) for the second time which ended in 10 articles to be involved in the scoping review.

Study selection (Fig.  1 )

Flow chart of study selection

Articles that met the following inclusion criteria were selected.

Research articles (of any design) available in full text.

The article addressed the maths anxiety concept.

The article identified the barriers and the facilitators of maths anxiety.

The article had a study population comprised of university students.

The article was in Arabic or English languages.

Articles that are systematic and scoping reviews, abstracts, editorials and letters for editors were excluded.

Charting the data

This stage allows data extraction from the included studies for more data description. A narrative review method was used to extract the data from each study. Narrative reviews summarise studies from which conclusions can be drawn into more holistic interpretation by the reviewers [ 17 ]. The data included: the author and the year of publication, the country the study was conducted in, the study design or type, the sample size, results and the theme emerges from the study (Table 2 ). Four themes emerged following full-text review of the 10 included papers, these included: gender, self-awareness, numerical ability and learning difficulties.

Collating, summarising and reporting the results

The data extracted from the included studies are reported in Table 2 . The table shows a summary of the selected articles in this scoping review study. It presents data on the different scales used to evaluate the maths anxiety across the different disciplines. Key outcome data from each of the included studies is presented and includes some of the causes or predictors of maths anxiety in university students such as gender and self-efficacy.

Consultation (optional)

Two experts were contacted for consultation to ensure no new or existing literature was missed; however no new articles were added following this consultation.

Maths anxiety is an issue that effects many disciplines across multiple countries and sectors. Literature analysed in this scoping review spanned disciplines as diverse as education, engineering, health and science while covering diverse geographical locations such as United States (US), Austria, United Kingdom (UK), Israel, Portugal and Canada. The included articles utilised an array of varied study designs, including, cross-sectional, randomised control trial, and prospective cohort studies. The main themes that emerged from this review include gender, self-awareness, numerical ability, and learning difficulty each of these will now be synthesised and discussed.

Six articles addressed the gender concept; two American studies, three European and one Israeli study with mixed findings for the role gender plays in maths anxiety. Some of these articles found that gender has a role in maths anxiety [ 18 , 18 , 20 , 21 ], while others found there was no significant difference between males and females [ 20 , 22 ]. For example, a study of female psychology students in the US reported more maths anxiety than males [ 19 ] whereas there was no significant difference between males and females in maths anxiety in psychology students reported in the UK [ 20 ]. Psychology female students in the US [ 19 ] and Austria [ 21 ], and social science and education female students in Israel showed more maths anxiety than male students [ 22 ]. While in another study there was no significant difference in maths anxiety between males and females in the Portuguese engineering students [ 23 ].

The reasons why females frequently report higher maths anxiety than males is not well understood [ 24 ]. One explanation might be the different gender socialisation during childhood may differentially affect the anxiety experienced by males and females in certain situations which is known as the sex-role socialization hypothesis [ 24 ]. The sex-role socialization hypothesis argues that because mathematics has been traditionally viewed as a male domain, females may be socialised to think of themselves as mathematically incompetent and therefore females may avoid mathematics. When females do participate in mathematical activities they may experience more anxiety than males [ 24 ].

The pattern of gender effect on maths anxiety is different among disciplines and countries. In a recent study, Paechter et al. [ 21 ] administered the Revised Maths Anxiety Ratings Scale (R-MARS) to 225 psychology students at the University of Graz, Austria. This study showed that there were three antecedents of maths anxiety. Firstly, female gender who reported a higher level of maths anxiety β  = − 0.660. Secondly, a high proneness to experience anxiety in general report higher levels of maths anxiety β  = 0.385. Finally, poor grades in maths. According to Paechter et al. [ 21 ] maths anxiety is inversely related to maths grades β  = 0.393. Of the above three factors, female gender was the most strongly related to maths anxiety and is supported by the findings of other studies such as Devine et al. [ 23 ]. Developing anxiety toward maths might be effected by gender and highlights a specific area for future empirical work.

Self-awareness

Self-awareness helps people to manage themselves and improve performances while the opposite is true that lacking self-awareness leads to making the same mistakes repeatedly [ 25 ]. Being self-aware enables us to determine our strengths and areas that can be improved [ 25 ]. Four studies addressed the self-awareness concept in relation to maths anxiety, one American study, one UK study, one Israeli study and one Portuguese study. Under the self-awareness theme, a number of other subthemes emerged including self-efficacy, maths confidence, maths value, maths barriers and performance. McMullan et al. [ 26 ] developed a Drug Calculations Self-Efficacy Scale that measured critical skills of medication calculations (dose of liquid oral drugs, solid drugs, injections, percentage solutions and infusion and drip rates). McMullan et al. [ 26 ] reported that there was a significant positive correlation between students’ maths self-efficacy and maths performance and between maths self-efficacy, drug calculation self-efficacy and drug calculation performance. Low level of maths anxiety was demonstrated by 10% of the students, medium level by 70% and high level by 20% of the students. McMullan et al. [ 26 ] also noted that numerical skills can be improved by remedial approaches as lectures, study groups, workshops and computer assisted instructions [ 27 ]. The authors suggested that the lectures should be more student-directed not only didactic in nature. Study groups increase the cooperation and encourage students to exchange and clarify information leading to improve the self-efficacy.

Maths confidence, maths value and maths barriers are related to maths behaviour and performance. Hendy et al. [ 28 ] studied maths behaviours in 368 university maths students. They reported maths behaviours (attending class, doing homework, reading textbooks and asking for help) at week 8 of the 15 week-semester using self-reported questionnaires. The aim of their study was identify the subclasses of maths beliefs and their role in maths behaviours. The most commonly reported maths belief was maths confidence (mean rating = 3.79, SD = 0.90). This study reported that students with low maths confidence or high maths anxiety might benefit from the maths self-evaluation and self-regulation interventions. These interventions utilised suggestions which include: maths skills are learnable not innate, assessing current skills and believing in their development abilities, teaching student the specific strategies to solve maths problems and keeping self-regulatory records to track development in overcoming maths anxiety. These interventions may be used in overcoming maths anxiety. This study outlined the approach to develop interventional teaching methods that can be applied to students or course curriculum to help in reducing maths anxiety. Self-awareness might determine the person’s areas of strength that might help future career selection. Self-efficacy, maths confidence and values, maths barriers and performance are factors that related to self-awareness. Assessing these factors can determine the methods of improving self-awareness which may end in overcoming maths anxiety.

Numerical ability

Two articles addressed the numerical ability concept [ 25 , 2 ]. In their efforts to understand the origin of maths anxiety, Maloney et al. [ 29 ] investigated the processing of symbolic magnitude by high and low maths anxious individuals. They reported that high maths anxious individuals have less precise representations of numerical magnitude than their low maths anxious peers. Two experiments were performed on 48 undergraduate students in the University of Waterloo. A single Arabic digit in 18-font Arial font was presented at fixation. Numbers ranged from 1–4 to from 6–9. The participants were told to identify whether the number above five or below it. This study revealed that high maths anxious individuals have a less precise representation of numerical magnitude than the low maths anxious individuals. The results suggest that maths anxiety is associated with low level numerical deficits that compromise the development of higher level mathematical skills.

On the other hand, McMullan et al. [ 26 ] reported that numerical ability and maths anxiety are the main personal factors that might influence drug calculation ability in nursing students. The numerical ability test (NAT), used by McMullan et al. [ 26 ], is comprised of 15 questions that covered calculation operations like multiplication, addition, fraction, subtraction, percentage, decimals and conversion. McMullan et al. [ 26 ] reported that both numerical ability and drug calculation abilities of the participants (229 UK nursing students) were poor which might have been to an over-reliance on using calculators or not having adequate maths education in the past. Improving numerical ability and reducing maths anxiety can be achieved through teaching in a supportive environment using multiple teaching strategies that address the needs of all students and not being didactic [ 26 ]. Examples of these strategies include: accept and encourage students creative thinking, tolerate dissent, encourage students to trust their judgments, emphasise that everyone is capable of creativity, and serve as a stimulus for creative thinking through brainstorming and modelling [ 30 ].

Learning difficulty

Australian surveys have indicated that 10 to 16 per cent of students are perceived by their teachers to have learning difficulties according to Learning Difficulty Australia (LDA) (2012). Within the population of students with learning difficulties, there is a smaller subset of students who show persistent and long-lasting learning impairments and these are identified as students with a learning disability. It is estimated that approximately 4 per cent of Australian students have a learning disability (LDA 2012).

In this scoping review, one UK study addressed this concept, comparing undergraduate psychology students who represent 71% of the sample and nursing students who represent 14% of the sample who either had dyslexia ( n  = 28) or were assigned to the control group ( n  = 71). In 2014 Jordan et al. [ 31 ] reported that students with dyslexia had higher levels of maths anxiety relative to those without [ 31 ]. This study showed that significant correlations with maths anxiety were found for self-esteem ( r  = − 0.327; n  = 99, p .001), worrying ( r  = 393; n  = 99; p  < 0.001 the denial ( r  = 0.238; n  = 99; p  = 0.018, seeking instrumental support ( r  = 0.206; n  = 99; p  = 0.040 and positive reinterpretation ( r  = − 0.216; n  = 99; p  = 0.032). In addition, this study found that seeking instrumental support served as an indicator of students at high risk of maths anxiety. In explaining variation in maths anxiety. Jordan et al. [ 31 ] claimed that 36% of this variation is due to dyslexia, worrying, denial, seeking instrumental support and positive reinterpretation. The limitation of this study is that not all dyslexia cases were disclosed by the students. As long as some of the students with dyslexia are not reported, the generalisation of this study would be limited. This study recommends positive reframing and thought challenging as techniques to overcome difficult emotions and anxiety.

Limitations and future research

While multiple databases were used in this scoping review, some articles may be missed due to using specific terms in the search strategy. The disciplines covered in this scoping review were psychology, engineering, mathematics and some of the health disciplines such as nursing. Future research might focus on numerical ability and maths anxiety in university students who need maths and calculation in their future careers as engineers and health care professionals.

For example, the relationship between medication and drug calculation errors and maths anxiety in the health care field can be researched. Moreover, the relationship between self-awareness and numerical ability and maths anxiety and their impact on the performance and ability of the university students can be a future research topic. Finally, developing a new teaching package or strategy that reduces maths anxiety can be tested on university students.

Maths anxiety,which is an issue that affects many disciplines across multiple countries and sectors, is affected by gender, self-awareness, learning difficulties and numerical ability. Maths anxiety and its contributing factors at tertiary education should be researched more in the future addressing interventions and strategies to overcome maths anxiety. Maths anxiety level measuring tools should be used in determining its level among university students.

Availability of data and materials

It is a scoping review and all the articles that are analysed in this review are listed in the references section.

Abbreviations

Cumulative Index of Nursing and Allied Health Literature

Education Resources Information Centre

High Maths Anxious

Learning Difficulty Australia

Low Maths Anxious

Maths Barrier Scale

Maths Confidence Scale

Medical Subject Headings

Maths Value Scale

United Kingdom

United States

Revised Maths Anxiety Rating Scale

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EK conceived, designed and carried out the study, interpreted the analysis, and drafted and revised the manuscript. BW conceived, designed, drafted and revised the manuscript. CG helped conceive, drafted and revised the manuscript. All authors read and approved the final manuscript.

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Mathematics anxiety among STEM and social sciences students: the roles of mathematics self-efficacy, and deep and surface approach to learning

• Dmitri Rozgonjuk   ORCID: orcid.org/0000-0002-1612-2040 1 , 2 ,
• Tiina Kraav 2 ,
• Kristel Mikkor 2 ,
• Kerli Orav-Puurand 2 &
• Karin Täht 2 , 3  

International Journal of STEM Education volume  7 , Article number:  46 ( 2020 ) Cite this article

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Although mathematics anxiety and self-efficacy are relatively well-researched, there are several uninvestigated terrains. In particular, there is little research on how mathematics anxiety and mathematics self-efficacy are associated with deep (more comprehensive) and surface (more superficial) approaches to learning among STEM and social sciences students. The aim of the current work was to provide insights into this domain.

Bivariate correlation analysis revealed that mathematics anxiety had a very high negative correlation with mathematics self-efficacy. However, while mathematics anxiety correlated positively with surface approach to learning in the STEM student sample, this association was not statistically significant in the social sciences student sample. Controlled for age and gender, regression analysis showed that lower mathematics self-efficacy and female gender predicted higher mathematics anxiety, while only mathematics self-efficacy predicted mathematics anxiety in the social sciences student sample. Interestingly, approaches to learning were not statistically significant predictors in multivariate analyses when mathematics self-efficacy was included.

Conclusions

The results suggest that mathematics self-efficacy plays a large role in mathematics anxiety. Therefore, one potential takeaway from the results of the current study is that perhaps improving students’ mathematics self-efficacy could also be helpful in reducing mathematics anxiety. Since the current study was cross-sectional, it could also be that reducing students’ mathematics anxiety could be helpful in boosting their mathematics self-efficacy. Future studies should aim to clarify the causal link in this relationship.

Introduction

One could argue that mathematics is an important component in science, technology, engineering, and mathematics (STEM) education, since most domains rely on applying mathematical thinking. Research on teaching and learning mathematics has received a lot of attention over the years, as mathematical knowledge is a crucial factor for students’ successful future careers (Claessens & Engel, 2013 ; Konvalina, Wileman, & Stephens, 1983 ). As mathematics is commonly perceived to be difficult (Fritz, Haase, & Räsänen, 2019 ), it has been proposed that instead of instructing the content and practices of mathematics, the main focus should be on students’ experience of the discipline and providing mathematical sense-making (Li & Schoenfeld, 2019 ). Research in tertiary mathematics education is also a growing field as the role of mathematics in learning other disciplines is widely acknowledged.

Little research has investigated the relationships between mathematics anxiety, mathematics self-efficacy, and approaches to learning in the context of mathematics education among STEM and social sciences students. Do students with higher mathematics anxiety also have a more superficial approach to learning? Or does mathematics self-efficacy also contribute to a more thoughtful and integrative learning process? Are there significant differences in mathematics self-efficacy, mathematics anxiety, and approaches to learning between STEM and social sciences students? Thus far, these questions have not received a lot of attention in the academic literature. Therefore, the main aim of this study is to provide some insights into the relationships between mathematics anxiety, mathematics self-efficacy, and approaches to learning, and the potential differences in those variables between STEM and social sciences students. While several associations have been investigated in earlier works (see below), this is the first study where the relationships between all these variables are compared among STEM and social sciences students.

Literature overview

Mathematics anxiety has been described as experiencing feelings of panic and helplessness when asked to solve a mathematical task or problem (Tobias & Weissbrod, 1980 ). Psychological as well as physiological symptoms may appear when feeling anxious about mathematics (Chang & Beilock, 2016 ). Mathematics anxiety is known as a common problem in K-12 as well as tertiary education (Ashcraft & Moore, 2009 ; Luttenberger, Wimmer, & Paechter, 2018 ; Yamani, Almala, Elbedour, Woodson, & Reed, 2018 ) and, therefore, has received considerable attention as a researched topic among educational scientists (Dowker, Sarkar, & Looi, 2016 ; Hoffman, 2010 ; Jansen et al., 2013 ). For instance, in the Programme for International Student Assessment (PISA) 2012, across the 34 participating Organisation for Economic Co-operation and Development (OECD) countries, 59% of the 15-year-old students reported that they often worry that math classes will be difficult for them and 31% reported they get very nervous doing math problems (OECD, 2013b ).

Mathematics anxiety can be caused by several different factors. For instance, unpleasant teaching and assessment strategies for students, like time testing (Ashcraft & Moore, 2009 ) and assigning mathematics as punishment (Oberlin, 1982 ), that are still widely in use in all school levels, may influence the spread of mathematics anxiety. Although mathematics anxiety may have been appearing relatively early in life, it has been shown that there are possibilities to reduce mathematics anxiety in all levels of schooling (Hembree, 1990 ). As appropriate mathematics-related instruction and teacher’s enthusiasm toward mathematics are important in the development of mathematics anxiety of students (Jackson & Leffingwell, 1999 ), reduction of pre-service teachers’ own mathematics anxiety is crucial and it could be helpful in reducing the students’ mathematics anxiety (Gresham, 2007 ; Vinson, 2001 ). Applying more active learning (such as group work) may also reduce anxiety (Cooper, Downing, & Brownell, 2018 ).

Mathematics anxiety has been shown to be associated with poorer performance in mathematics (Ashcraft & Faust, 1994 ; Devine, Fawcett, Szűcs, & Dowker, 2012 ; Fan, Hambleton, & Zhang, 2019 ). In addition, it has been shown, that mathematics anxiety also correlates with other variables (e.g., learning behavior, self-efficacy) that influence academic performance (Feng, Suri, & Bell, 2014 ; McMullan, Jones, & Lea, 2012 ). For example, Paechter, Macher, Martskvishvili, Wimmer, and Papousek ( 2017 ) investigated psychology students and showed a correlation between mathematics and statistics anxiety and learning behavior. In addition, Royse and Rompf ( 1992 ) compared social work and non-social work university students and found that the former had higher levels of mathematics anxiety than the latter group. Nevertheless, there are no studies comparing STEM and social sciences students with regard to mathematics anxiety.

Attitudes toward mathematics is another construct that plays an important role in mathematical studies, as well as its outcomes (Ahmed, Minnaert, Kuyper, & van der Werf, 2012 ; House, 2005 ). Mathematics attitudes and anxiety are often studied together; nevertheless, they cannot be equated with each other. As Zan and Martino ( 2007 ) describe, many studies about mathematics attitudes do not provide a clear definition for the construct. It always has an emotional dimension (positive or negative emotional disposition toward mathematics), usually also involving conceptualization of mathematics (Dowker et al., 2016 ), and/or mathematics-related behavior, depending on the specific research problem. In addition, one may argue that, to some extent, attitudes toward mathematics also reflect mathematics self-efficacy (Yusof & Tall, 1998 ). Self-efficacy could be defined as one’s belief in one’s ability to succeed in specific situations. The academic aspect of this concept is called academic self-efficacy, and is described as an individual’s belief that they can successfully achieve at a designated level on an academic task (Bandura, 1997 ). Mathematics self-efficacy is one’s belief about how their own action and effort could lead to success in mathematics (Luttenberger et al., 2018 ; OECD, 2013b ). Higher mathematics self-efficacy has been shown to be correlated with lower mathematics anxiety, more positive, and less negative attitudes toward mathematics (Akin & Kurbanoglu, 2011 ). In addition, higher mathematics anxiety is related to more negative attitudes toward mathematics (Vinson, 2001 ). These findings underscore the importance of mathematics anxiety in attitudes toward mathematics, as well as mathematics self-efficacy.

More general attitudes toward learning are also important to be considered. Marton and Säljö ( 1976 ) referred to a co-existence of intention and process of learning and described deep and surface learning approaches. Students with a deep approach to learning look for the meaning of the studied material and try to relate new knowledge with prior information, whereas students with a surface approach to learning use rote learning and un-meaningful memorization. How students approach to learning in higher education is an important factor when speaking about educational outcomes (Duff, Boyle, Dunleavy, & Ferguson, 2004 ; Fryer & Vermunt, 2018 ; Maciejewski & Merchant, 2016 ). Deep approach to learning is associated with better general academic outcomes, as well as, specifically, better mathematical performance (Murphy, 2017 ; Postareff, Parpala, & Lindblom-Ylänne, 2015 ). Although it is not the sole factor influencing mathematics achievement, it is still important to determine students’ approaches to learning mathematics, as it enables educators to analyze and shape the students’ classroom experience toward more effective learning.

Little research has been done in the domain of approaches to learning in relation to mathematics anxiety and self-efficacy in tertiary education. Anxiety in general is associated with higher surface and lower deep approach to learning (Marton & Säljö, 1984 ). In one study, surface approach to learning has been found to correlate with mathematics anxiety (Bessant, 1995 ). It has also been demonstrated that students with positive attitudes toward mathematics tend to use more deep and less surface approach when learning mathematics (Alkhateeb & Hammoudi, 2006 ; Gorero & Balila, 2016 ). Another common finding in educational research is that students who have higher self-efficacy adopt more deep approach to learning (Papinczak, Young, Groves, & Haynes, 2008 ; Phan, 2011 ; Prat-Sala & Redford, 2010 ).

There are not many studies investigating the role of deep and surface approaches to learning in mathematics anxiety. Although a study by Bessant ( 1995 ) showed that mathematics students scored lower on mathematics anxiety measure than psychology/sociology students, the relations between mathematics anxiety and approaches to learning in STEM and social sciences students is a largely unexplored area.

Conceptual framework

Several studies have aimed to explain the potential causes for mathematics anxiety. It has been proposed that the origins of mathematics anxiety could be categorized into three groups (Baloglu & Kocak, 2006 ): situational, dispositional, and environmental factors. Situational factors are direct stimuli related to feelings of anxiety in relation to mathematics. Dispositional factors include individual characteristics, such as personality traits; for instance, it has been shown that people with higher trait neuroticism (the tendency to experience negative effect; McCrae & Costa, 2003 ) worry more and tend to be more anxious in general (Costa & McCrae, 1985 ), although this typically decreases with age (Mõttus & Rozgonjuk, 2019 ). Finally, environmental factors include prior perceptions, attitudes, and experiences that may have affected the individual (Baloglu & Kocak, 2006 ).

In the current work, mathematics self-efficacy as well as approaches to learning could be conceptualized as environmental factors that could potentially affect the development of mathematics anxiety. Furthermore, students’ age, gender, and the curricula could be considered as environmental factors potentially affecting mathematics anxiety (Baloglu & Kocak, 2006 ).

Aims and hypotheses

The general aim of this study is to investigate how mathematics anxiety and self-efficacy, as well as approaches to learning (deep and surface), are related to each other. Furthermore, these relationships are also compared across STEM and social sciences student samples. Based on the previous literature, we have posed some hypotheses that are rather confirmatory of previous findings. Based on the previous literature, we hypothesize the following:

H1: Mathematics anxiety and mathematics self-efficacy are negatively correlated .

Previously it has been demonstrated that mathematics anxiety and self-efficacy are inversely associated (Akin & Kurbanoglu, 2011 ; Vinson, 2001 ).

H2: Mathematics anxiety is positively correlated with surface approach to learning and negatively with deep approach to learning . Even though one study found that mathematics anxiety correlates positively with surface approach to learning (Bessant, 1995 ), it would also be natural to assume that deep approach to learning is negatively associated with mathematics anxiety, since typically surface and deep approaches to learning are inversely correlated (Rozgonjuk, Saal, & Täht, 2018 ).

H3: Mathematics self-efficacy is positively associated with deep and negatively with surface approach to learning. It has previously been shown that high self-efficacy, in general, is associated with more deep and less surface approach to learning (Chou & Liang, 2012 ; Papinczak et al., 2008 ). Therefore, it would be logical to assume that also in the context of mathematics, these constructs would be correlated.

H4: STEM students have less mathematics anxiety than social sciences students . Previously, Bessant ( 1995 ) have demonstrated that mathematics students had lower scores on mathematics anxiety measure than psychology/sociology students. However, our study goes beyond comparing only mathematics students, and includes students from other disciplines (e.g., biology) as well, forming a more heterogeneous STEM student group.

H5: Approaches to learning and mathematics self-efficacy predict mathematics anxiety when age and gender are controlled for. Based on previous research and hypotheses mentioned above, there is evidence to believe that the associations between approaches to learning, mathematics self-efficacy, and mathematics anxiety would hold also when covariates are included.

There is relatively little research in this domain and knowing the associations between these variables may help educators to improve and adjust their teaching strategies to potentially improve the learning process. The results of this study aim to outline the important predictors of mathematics anxiety, and, therefore, expand the existing research in this field of study, and influence future teaching strategies. The results of this work could be helpful for the teacher/lecturer when he/she aims toward reducing mathematics anxiety by, e.g., using teaching strategies that could enhance deeper (and less surface) approach to learning, increase mathematics self-efficacy, or both.

Material and methods

Sample and procedure.

The study participants were students who either took an introductory calculus course (dealing with more elaborate topics than in secondary education) for university students or an introductory statistical modeling course at a major Estonian university. Importantly, these courses were mandatory in order to complete the student’s curriculum and, in most cases, were prerequisite courses for other courses in the curriculum. While most of the students in the introductory calculus course were STEM curricula students, mainly psychology and political sciences majors were enrolled in the statistical modeling course. However, because it is possible to take these courses as electives as well, students with various backgrounds could participate in these courses. This means that, theoretically, both student groups could enroll in either the calculus or statistical modeling course. For instance, as could be seen in Supplementary Table 1 there are some Economics students who enrolled in a Calculus course, while all other social sciences students were enrolled in the statistical modeling course. Students’ responses across variables of interest across curricula are depicted in Supplementary Figures 1 to 4 .

The data were collected during the start of both courses, in September 2019. Students were asked to take part in a web survey which aimed to investigate the role of different factors in mathematics education. Participation in the study was voluntary, anonymous, and in line with the Helsinki Declaration.

In total, there were 358 responses. However, many rows were empty or most of the data were missing, after some initial data cleaning, 234 rows of responses were kept. The reason for the aforementioned “missing data” lies in the fact that whenever a person opens the questionnaire environment, this gets logged as a response row. However, it does not necessarily mean that a person provides any responses to the questionnaire. Therefore, as mentioned, out of 358 rows logged, only 234 were actually partially or fully filled in with responses. Finally, because n = 3 people did not specify their major, we excluded those rows. Therefore, the effective sample comprised 231 students (age M = 21.39, SD = 5.12; 79 (34.2%) men, 152 (65.8%) women). There were 147 (63.6% of total sample) STEM students (age M = 20.55, SD = 4.51; 57 men, 90 women), and 84 (36.4%) social sciences students (age M = 22.87, SD = 5.78; 22 men, 62 women).

We queried about the study participants’ socio-demographic variables (e.g., age, gender, curriculum/major), mathematics anxiety and mathematics self-efficacy, and approaches to learning (deep and surface).

• Mathematics anxiety

Mathematics anxiety was measured with the 5-item mathematics anxiety questionnaire used in the international PISA 2012 survey (OECD, 2013a ). Students were asked to assess on a 4-point scale (1 = strongly disagree to 4 = strongly agree ) the extent of agreement with the following statements: (1) I often worry that mathematics classes will be difficult for me ; (2) I get very tense when I have to do mathematics homework ; (3) I get very nervous doing mathematics problems ; (4) I feel helpless when doing a mathematics problem ; (5) I worry that I will get poor grades in mathematics . The psychometric properties of this scale in an adolescent population could be found in OECD report ( 2014 ; Table 16.7 on page 320). As a side comment, we opted for using this measure as opposed to, e.g., the Abbreviated Mathematics Anxiety Scale (AMAS; Hopko, Mahadevan, Bare, & Hunt, 2003 ), because the PISA-study mathematics anxiety scale fits better with contemporary classroom where the role of digitalization is increasing (e.g., the AMAS items include words like “book” and “blackboard,” but not digital resources). Secondly, PISA mathematics anxiety scale has demonstrated good psychometric properties, it has probably been administered in a larger variety of cultural settings (as opposed to the AMAS), and it has been validated against mathematics aptitude test in all these cultures (e.g., see the report by OECD ( 2014 ), p. 320, Table 16.7, ANXMAT). Finally, in all PISA survey questionnaires, stringent quality-assurance mechanisms are implemented by experts in translation, sampling, and data collection, resulting in a high degree of reliability and validity (OECD, 2017 ). Cronbach’s alpha for the effective sample of this measure was very good, α = 0.90.

• Mathematics self-efficacy

Mathematics self-efficacy was measured with three items, measuring the extent of agreement on a four-point scale (1 = strongly disagree to 4 = strongly agree ) from Yusof and Tall ( 1998 ). All items from the mathematics self-efficacy scale (Yusof & Tall, 1998 ) were translated into Estonian by the members of our mathematics education team and were reviewed by a professional Estonian philologist. The questionnaire was then translated back into English by another translator, and the back-translated English version was reviewed by an English-speaking student in order to estimate the content and the similarities between the original and the back-translated items. The items were the following: (1) I usually understand a mathematical idea quickly; (2) I have to work very hard to understand mathematics ; (3) I can connect mathematical ideas that I have learned . Cronbach’s alpha for this three-item measure was α = 0.83.

• Approaches to learning

Approaches to learning were measured with the Estonian adaptation of the Revised Study Process Questionnaire (Biggs, Kember, & Leung, 2001 ; Valk & Marandi, 2005 ). It is a 16-item measure (8 items for deep and 8 items for surface approach to learning) that measures deep and surface approaches to learning on a five-point scale (1 = do not agree at all to 5 = totally agree ). Example items for the deep approach to learning scale are as follows: I find most new topics interesting and often spend extra time trying to obtain more information about them , and I learn because I want to understand the world . Example items for the surface approach to learning scale are as follows: I see no point in learning material which is not likely to be in the examination , and In case of difficult topics, learning by rote is one way to pass an exam . The internal consistency of deep and surface approaches to learning were acceptable, Cronbach’s α = 0.71 for both scales.

Data analysis was conducted in the R software version 3.5.3 (R Core Team, 2020 ). As mentioned in the “Sample and procedure” section, we first removed the data rows that were not valid responses (empty rows) or where people did not specify their major ( n = 3). After this procedure, there were no missing data in key variables. Internal consistency statistics were calculated with the alpha() function from the psych package (Revelle, 2018 ). Since the sample sizes were not equal, Mann-Whitney U tests to analyze the potential group differences between STEM and social sciences students in age, math anxiety and self-efficacy, and deep and surface approach to learning were used. Chi-square test was used to see if there are differences in gender distribution among those student groups.

We then computed descriptive statistics and conducted Spearman correlation analysis (with p values adjusted for multiple testing with the Holm’s method), using the rcorr.adjust() function from the RcmdrMisc package (Fox, 2020 ). Finally, we computed regression models where mathematics anxiety was treated as the outcome variable, either surface or deep approach to learning as the predictor, age and sex were covariates, and we also computed additional regression models where mathematics self-efficacy was additionally included as a predictor variable. We ran these analyses for the whole sample, as well as for STEM and social sciences students separately.

The data as well as the analysis script are included with this work as Supplementary Materials .

Firstly, we analyzed if STEM and social sciences students had group differences in key variables. There were no statistically significant group differences in deep and surface approaches to learning, mathematics anxiety, as well as in gender distribution (all ps > 0.01). However, the social sciences student group was slightly older ( M = 22.87, SD = 5.78) than the STEM student group ( M = 20.55, SD = 4.51), W = 9742, p < 0.001. In addition, STEM students ( M = 8.39, SD = 1.92) had higher mathematics self-efficacy scores than social sciences students ( M = 7.77, SD = 2.03), W = 5080.50, p = 0.023.

Descriptive statistics and correlations for mathematics anxiety and self-efficacy, and approaches to learning

The descriptive statistics and Spearman correlation coefficients between the variables are in Table 1 .

According to Table 1 , mathematics anxiety was very strongly negatively correlated to mathematics self-efficacy across all samples. Additionally, surface learning was positively significantly associated with mathematics anxiety in the total and STEM student sample, but it was not significant among social sciences students. Deep approach to learning and age were not statistically significantly associated with mathematics anxiety.

Mathematics self-efficacy was negatively significantly associated with surface approach to learning in total and STEM student samples, but not in social sciences students. Mathematics self-efficacy did not correlate with deep approach to learning.

Surface approach to learning was negatively correlated to deep approach to learning in total and STEM student samples (but not in social sciences student sample) and had a statistically significant negative correlation with age only in social sciences student sample. Deep approach to learning did not correlate with age.

Which factors predict mathematics anxiety?

Next, we computed several regression models where mathematics anxiety was treated as the outcome variable. We computed models for three samples of students: the full sample ( N = 231), the STEM student sample ( N = 147), and the social sciences students ( N = 84). For each sample of students, we computed two models. Model 1 included age, gender, and surface and deep approaches to learning as predictors. In model 2, mathematics self-efficacy was added as an additional predictor. For the full sample, we also included the student group (STEM vs social sciences) as a predictor.

According to results in Table 2 , when regression models are computed across the full sample, female students tend to have greater mathematics anxiety than male students. Approaches to learning, age, and being a STEM versus social sciences student did not predict mathematics anxiety. Finally, including the mathematics self-efficacy variable was negatively associated with mathematics anxiety in this multivariate model. In addition, it seems that mathematics self-efficacy explains a large proportion of mathematics anxiety, as inclusion of this variable improved the explained variance by almost 50% in the regression model full sample level.

However, the regression analysis results are somewhat different when the sample is broken down into the STEM and social sciences student group. In STEM students, it seems higher mathematics anxiety is associated with older age, female gender, and more surface and less deep approach to learning. However, when mathematics self-efficacy is included in the model, only gender and mathematics self-efficacy effects are significant.

Interestingly, when mathematics self-efficacy is not included as a predictor of mathematics anxiety, there are no statistically significant predictors in the social sciences student sample; however, once it is included in the regression model, mathematics self-efficacy is statistically significantly and negatively associated with mathematics anxiety.

The aim of the current study was to investigate the relationships between mathematics anxiety, mathematics self-efficacy, and approaches to learning (deep and surface) among STEM and social sciences students. We had posed several hypotheses to meet that aim.

Based on the literature (Akin & Kurbanoglu, 2011 ; Vinson, 2001 ), we expected mathematics anxiety and mathematics self-efficacy to have a negative association (H1). This hypothesis found support from the data. The very high negative correlation of r = −0.768 (across the full sample) suggests that these variables explain each other’s variance relatively well. These results were expected, since students who perceive that they can succeed in mathematics and who have a more positive attitude toward this topic, should experience less anxiety; furthermore, as mentioned earlier, these findings are coherent with previous research (Akin & Kurbanoglu, 2011 ).

Our second hypothesis (H2) regarded the relationship between mathematics anxiety and approaches to learning. Specifically, we expected that mathematics anxiety correlates positively with surface approach to learning and negatively with deep approach to learning. While surface approach to learning should be associated with increased and deep approach to learning with decreased anxiety in general, a study found that only higher levels of surface approach to learning correlated with more mathematics anxiety (Bessant, 1995 ). The results of the current study supported this hypothesis on the full and STEM student sample level; however, surface approach to learning did not correlate significantly with mathematics anxiety in social sciences students. Furthermore, deep approach to learning was negatively correlated with mathematics anxiety in the STEM student sample. This is the first study demonstrating that there are discrepancies in approaches to learning in association with mathematics anxiety between STEM and social sciences students. Although it is hard to explain these discrepancies based on our data, it is certainly a topic that needs to be pursued further.

According to the third hypothesis (H3), we expected mathematics self-efficacy to be positively correlated with deep and negatively with surface approach to learning, in line with some previous findings (Alkhateeb & Hammoudi, 2006 ; Gorero & Balila, 2016 ). This hypothesis found partial support from the data. Deep approach to learning was not associated with mathematics self-efficacy, while surface approach to learning had a negative correlation with mathematics self-efficacy on the full and STEM student sample level.

We expected that STEM students have less mathematics anxiety than social sciences students in our fourth hypothesis (H4). Royse and Rompf ( 1992 ) compared groups of students who did and did not study social work and found that the former had higher mathematics anxiety. However, this was not the case in the current study. STEM and social sciences students did not differ from each other in group comparison analysis. Therefore, this hypothesis did not find support from data. These results are surprising, since one may logically think that if a student chooses to major in a subject that has a strong mathematics component, the student’s anxiety toward mathematics could be lower than among students who choose a curriculum where the share of mathematics may be rather small (on an undergraduate level). Furthermore, STEM students are more likely to have mathematics in different courses throughout their studies as well as professionally after graduation. Therefore, these results are certainly interesting, since they demonstrate that STEM and social sciences students are as much or as little anxious toward mathematics.

Finally, to understand how mathematics anxiety would be predicted from approaches to learning and mathematics self-efficacy when age and gender are controlled for, we conducted regression models on the total, STEM, and social sciences student samples. We hypothesized that approaches to learning and mathematics self-efficacy predict mathematics anxiety, also when age and gender are controlled for (H5) . The regression model results showed that among STEM student sample, older age, female gender, higher surface, and lower deep approach to learning predicted higher mathematics anxiety. However, when mathematics self-efficacy was included in the model, only female gender and lower mathematics self-efficacy were significant predictors of mathematics anxiety. Gender differences are somewhat in line with research finding that female students tend to experience more anxiety in STEM classroom settings (Pelch, 2018 ). Interestingly, only lower mathematics self-efficacy predicted higher mathematics anxiety in social sciences student sample.

One potential takeaway from the results of this study is that in order to lower one’s mathematics anxiety, it could be necessary to boost one’s mathematics self-efficacy. However, this may prove to be a rather difficult task, since there is a potential problem of a “vicious circle:” one’s mathematics self-efficacy may be dependent on one’s performance in mathematics, and vice versa (Carey, Hill, Devine, & Szücs, 2016 ). Therefore, if a student performs well on a mathematics task, their self-efficacy may get a boost, consequently lowering mathematics-related anxiety. On the other hand, if a student performs poorly, their self-efficacy may drop, followed by increased anxiety. Mathematics anxiety, in turn, could further hamper one’s mathematics performance, resulting in poorer perceived self-efficacy. It would be, therefore, necessary to further study—preferably experimentally and in a longitudinal study design—how working with one’s mathematics self-efficacy could be helpful against mathematics anxiety.

While we discussed the association between mathematics anxiety and self-efficacy, it is nevertheless noteworthy that approaches to learning seem to play a significant role in mathematics anxiety among STEM students. Somewhat coherent with previous findings, more surface approach to learning predicted more mathematics anxiety (Bessant, 1995 ). These results suggest that perhaps—at least among STEM students—there is a possibility to tailor the classroom experience so that it would promote more synthesis of study materials, and decrease fact-based, rote-learning. STEM subjects likely have more universal facts (e.g., equations, proofs) to be learned, possibly promoting superficial learning. Here, too, could be a potentially vicious circle in play: a student who has to study materials that may seemingly be isolated facts, could implement rote-learning. This results in superficial knowledge, which may not prove to be useful when synthesis with other materials is needed. In turn, this may lead to poor performance and higher mathematics anxiety due to that. As discussed earlier, mathematics self-efficacy also likely plays a crucial role in this process. On the other hand, this reasoning does not entirely explain why approaches to learning did not predict mathematics anxiety among social sciences students. It could be that STEM students differ in how they perceive mathematics in general due to having to use this more in their studies. We believe that this should receive more attention in future research.

The main contribution of this study is providing insights into the potential role of mathematics self-efficacy, and deep and surface approaches to learning in mathematics anxiety in STEM and social sciences students. All in all, it could be inferred from this study that while surface approach to learning may be, to some extent, an important factor possibly predicting mathematics anxiety, the role of mathematics self-efficacy should be further studied in combination with approaches to learning in order to understand mathematics anxiety. It could be further hypothesized that by improving mathematics self-efficacy, it could also be helpful in reducing mathematics anxiety, as well as surface approaches to learning. Interestingly, while STEM and social science students differ in attitudes toward mathematics (with STEM students scoring higher), there were no differences in mathematics anxiety between these student groups.

There are limitations that need to be mentioned. Firstly, we used self-reports in our study. It could be helpful to include other important variables, such as grades and test scores, to complement the results. In addition, methods such as experience sampling may also provide more valid results (Lehtamo, Juuti, Inkinen, & Lavonen, 2018 ). Secondly, there were significantly fewer social sciences students than STEM students in the total sample, and social sciences students were slightly older than STEM students. Although age was accounted for in multivariate analyses, future studies should aim toward equal sample sizes as well as higher similarity in other demographic characteristics (e.g., age, gender). A third limitation was the absence of controlling for students’ prior academic ability (e.g., grade point average, course grades, ability test results). It could be that there are inherent differences between the past performance in mathematics-related courses and mathematics self-efficacy and anxiety. Future works should include variables of prior academic ability as control variables. In addition, future works could also collect data among STEM and social sciences students across multiple semesters, providing more robust results. The fourth limitation regards the use of the mathematics anxiety scale that has been validated in a sample of adolescents. Some additional measures of mathematics anxiety designed for tertiary-education settings, such as the AMAS (Hopko et al., 2003 ), could further validate the findings. Finally, future studies could also include other external factors to models predicting mathematics anxiety (Martin-Hansen, 2018 ).

In conclusion, we found that STEM and social sciences students do not differ largely with regard to mathematics anxiety, while STEM students do have higher mathematics self-efficacy. It may be that surface approach to learning plays a larger role in mathematics anxiety in STEM students than in social sciences students. This is the first work to investigate the differences between STEM and social sciences students in mathematics anxiety and self-efficacy, as well as deep and surface approaches to learning. The results could be helpful for mathematics educators, as it is relevant for them to learn about and understand the interplay between deep and surface approach to learning, mathematics anxiety and self-efficacy, and students’ curricula. It could be that improving students’ mathematics self-efficacy, as well as facilitating more synthesis among the learned materials could help as a remedy against mathematics anxiety. This, however, should be investigated in future research that, preferably, implements an experimental and longitudinal study design.

Availability of data and materials

The data as well as analysis script are available among the supplementary materials .

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Supplementary Table 1 Grouping of students to social sciences/STEM by self-reported curricula, and the distribution of students' curricula by course taken Notes . LT_Calc1 = Calculus I (LTMS.00.003); MT_Calc1 = Calculus I (MTMM.00.340); SH_StatM = Statistical Modeling (SHSH.00.002). Supplementary Figure 1: Students' mathematics anxiety summed scores plotted by curricula. Note: points are jittered on the graph (with the geom_jitter() function). Supplementary Figure 2: Students' mathematics self-efficacy summed scores plotted by curricula. Note: points are jittered on the graph (with the geom_jitter() function). Supplementary Figure 3: Students' deep approach to learning summed scores plotted by curricula. Note: points are jittered on the graph (with the geom_jitter() function). Supplementary Figure 4: Students' surface approach to learning summed scores plotted by curricula. Note: points are jittered on the graph (with the geom_jitter() function). Math anxiety study

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First-year students’ math anxiety predicts STEM avoidance and underperformance throughout university, independently of math ability

• Richard J. Daker   ORCID: orcid.org/0000-0002-7416-4791 1 ,
• Sylvia U. Gattas 2 ,
• H. Moriah Sokolowski 3 ,
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Math anxiety is widely considered a potential barrier to success in STEM. Current thinking holds that math anxiety is directly linked to avoidance of and underperformance in STEM domains. However, past evidence supporting these claims is limited in important ways. Perhaps most crucially, it is possible that math anxiety predicts STEM outcomes merely as a proxy for poor math skills. Here, we tested the link between math anxiety and subsequent STEM outcomes by measuring math anxiety, math ability, and several covariates in 183 first-semester university students. We then tracked students’ STEM avoidance and achievement through four years at university via official academic transcripts. Results showed that math anxiety predicted both a reduction in how many STEM courses students took and, separately (i.e., controlling for one another), lower STEM grades. Crucially, these associations held after controlling for math ability (and other covariates). That math anxiety predicts math-related academic achievement independently of Math Ability suggests that, contrary to current thinking, math anxiety’s effects on academic performance likely operate via mechanisms other than negatively affecting math ability. Beyond this, we show evidence that math anxiety can account for associations between math ability and STEM outcomes, suggesting that past links between math ability and real-world outcomes may, in fact, be at least partially explainable by attitudes toward math. These findings provide clear impetus for developing and testing interventions that target math anxiety specifically and suggest that focusing on math ability without additional attention to math anxiety may fail to optimally boost STEM outcomes.

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Introduction.

An important goal of researchers, policy-makers, and educators is to foster engagement and success in science, technology, engineering, and mathematics (STEM), especially at the university level where specialized STEM training often begins. Researchers and educators alike believe that anxiety specific to math, or math anxiety, acts as an important barrier to both STEM participation and achievement 1 , 2 , 3 . This is a powerful idea because if it is correct, this suggests that fulfilling the promise in STEM is not just a matter of one’s cognitive ability but also depends on one’s emotions. The idea that math anxiety acts as a barrier to STEM outcomes has important practical implications as well—if anxiety toward math plays an active role in holding students back from succeeding in STEM, then educational interventions aiming to boost STEM outcomes should target math anxiety. Theory on math anxiety holds that math anxiety has two key negative consequences: (1) avoidance of math and (2) underperformance in math 4 . When applied to academic situations, both of these theorized consequences might plausibly affect students’ prospects of success in STEM—if math anxiety causes students to avoid coursework in STEM and/or to underperform in STEM courses, this would stifle students’ ability to be successful in STEM fields. However, the evidence supporting these putative negative academic consequences of math anxiety is limited in important ways that constrain both our theoretical understanding of the potential negative effects of math anxiety on academic STEM outcomes and our ability to make recommendations on the development of targeted interventions to boost STEM outcomes. Below, we briefly summarize the evidence supporting links between math anxiety and these theorized negative outcomes before turning to a discussion of crucial limitations in this body of evidence.

Highly math-anxious individuals are thought to avoid math whenever possible 1 , 4 . The evidence supporting this stems largely from work showing that individuals higher in math anxiety tend to report having taken fewer high school and university-level math courses than their less math-anxious counterparts 5 . Meece, Wigfield, and Eccles 6 also showed that math anxious individuals report being less likely to take additional math courses in the future. Another source of evidence for a link between math anxiety and math avoidance has focused on decisions to engage in STEM, examining the relative math anxiety levels of students in STEM vs. non-STEM majors and of adults in STEM vs. non-STEM careers. Individuals in non-STEM majors and in non-STEM careers report significantly higher levels of math anxiety than those in STEM majors 5 , 7 and careers 8 , respectively. Longitudinal work by Ahmed 9 found that twelfth-grade high school students who had either been consistently high in math anxiety since middle school or who had become highly math-anxious over time were less likely to hold a STEM career as adults than students who either had consistently low levels of math anxiety from middle school through high school or who had become less math-anxious since middle school. Math anxiety is also thought to negatively affect performance in math-related courses 4 , 10 . Previous studies have shown that math anxiety is associated with poorer performance in high school and university-level math classes 5 . Math anxiety has also been shown to negatively predict grades earned in psychology methods and statistics course 11 .

The work reviewed above provides some evidence to suggest that math anxiety may lead students to avoid STEM courses when possible and to underperform in STEM courses that they cannot avoid. However, the body of evidence supporting math anxiety as a barrier to participation and achievement in STEM is limited in important ways, and several key theoretical questions have not yet been tested.

One crucial limitation is that nearly every previous study supporting a link between math anxiety and STEM academic outcomes (with the exception of work by LeFevre, Kulak, and Hemans 7 ) did not account for the fact that high math anxiety and poor math ability are robustly linked 12 , 13 . Previously observed links between math anxiety and STEM outcomes (both avoidance of STEM and underperformance in STEM) could therefore be explained by shared associations with math ability. This is a critical weakness in the evidence base linking math anxiety to STEM outcomes, especially if the goal is to use research to inform educational interventions. If math anxiety is merely a proxy for poor math skills when predicting STEM outcomes, then interventions to boost STEM outcomes might do better to simply focus on improving math skills. But if math anxiety predicts STEM outcomes over and above math skills, this would suggest interventions that ignore math anxiety may miss an opportunity to effectively increase STEM participation and achievement.

Addressing whether math anxiety predicts STEM outcomes even when controlling for math ability would also inform our understanding of the mechanisms that link math anxiety with potential negative academic consequences. First considering avoidance of math as a consequence of math anxiety, it is fairly straightforward to hypothesize that math anxiety would predict avoidance of math-related courses over and above math ability—when students are making decisions about what courses to choose, for instance, their attitudes toward math are likely to matter just as much as, if not more than, their objective ability in math. Directly testing this hypothesis would nevertheless provide valuable evidence as to whether math anxiety is relevant in shaping decisions to pursue or avoid STEM even when individual differences in Math Ability are accounted for.

In a similar vein, asking whether math anxiety predicts grades earned in STEM courses over and above math ability may provide a more nuanced understanding of the mechanisms by which math anxiety relates to poor STEM achievement . There are two main mechanisms by which math anxiety is thought to lead to poor performance in math-related courses. One account focuses on previous avoidance of math: if students consistently avoid math courses, over time, they are likely to gain less practice with math, thereby stunting the development of their math ability 1 , 4 . The other account focuses on the in-the-moment effects of math anxiety on math performance. For students who are high in math anxiety, the prospect of having to do math is anxiety-inducing. This online anxiety response is thought to co-opt working memory resources that are necessary for doing difficult math, thereby causing math-anxious students to underperform on working memory-demanding math tests 4 , 14 . In both of these explanations, math anxiety is related to academic performance via its influence on math ability, either in the past by leading to a reduction in experience with math, or in the moment by taking up working memory resources. If differences in math ability were found to explain associations between math anxiety and STEM achievement, this would provide support for these kinds of models of the academic consequences of math anxiety. If, on the other hand, math anxiety predicted individual differences in STEM performance over and above math ability, this would suggest that math anxiety and STEM outcomes are associated through mechanisms that are not dependent on math ability, pointing to a need to update theories by which math anxiety is related to academic outcomes.

A simple way to overcome this limitation of previous work and to address these theoretical questions would be to measure math ability alongside math anxiety and assess whether math anxiety continues to predict unique variance in STEM outcomes when math ability is controlled for. Doing so would inform theory on math anxiety by allowing for an understanding of the extent to which the predictive effects of math anxiety on STEM avoidance and underperformance can be explained by math ability. Interestingly, the reverse is true as well. A great deal of research has linked math ability with important life outcomes, including grades in math courses 15 , decisions to pursue STEM careers 16 , 17 , 18 , and even income levels and health outcomes 19 , 20 . None of this previous research, however, has accounted for differences in math anxiety. Just as it is possible that math ability may have confounded previously observed relations between math anxiety and STEM outcomes, the reverse is also true: Prior reports of relations between maths ability and STEM outcomes may have been inflated by failing to control for anxiety about math. By including both types of math measures, one can test the extent to which each uniquely predicts STEM outcomes (i.e., controlling for one another).

A second limitation concern claims that math anxiety has negative consequences for STEM outcomes broadly considered 1 , 2 , 3 . The issue is that studies supporting a link between math anxiety and academic outcomes have largely focused specifically on math outcomes rather than on STEM outcomes more broadly. For instance, existing evidence examining the relation between math anxiety and STEM achievement has focused either on a handful of math courses 5 or on a single psychology research methods course 11 . This is not necessarily a flaw of the individual studies themselves (it is perfectly reasonable to assess the effects of math anxiety on math outcomes), but it does limit confidence that math anxiety has negative consequences for STEM outcomes more broadly. No research we are aware of has assessed whether math anxiety predicts performance in STEM courses in a manner that includes all sub-areas of STEM (namely, science, technology, engineering, and math).

Furthermore, while there are a small number of studies showing that math anxiety correlates with avoidance of STEM majors or careers 5 , 7 , 8 , 9 , the majority of these studies were in fact retrodictive. The measure of math anxiety was collected after the STEM-related behavior in question (e.g., math anxiety was collected after individuals had declared a STEM major or attained a STEM career). From both a practical and a theoretical standpoint, it would be preferable to establish the predictive validity of math anxiety—namely, does math anxiety predict subsequent STEM outcomes? The lone study that measured math anxiety prior to the STEM outcome in question (STEM career choice 9 ) is limited by the absence of control for math ability, as discussed above. (Conversely, the lone study that controlled for math ability 7 was retrodictive.) Addressing these gaps requires is a single study that collects measures of math anxiety at the outset—for instance, as students matriculated at university—and predicts subsequent STEM outcomes, while also controlling for objective math ability.

A third limitation of previous work linking math anxiety to STEM outcomes is that STEM avoidance and STEM achievement are often conflated. That is, no single study to our knowledge has linked math anxiety with both STEM avoidance and STEM achievement. As a result, the two types of STEM outcomes are often used interchangeably when discussing the implications of math anxiety for STEM. However, whether one chooses to take courses in STEM (or not), and how well one does in those STEM courses are not necessarily the same thing. Are these two measures so highly correlated that using one as a proxy for another is not in fact all that problematic? Alternatively, if these two aspects of STEM relatively uncorrelated, one can then ask whether math anxiety is primarily predictive of taking fewer STEM courses (STEM avoidance), how well one does in the courses one does take (STEM achievement), or both. If in fact Math Anxiety independently predicts one or both types of STEM outcomes (i.e., controlling for one another), this would suggest that both of the theorized consequences of math anxiety—avoidance and poor performance—may operate via independent mechanisms. This in turn can potentially enrich our theoretical understanding by pointing to specific routes through which math anxiety is linked to negative STEM outcomes. On a practical level, answering these questions may also help shape expectations about how interventions aimed at curbing math anxiety might realistically impact specific STEM outcomes. The present study aims to fill this gap in present understanding by collecting measures of both STEM participation (or the lack thereof) and STEM achievement in the same dataset.

We contend that if we are to take seriously the idea that math anxiety is a key leverage point for researchers and educators interested in fostering better university STEM outcomes, more direct evidence that overcomes the limitations of previous work is needed. We, therefore, measured math anxiety among first-semester university students and predicted real-world university STEM participation and STEM achievement over the ensuing four years of university. Importantly, we assessed the extent to which math anxiety predicted each of these STEM outcomes, even when controlling for one another, for individual differences in math ability, and several other covariates. This allowed us to ask whether anxiety toward math and objective ability in math both predict unique variance in STEM participation and achievement. Further, rather than relying on student self-reports of academic outcomes, we used actual university transcripts to tabulate STEM outcomes. Transcripts provided a comprehensive account of the extent to which students participated in STEM courses and their level of achievement in those courses throughout the university. Together, this design allowed us to test long-standing assumptions in the literature about the role of math anxiety in real-world STEM outcomes, and to establish greater specificity in terms of the scope and limitations of this role.

We also leveraged this design to address two secondary questions. First, we sought to use a mediation approach to directly quantify the extent to which associations between math anxiety and STEM outcomes can be accounted for by individual differences in math ability. We also used a similar framework to test the more counterintuitive idea that prior reports of relations between maths ability and STEM outcomes may in fact be explained—at least in part—by math anxiety. Second, we asked whether math anxiety was especially predictive of university STEM outcomes for certain types of students. math anxiety tends to be higher in women on average 5 , 21 , and it tends to most strongly affect performance among those who tend to be higher in general cognitive ability 22 , 23 , 24 . Thus, we tested whether the link between math anxiety and STEM outcomes depended on (1) Gender and (2) non-STEM achievement levels.

Relations between math measures and between STEM outcomes

Before addressing the main theoretical question of the extent to which first-semester math anxiety predicts university-level STEM outcomes, we first asked some more basic questions of this sample. First, we tested the extent to which Math Anxiety and Math Ability were related in the present sample. Results showed that Math Ability and Math Anxiety were negatively correlated [ r (181) = −.346, p  = 2E − 6; this and all other statistical tests presented are two-sided]. This negative relation and its magnitude are consistent with a large body of the previous research 5 , 10 , 12 , 13 , suggesting that these measures are operating as expected in the present sample.

Second, we tested the extent to which % STEM Courses and STEM Grades were associated with one another. Perhaps surprisingly, we found no significant relationship between the two [ r (181) = .119, p  = .107]. University students who do not intend to ultimately pursue STEM disciplines, however, often take STEM courses in their first semester or two to satisfy general education requirements. Students who left the university early may therefore have inflated estimates of the % STEM Courses they would have taken throughout the normal course of a four-year degree. When the partial correlation between % STEM Courses and STEM Grades controlling for Semesters Absent was computed, we found that there was a significant relation between % STEM Courses and STEM Grades [partial- r -value, r p (180) = .191, p  = .010], and the zero-order relation between % STEM Courses and STEM Grades among those with no Semesters Absent was also significant [ r (146) = .163, p  = .047]. However, even the highest of these estimates suggests that less than 5% of the variance in one STEM outcome can be explained by the other. This provides evidence that STEM participation and STEM achievement are distinct, which underscores the importance of examining % STEM Courses and STEM Grades as separate outcome measures.

For descriptive statistics and zero-order correlations between all measures, including all covariates, see Table S2 .

Zero-order relations between first-semester Math Anxiety and Math Ability and university STEM outcomes

We next assessed whether Math Anxiety and Math Ability predicted % STEM Courses and STEM Grades without controlling for any covariates. Zero-order correlations showed that Math Anxiety and Math Ability were each predictive of individual differences in both % STEM Courses and STEM Grades (all p s ≤ .001). The observed pattern of associations—Math Anxiety and Math Ability both predict differences in STEM participation and achievement and are themselves significantly associated—strongly underscores the need to control for Math Ability when assessing whether Math Anxiety predicts STEM outcomes. Any observed relations between Math Anxiety and STEM outcomes could very well be driven by shared associations with Math Ability if differences in Math Ability are not accounted for.

In the native units of each STEM outcome measure, an increase of one standard deviation in Math Anxiety was associated with a 13.1% decrease in % STEM Courses [ r (181) = −0.390, p  = 5E − 8] and a 3.47 point drop in STEM Grades [ r (181) = −0.324, p  = 8E − 6]. An increase of one standard deviation in Math Ability was associated with an 8.1% increase in % STEM Courses [ r (181) = 0.241, p  = 0.001] and a 3.00 point boost in STEM Grades [ r (181) = 0.280, p  = 1E − 4]. Note that controlling for Semesters Absent does not substantially affect these relations: [Math Anxiety and % STEM Courses r p (180) = −0.396, p  = 3E − 8; Math Anxiety and STEM Grades r p (180) = −0.339, p  = 3E − 6; Math Ability and % STEM Courses r p (180) = 0.282, p  = 1E − 4; Math Ability and STEM Grades r p (180) = 0.272, p  = 2E − 4].

Unique predictive effects of first-semester Math Anxiety and Math Ability on four-year STEM outcomes

In this section, we assessed the extent to which students’ math anxiety and math ability during the first semester of university uniquely predicted university STEM participation and achievement over four years at university, when controlling for one another and for other relevant cognitive, affective, and academic variables.

To do this, we ran two multiple regression models, one predicting % STEM Courses and the other predicting STEM Grades. The predictors of interest for each model were Math Anxiety and Math Ability. Within these models, we also included several predictors as covariates: Trait Anxiety, Verbal Working Memory, Gender, non-STEM Grades, and Semesters Absent. As an important additional covariate, each model also included the other STEM outcome—i.e., when % STEM Courses was the DV, we controlled for STEM Grades, and vice versa. Thus, the two models can be seen as tests for the extent to which the predictors of interest both uniquely and independently predict STEM participation and achievement. For full regression model details, see Table 1 . The key results of these models are visualized in Fig. 1 .

Figure a shows the change in % STEM Courses associated with a 1 SD (standard deviation) increase in Math Anxiety and Math Ability. Zero-order relations between each predictor and % STEM Courses are plotted alongside unique relations between each predictor and % STEM Courses predicted by a multiple regression model including the following measures as predictors: Math Anxiety, Math Ability, STEM Grades, Trait Anxiety, Verbal Working Memory, Gender, non-STEM Grades, and Semesters Absent. Figure b is the same as Fig. a but displays the change in STEM Grades (in points out of 100) associated with a 1 SD increase in Math Anxiety and Math Ability as the dependent variable. The multiple regression model that generated the unique predictions included the same measures as predictors as that of Fig. a , but substituted % STEM Courses for STEM Grades. In both figures, the left y -axis shows the DV in standardized units, which corresponds to standardized β coefficients. The right y -axis shows the DV in the native units of each measure. Error bars reflect standard errors.

The results displayed in Fig. 1a show that both Math Anxiety and Math Ability significantly predicted % STEM Courses when no variables were controlled for (zero-order effects). However, when controlling for one another and for relevant cognitive, affective, and academic measures, Math Anxiety robustly predicted unique variance in % STEM Courses ( β  = −.325, t (174) = −4.20, p  = 4E − 5, Cohen’s d  = −.637), but Math Ability did not ( β  = .129, t (174) = 1.91, p  = .058, Cohen’s d  = .290). These results indicate that even when holding Math Ability, STEM Grades, and all other covariates constant, a one standard deviation increase in Math Anxiety accounted for a 10.9% reduction in the proportion of STEM courses students chose to take. Given that students took an average of 36.13 courses over four years, this corresponds to a reduction of 3.93 STEM courses over four years of university, or about 1 course per year.

Similarly, the results displayed in Fig. 1b show that both Math Anxiety and Math Ability significantly predicted STEM Grades when no variables were controlled for (zero-order effects). When we tested whether these variables predicted unique variance in STEM Grades when controlling for each other and for other relevant covariates, we found that Math Anxiety predicted unique variance in STEM Grades ( β  = −.225, t (174) = −3.45, p  = 7E − 4, Cohen’s d  = −.524) and that Math Ability did not ( β  = .086, t (174) = 1.53, p  = .129, Cohen’s d  = .232). These results indicate that even holding Math Ability, % STEM Courses, non-STEM Grades, and all other covariates constant, a one standard deviation increase in Math Anxiety uniquely accounted for a 2.41 point reduction specifically in STEM Grades.

Together, the results of Fig. 1a and b show that, when controlling for relevant cognitive, affective, and academic variables, anxiety about math robustly predicted unique variance in both STEM outcomes of interest. To better contextualize these results, one can conceptualize individuals as ‘high’ and ‘low’ in Math Anxiety, corresponding to 1 standard deviation above and below the mean, respectively (note that this definition is in line with prior research 14 , 23 ). From that perspective, our results indicate the average high math-anxious person would be expected to take an average of 7.86 fewer STEM courses (nearly 2 courses per year) and perform worse in those courses by 4.82 points (almost half of a letter grade) than their low math-anxious peers. Note this was true even after holding constant (i.e., controlling for) factors like objective math ability, general anxiety, verbal working memory, and relevant academic measures.

The results described thus far show that math anxiety measured in first-semester university students predicts independent variance in both STEM participation and achievement, over and above math ability and other important covariates. We next sought to further understand the predictive effects of math anxiety on these STEM outcomes by asking two additional questions of the data. First, we assessed the extent to which individual differences in math ability account for associations between math anxiety and STEM outcomes, and, conversely, the extent to which individual differences in math anxiety account for associations between math ability and STEM outcomes. Addressing this question can shed additional light on the extent to which relations between anxiety or ability in math are confounded by one another when predicting real-world STEM outcomes. Second, we sought to understand whether math anxiety was particularly predictive of STEM outcomes among particular types of students. This allowed us to address the question of for whom math anxiety may play an especially strong role in shaping university STEM outcomes.

Secondary analysis 1: To what extent are associations between Math Anxiety and STEM outcomes accounted for Math Ability, and vice versa?

As discussed in detail above, a key limitation of much of the previous body of work establishing links between math anxiety and STEM participation and achievement is that, with few exceptions, individual differences in math ability are not controlled for, leaving these associations open to being confounded by math ability. However, this critique could also be applied in the opposite direction as well—there is a large body of work linking math ability to real-life STEM outcomes 15 , 16 , 17 , 18 , 19 , 20 , but because none of this work controls for differences in math anxiety, these findings are possibly confounded by math anxiety. Here, we sought to assess the extent to which the predictive effects of math anxiety on STEM outcomes could be accounted for by math ability and vice versa. To do so, we arranged our key math variables from the primary multiple regression results (Table 1 , Fig. 1 ) in a mediation framework, which allowed us to directly quantify the extent to which math anxiety and math ability can account for one another’s association with each STEM outcome.

The mediation models were computed using the mediation package in R 25 , 26 , 27 . The strength and significance of all mediation models were tested using the bootstrapping method with 10,000 iterations 28 . Importantly, this analysis package provides an estimate of the proportion mediated (% C), which quantifies how much of the association between the independent variable (e.g., Math Anxiety) and the dependent variable (e.g., % STEM Courses) can be attributed specifically to the presence of the mediator (e.g., Math Ability) in the model. Proportion mediated (%C) is thus ideal for testing the extent to which relations between Math Anxiety and STEM outcomes are accounted for by Math Ability, and vice versa. The analyses are shown in Fig. 2a and b to test the extent to which Math Ability accounts for (i.e., reduces) the associations between Math Anxiety and % STEM Courses (Fig. 2a ) and between Math Anxiety and STEM Grades (Fig. 2b ). The analyses are shown in Fig. 2c and d test the opposite: the extent to which Math Anxiety accounts for (i.e., reduces) the associations between Math Ability and % STEM Courses (Fig. 2c ) and between Math Ability and STEM Grades (Fig. 2d ). Note that mediation models included the same covariates (Trait Anxiety, Verbal Working Memory, Gender, non-STEM Grades, and Semesters Absent) as the regression analyses in the previous section (see Table 1 ).

Figure 2 shows mediation models that assess the extent to which Math Anxiety and Math Ability can explain each other’s associations with % STEM Courses and STEM Grades. The following variables were controlled for in all models: Trait Anxiety, Verbal Working Memory, Gender, non-STEM Grades, and Semesters Absent. In models where % STEM Courses was the dependent variable ( a , c ), STEM Grades was included as an additional covariate. Likewise, in models where STEM Grades was the dependent variable ( b , d ), % STEM Courses was included as an additional covariate. ‘95% CI’ refers to bootstrapped 95% confidence intervals.

Mediation results in Fig. 2a and b show that only 12.6% of the association between Math Anxiety and % STEM Courses could be specifically attributed to Math Ability (%C = .126, CI 95 of %C: .005, .308, p  = .040); and only 11.5% of the association between Math Anxiety and STEM Grades was attributable to Math Ability (%C = .115, CI 95 of %C: −.002, .421, p  = .100). Note that only the former indirect effect reached traditional levels of significance ( p  = .040 and p  = .100, respectively).

In contrast, the results from the mediation models displayed in Fig. 2c and d show that 40.9% of the association between Math Ability and % STEM Courses could be specifically attributed to Math Anxiety (%C = .409, CI 95 of %C: .172, .950; p  = .001); and 40.0% of the association between Math Ability and STEM Grades was attributable to Math Anxiety (%C = .400, CI 95 of %C: .092, 1.282; p  = .010). Both indirect effects were significant at traditional significance levels ( p  < 2E − 16, and p  = .005, respectively).

To summarize, while there is some evidence to suggest that math ability partially accounts for associations between math anxiety and real-world STEM outcomes, the evidence supporting the reverse is stronger. Namely, these results suggest that math anxiety accounts for a substantial portion of the associations between math ability and real-world STEM outcomes.

Secondary analysis 2: for whom is Math Anxiety most predictive of University STEM outcomes?

As a final set of analyses, we sought to whether specific types of students might be especially susceptible to the negative effects of math anxiety on STEM outcomes, as this could allow for better targeting of resources to prevent these possible negative outcomes. Specifically, we assessed whether the unique predictive effects of Math Anxiety on % STEM Courses and STEM Grades we observed in our primary analyses were moderated by two key variables of interest: non-STEM Grades and Gender. We used the marks students earned outside of STEM areas (i.e., non-STEM Grades) as a proxy for potential academic aptitude, reasoning that students who demonstrate strong academic aptitude in other areas may have untapped potential in STEM. This afforded the opportunity to test the idea that math anxiety is most pernicious in depressing STEM success among those who might otherwise be most likely to succeed. Namely, we tested whether those with higher non-STEM Grades would show a stronger unique relation between Math Anxiety and STEM outcomes. In addition, gender has been shown in past research to moderate the relation between math anxiety and math grades such that math anxiety is more predictive of math grades among men than women 5 . Here we tested whether this finding would generalize to STEM outcomes more broadly.

All models that assessed moderation effects controlled for the same variables (Math Ability, Trait Anxiety, Verbal Working Memory, Gender, non-STEM Grades, Semesters Absent) that were controlled to assess the unique predictive effects shown in Fig. 1 . We first asked whether the negative relation between Math Anxiety and STEM outcomes differed between students with relatively high or relatively low non-STEM achievement (measured by non-STEM Grades). Results showed that non-STEM Grades did not moderate the relation between Math Anxiety and % STEM Courses ( β  = −.025, t (173) = −.40, p  = .687, Cohen’s d  = −.061) but did moderate the relation between Math Anxiety and STEM Grades ( β  = −.140, t (173) = −2.90, p  = .004, Cohen’s d  = −.441). For full regression model details, see Tables S3 and S4 . Separate effects for high and low non-STEM achievers are visualized in Fig. 3a (% STEM Courses) and Fig. 3b (STEM Grades). Figure 3b indicates that Math Anxiety is more negatively predictive of STEM Grades among students who demonstrate high aptitude in non-STEM courses relative to those with lower aptitude, possibly suggesting that higher levels of math anxiety may be holding students back from realizing their potential to succeed in STEM. These results indicate that among students with high non-STEM Grades, those high in math anxiety (1 standard deviation above the mean) would be predicted to score 8.48 points worse (or almost a full letter grade) than their low math-anxious (1 standard deviation below the mean) peers, even holding constant important factors like objective math ability, general anxiety, verbal working memory, and the number of STEM courses students choose to take.

Figure 3 shows the predicted change in STEM outcomes associated with a 1 SD (standard deviation) increase in Math Anxiety among different groups of students. The estimates are derived from multiple regression models that include all predictors (including Math Ability) used in Fig. 1 , as well as the relevant interaction term. The p -value associated with the relevant interaction term (Fig. a – b : Math Anxiety × non-STEM Grades; Fig. 3 c – d : Math Anxiety × Gender) is shown at the bottom of each figure. This interaction term in effect formally tests for a difference between the two bars in that subfigure. Figure a and b show the predicted change in STEM outcomes associated with a 1 SD increase in Math Anxiety in students with 1 SD below or above the mean in non-STEM academic achievement (high vs. low non-STEM Grades). Figure c shows the predicted change in STEM outcomes associated with a 1 SD increase in Math Anxiety in female and male students. In each figure, the left y -axis shows the DV in standardized units, which corresponds to standardized β coefficients. The right y -axis shows the DV in the native units of each measure. Error bars reflect standard errors.

We also asked whether Gender moderated the relation between Math Anxiety and either % STEM Courses or STEM Grades. From Fig. 3c–d , Math Anxiety tended to be more negatively predictive of university STEM outcomes among men than women, despite the fact that, consistent with the previous literature 21 , 29 , 30 , women reported significantly greater levels of Math Anxiety [ t (181) = −5.35, p  = 3E − 7, Cohen’s d  = −.823]. That said, we urge strong caution in interpreting these results because the Gender × Math Anxiety term failed to reach traditional significance levels ( α  = .05) for either % STEM Courses ( β  = .295, t (173) = 1.79, p  = .075, Cohen’s d  = .272) or STEM Grades ( β  = .267, t (173) = 1.97, p  = .051, Cohen’s d  = .299). On the other hand, both effects were near the ‘significance’ threshold and had effect sizes (Cohen’s d in this case) of ~.28, which may be of interest to some readers. For full regression model details, see Tables S5 and S6 .

Math anxiety is widely considered to be a barrier to success in STEM 1 , 2 , 3 . However, previous research supporting this idea has in fact provided only limited and indirect evidence that math anxiety is associated with STEM outcomes. By collecting math anxiety and math ability measures at the start of university, and by tracking objective and comprehensive STEM outcomes via four years of subsequent transcript data, we show that math anxiety collected in first-semester university students prospectively predicts both real-world university STEM participation and STEM achievement, even when controlling for individual differences in math ability. This work demonstrates clear support for the view that math anxiety plays a key role in suppressing STEM outcomes. This work also supports and further informs existing theory on the academically relevant consequences of math anxiety. The practical and theoretical implications of these findings, along with a discussion of their limitations, are described in detail below.

To our knowledge, the current results provide the most direct and robust evidence to date supporting links between math anxiety and two of its previously hypothesized consequences—avoidance of and underperformance in STEM. Zero-order associations showed robust associations between both math anxiety and math ability and both STEM outcomes (Fig. 1 zero-order effect). This result replicates previous work, while also highlighting the need to identify unique contributions of math anxiety and math ability to STEM outcomes. Importantly, we go beyond prior work by showing the relation between math anxiety and neither STEM avoidance nor STEM underperformance can simply be attributed to poor math skills (Fig. 1 unique effect). Furthermore, by focusing on a comprehensive list of all of the math-related courses students chose to take during their time at university as opposed to focusing more narrowly on a specific set of math courses, this work provides evidence that math anxiety is associated with both avoidance of and underperformance in STEM more broadly considered. In other words, this bolsters support for the idea that math anxiety may act as a barrier to STEM outcomes as opposed to simply math outcomes more narrowly.

Indeed, perhaps surprisingly, we found that math ability actually failed to predict unique variance in either STEM participation or achievement when individual differences in math anxiety were accounted for. These findings suggest that the way students feel about math, over and above their objective math ability, may be especially important for shaping decisions to avoid or pursue STEM topics, as well as for academic performance in those areas. As such, we suggest that future interventions developed with the aim of boosting STEM outcomes would do well to focus on math anxiety as a key leverage point.

Beyond their practical implications, these findings also inform theory on math anxiety in important ways. The finding that math anxiety predicted individual differences in STEM participation and achievement over and above math ability suggests that math anxiety is relevant for STEM outcomes independently of math anxiety’s already well-documented implications for math performance 4 , 5 , 12 , 13 . Indeed, when we assessed the extent to which associations between math anxiety and STEM outcomes could be explained by math ability, we found evidence that math ability accounted for only a relatively small portion of the associations between math anxiety and STEM outcomes (12.6% for STEM participation and 11.5% for STEM achievement; Fig. 2 ). Conversely, math anxiety accounted for 40.9% and 40.0% of the relations between math ability and STEM participation and STEM achievement, respectively. Taken together, these results suggest a need to update how we think about the specific ways and reasons why math anxiety may negatively affect STEM outcomes.

Avoidance of math is commonly assumed to be a consequence of math anxiety, but previous evidence supporting links between math anxiety and avoidance of math-related content has been limited. Much of the previous work that does exist relies on retrodictive associations between math anxiety and STEM avoidance, wherein math anxiety is measured after the avoidance behavior it is meant to explain. Moreover, most previous work has failed to control for differences in math ability, so it has been unclear whether it is truly anxiety toward math that is associated with avoidance of math, or whether it is simply ability in math that leads to avoidance of math-related areas. The present work addresses both of these limitations and shows that math anxiety predicts future avoidance of STEM over and above math ability. The scope of the present work is also broader than past work: we show that math anxiety predicts avoidance of STEM courses, broadly construed as courses that involve math, going beyond the more limited finding of previous work that math anxiety is associated with avoidance of math courses specifically 5 . These results thus provide some of the first clear evidence that highly math-anxious individual indeed avoids not just math courses, but STEM courses in general. Furthermore, this avoidance behavior cannot be attributed solely to poor math ability.

With respect to STEM achievement (grades), previous researchers have proposed two main ways in which math anxiety is thought to impact academic performance. In one account, math anxiety leads to avoidance of math over time, and this avoidance of math leads students to fail to fully develop their math skills, resulting in poor math ability 4 . This poor math ability then harms students’ ability to be successful in courses that require math. However, this account cannot explain the present findings—math anxiety predicted STEM Grades independently of differences in math ability, indicating that a more direct link between math anxiety and STEM achievement is needed.

Another possibility that operates in a more direct, real-time fashion is that students who are high in math anxiety experience an increase in state anxiety at the moment they have to do math-related tasks. This heightened anxiety then co-opts working memory resources that are necessary to complete difficult math tasks 1 , 4 , leading to a decrease in performance. For this explanation to be consistent with our observation that math ability did not mediate the relation between math anxiety and STEM achievement, it would need to be the case that the online effects of math anxiety (i.e., causing increased levels of state anxiety and worry when faced with math) are more pronounced during a true-stakes academic performance than during lab-based measures of math ability. Otherwise, the online effects of math anxiety on math performance would have already been captured in our lab-based measure of math ability, which, as we already noted, accounted for only a marginal portion of the relation between math anxiety and STEM Grades (Fig. 2 ). Thus, while our data cannot fully rule out this possibility, below we propose another possible explanation for our finding that math anxiety predicts STEM Grades independently of math ability, one that focuses on avoidance of math, but on a different scale than avoidance of math-related courses altogether.

While our results suggest that math-anxious students are more likely to avoid STEM courses when possible, importantly, we also showed that this avoidance of STEM courses cannot account for the observed robust relation between math anxiety and STEM Grades. This is because all models with STEM Grades as the outcome also included %STEM Courses as a covariate. Therefore, high-level decisions to avoid math-related courses—or what we term macro-avoidance of math—cannot explain poor STEM Grades. Instead, we propose that students with high levels of math anxiety may make shorter-term decisions to avoid math-related content—instances of what we call micro-avoidance . For instance, a highly math-anxious person might choose to focus less effort and attention on the more math-related elements of the STEM courses they take, leading to poorer grades in those courses. Importantly, this explanation is independent of students’ objective math ability, as well as their longer-term decisions to enroll in more or fewer STEM courses, thus making it consistent with the observed pattern of results demonstrating that math anxiety predicts STEM Grades even when controlling for math ability and the amount of STEM courses students chose to take. Instead, the crux of an explanation focusing on ‘micro-avoidances’ focuses more on how students choose to spend their limited time and effort in the courses in which they do enroll. This idea is of potentially broader theoretical consequence because research on math anxiety often discusses avoidance of math as a key consequence thereof, but researchers rarely provide greater specificity as to what this avoidance actually entails. In particular, high-level decisions to avoid math-related classes or careers and day-to-day (or even moment-to-moment) decisions to pay less attention in math class or expend less effort on math homework are often discussed interchangeably under the umbrella term “math avoidance”.

We should note that past work by Ashcraft and colleagues has introduced a distinction between types of math avoidance that is similar to the macro-avoidance vs. micro-avoidance distinction we make here. In Ashcraft and Faust 31 , for instance, the researchers find that math-anxious individuals tend to sacrifice accuracy in favor of speed on math tasks, which is interpreted as a form of “local avoidance of math” – this speed-accuracy tradeoff presumably reflects math-anxious individuals deciding not to expend effort on the math task they are asked to complete, instead of wishing to get through it as soon as possible. The idea of local avoidance of math (speed-accuracy tradeoffs while engaging in math tasks) as distinguished from global avoidance of math (avoiding math courses and career paths altogether) is raised in some of Ashcraft and colleagues’ later work as well 4 , 31 , 32 . On the one hand, we believe the terms ‘macro-avoidance’, as described here, and ‘global avoidance’, as described by Ashcraft and colleagues, are largely synonymous. On the other hand, while “local avoidance” of math has thus far in the literature referred specifically to the idea of speed-accuracy tradeoffs during math tasks, here we propose the idea of “micro-avoidance” of math that would also include relevant academic behaviors like paying less attention in class, skipping class altogether, studying less, etc. Returning to our interpretation of the relation between math anxiety and STEM achievement (controlling for math ability), if math-anxious individuals are likely to engage in class-related micro-avoidance behaviors in courses that involve math, this would make them less likely to be successful in these courses.

To unpack this hypothesis in greater detail, most of the work linking math anxiety to avoidance of math (including the present work) has focused on high-level avoidance behaviors (macro-avoidance)—avoidance of classes, majors, and careers that involve math 5 , 6 , 7 , 8 , 9 . This can be contrasted with the micro-avoidance of math, which refers not to high-level decisions about whether to pursue educational paths or careers that involve math, but instead to small-scale decisions about how much attention to pay in math class, how much effort to exert on math homework, and so on. Micro-avoidance behaviors like these are often assumed to lead math-anxious elementary-aged children (who, importantly, are all enrolled in math courses) to fail to fully develop their math abilities by causing students to get less practice (or less effective practice) with math over time 1 , 4 , 33 , 34 . However, only recently have studied directly assessed whether math anxiety is associated with micro-avoidance of math at all. Work by Pizzie and Kraemer 35 showed that math anxious individuals tended to shift their attention away from complicated mathematical formulas even when they were not required to do any math. A recent set of studies by Choe, Jenifer et al. 36 showed that math-anxious individuals have a tendency to avoid doing difficult math even when doing so entails a monetary cost. Together these studies suggest that math anxiety may indeed be associated with micro-avoidance of math, but on their own, they do not provide evidence that these micro-avoidance behaviors would occur in actual educational contexts. One recent study has begun to fill that gap by directly asking whether math anxiety does, in fact, predict the amount of attention and effort students expend in math-related courses 37 . In that study, researchers found that among seventh-grade students, math anxiety predicted the extent to which students paid attention in math class, which in turn predicted the development of their math abilities. Speculatively applying this finding to the present study, it may be the case that math anxiety led students enrolled in STEM courses to engage with or attend sub-optimally to math-related content in those courses, which in turn could explain variability in grades in those courses, over and above both math ability and macro-level avoidance of STEM content. In general, we see further exploration of micro-avoidance of math as a fruitful avenue for future research that attempts to understand the possible mechanisms by which math anxiety affects academic achievement.

More broadly, when considering why math anxiety would predict STEM achievement over and above math ability, we believe it is useful to consider the following question—what determines how successful a student will be in a STEM course? There is sometimes a tendency to assume that performance in a course is determined simply by how “good” a student is at the course material, which places the focus squarely on ability. However, there are clearly many factors that would determine how well a student does in a course: how often they attend class, how often they do the reading, how often they study, how much attention they devote to each of these things while they are doing them. These types of behaviors represent what Eccles, Wigfield, and colleagues refer to as “achievement-related choices” 38 , 39 , 40 , 41 . There are many more determinants of performance within a specific class, of course, but the key point here is that what determines an individual’s final grade in a course is perhaps determined as much by how much effort they put into the course as their preexisting abilities in the relevant domain. We suggest here that math anxiety may predict STEM achievement over and above math ability because math anxiety is more likely to be directly associated with a tendency to avoid expending effort in courses that involve math.

It should be noted that the approach taken in this paper is different from past work assessing the extent to which math anxiety and math grades in one year of schooling predict math anxiety and math grades in future years (e.g., Meece, Wigfield, and Eccles 6 ) in that the goal was not to assess how past grades in math-related courses predict achievement and participation levels in future math-related courses alongside math anxiety, but rather how a measure of math ability predicts these important outcomes alongside math anxiety. Previous work has shown that past grades tend to be strong predictors of future grades 6 , 38 , 39 , 40 . However, it is important to interrogate why past academic performance would predict future academic performance—how much of it is because students have a set ability level for that kind of course, and how much of it is a result of things like how much effort a student chooses to expend in that course? By collecting a measure of math ability at the beginning of university alongside our measure of math anxiety, here we were able to isolate preexisting differences in math ability as a possible explanation of differences in future STEM performance. It is of course possible that math-anxious students’ past struggles in math-related courses can in part explain why they are math-anxious in the first place (for a review, see Ramirez, Shaw, and Maloney 42 ). Importantly, however, the present results indicate that math anxiety was a better predictor of future STEM achievement than math ability, suggesting that while math-anxious students do, on average, have lower math ability than their less-anxious counterparts, these preexisting differences in math ability cannot explain why math-anxious students ultimately do worse in STEM courses. This indicates that other mechanisms are at play, and we hypothesize that the kinds of class-relevant micro-avoidance behaviors described here are one such mechanism.

In addition to assessing whether math ability can explain associations between math anxiety and STEM outcomes, we also examined the opposite: whether math anxiety could explain associations between math ability and STEM outcomes. Math ability is often discussed as a possible confound for associations between math anxiety and real-world outcomes, but the opposite—that math anxiety may actually confound relations between math ability and real-world outcomes—is seldom mentioned but in principle no less likely. Our results showed that math anxiety accounted for approximately 40% of the associations between math ability and both STEM participation and achievement (or about 3–4 times what math ability was able to account for of the associations between math anxiety and STEM outcomes). These findings suggest that, while math ability does predict differences in these important university STEM outcomes, a large portion of those associations can be explained by math anxiety. On a practical level, this suggests that interventions hoping to boost these STEM outcomes perhaps ignore students’ anxiety about math at their peril.

More broadly, this finding has significant implications for previous work linking differences in math ability to real-world outcomes like grades earned in math courses 15 , attainment of STEM careers 16 , 17 , 18 , and income levels and health outcomes 19 , 20 . Just as we have pointed out that a great deal of previous work linking math anxiety to real-world outcomes did not control for differences in math ability, the vast majority of work linking Math Ability to these important real-world outcomes did not control for differences in math anxiety. Although a subset of these studies did control for other math attitudes, like math confidence 19 , none of this previous work, examined the extent to which associations between math ability and real-world outcomes could be accounted for by attitudes—positive or negative—toward math. Our present findings suggest the real possibility that many previously observed links between math ability and real-world outcomes may be, at least in part, explainable by negative attitudes toward math—namely, math anxiety. Thus, we propose future research revisit some of these earlier findings to understand the extent to which it is truly ability in math, rather than feelings of anxiety toward math, that better account for these various real-world outcomes. Doing so would not only inform theory on the ways in which math ability and math anxiety shape future outcomes, but it would also allow for better-targeted interventions to focus more on math ability or anxiety depending on what the evidence points to.

The present work also demonstrated that math anxiety independently predicted two key academically relevant consequences—avoidance of and underperformance in math-related courses. This was evidenced by the finding that math anxiety continued to negatively predict the proportion of STEM courses students took even controlling for STEM Grades, and vice versa. The predictive effects of math anxiety on avoidance of STEM can therefore not be explained by recent underperformance in STEM, and vice versa. This suggests that both of math anxiety’s key theorized academic consequences—avoidance of and underperformance in math-related coursework—operate independently to shape academic outcomes, suggesting the need to posit separate potential mechanisms to account for these disparate effects (as we have done in the preceding sections). From an intervention standpoint, it may therefore be the case that an intervention that reduces the impact of math anxiety on one outcome (underperformance in STEM, for instance) would be unlikely to reduce the impact of math anxiety on the other outcome (avoidance of STEM). Several recent math anxiety interventions have focused not on reducing Math Anxiety levels directly, but on alleviating math anxiety’s negative effects on math performance. The expressive writing intervention, for instance, in which students write about their worries about an upcoming math test just before the test begins, aims to help students deal with math anxiety-induced worry before the test, and the goal is to boost test scores 43 . The same is true for cognitive reappraisal-based interventions, in which participants are instructed to think about the situation differently in an effort to reduce in-the-moment anxiety levels 44 . Even if these interventions were scaled up and found to be effective at boosting STEM Grades, our finding that math anxiety predicts avoidance of STEM courses over and above STEM Grades suggests that these interventions would be unlikely to affect student decisions to enroll in more STEM courses. The present results suggest that to effectively intervene to boost both STEM participation and STEM achievement of math-anxious individuals, interventions would need to be developed that either focuses separately on both of these outcomes or that attempt to reduce math anxiety levels directly.

We also found evidence that the negative association between math anxiety and STEM Grades was strongest among students with high academic performance in non-STEM courses (Fig. 3b ). This result supports the notion that math anxiety can prevent otherwise high-achieving students from realizing their potential in STEM, suggesting that math anxiety may be a particularly pernicious contributor to the ‘leaky pipeline’ in STEM, possibly preventing talented students from succeeding in STEM courses. One possible explanation for this finding may be that for otherwise high-achieving students, the online negative effects of math anxiety on performance may be especially pronounced. This would be consistent with work showing that high-aptitude students are often the ones who are most harmed by anxiety and pressure 22 . Another possible explanation for this finding relates back to the possibility that math anxiety predicts STEM Grades largely by determining how students choose to spend their limited time and resources. It is possible, for instance, that students who have a high non-STEM aptitude and are high in math anxiety may be especially likely to choose to devote more of their limited time and effort to non-STEM and devote less of their attention to the courses they are enrolled in that involve math.

While this study addresses several important limitations of previous work linking math anxiety to academic STEM outcomes, its own limitations should also be noted. The present study takes care to rule out confounds by controlling for several covariates (including math ability, general Trait Anxiety, working memory, and non-STEM Grades), and it also addresses previous issues of directionality by collecting our measure of math anxiety at the beginning of students’ time at university before decisions to pursue or avoid STEM and performance levels in STEM courses had occurred (making it impossible that individual differences in university-level STEM outcomes caused differences in math anxiety). However, the design is still fundamentally correlational, limiting our ability to make strong inferences about the causal effects of math anxiety on STEM outcomes. We see this work as strongly suggesting that math anxiety may play a causal role in determining STEM outcomes, but intervention-based work that aims to reduce the effect of math anxiety on these STEM outcomes is needed to conclusively infer that Math Anxiety can cause the specific STEM outcomes we considered here. In addition, this study focused on students at a large public Canadian university, and future work would need to be done to assess whether the findings would generalize to different educational contexts.

Another limitation of this work is that our measure of math ability—a difficult mental arithmetic task—does not capture all of the possible types of math skills (reasoning about mathematics, for instance) that may affect success in STEM courses. As we note in the Methods section, we chose this as our math ability measure because all students were likely to have the requisite knowledge to complete the task (i.e., it does not rely on knowledge of advanced math, like calculus) and because this type of foundational math skill is likely to be broadly applicable across almost all types of specialized math that students are likely to encounter in any STEM discipline. Moreover, past work has demonstrated that mental arithmetic ability is a reliable predictor of ability in more complex math 45 , 46 . Nevertheless, it remains possible that ability on other types of math measures may explain, in part, the association between math anxiety and STEM outcomes. However, given the association between ability in arithmetic and more complex math skills, there would need to be something specific about these more advanced math skills that explain the association between math anxiety and STEM outcomes that are not captured by ability on the complex mental arithmetic task we used here. Future work could be done to explore whether other forms of math ability could explain the predictive associations between math anxiety and STEM outcomes, and such work would refine our theoretical understanding of the association between math anxiety and STEM outcomes. The present work, however, provides an important demonstration that the predictive effects of math anxiety on university STEM outcomes are largely independent of its effects on difficult mental arithmetic.

Together, the present findings provide some of the strongest evidence to date that math anxiety, over and above math ability, serves as a barrier to multiple facets of STEM success, supporting key predictions made by theory on math anxiety. Specifically, we show that predictive effects on STEM achievement are not explainable by differences in math ability, prompting a reevaluation of the mechanisms by which math anxiety may lead to poor performance in math-related courses. We also provide evidence that math anxiety can in fact account for associations between math ability and real-world outcomes, suggesting that math anxiety may confound previously observed associations between math ability and real-world outcomes that largely ignored math anxiety. Moreover, we show that math anxiety predicts STEM achievement and participation independently of one another, suggesting that the effects of math anxiety on avoidance of and underperformance in STEM can operate through separate mechanisms. Finally, we found evidence that math anxiety is particularly negatively predictive of STEM achievement for those who have high non-STEM Grades. In sum, while this correlational study cannot establish a causal role for math anxiety shaping university-level STEM participation and achievement, it provides clear theoretical grounds for devoting resources to test whether interventions that alleviate the negative effects of math anxiety as students enter university can bolster their STEM outcomes.

Participants

One hundred and eighty-six first-year undergraduates at the University of Western Ontario participated. Participants were recruited widely, both through flyers posted throughout campus and through research assistants recruiting students directly at places where many students congregate. All first-year students were eligible to participate. We recruited as many participants as possible within students’ first semester of university—this limitation was made to enable us to assess the extent to which math anxiety and other variables collected at the start of university prospectively predicted student outcomes throughout their time at university. Of this initial sample, three were removed from all analyses either because they were not actually a first-year student or because they missed more than one-third of attention checks, resulting in a total analytic sample size of 183 (117 female; mean age = 18.55, SD = .41). Power analysis (assuming power of .80 and an alpha level of .05) showed that this sample was suitable to detect correlation effect sizes as small as Pearson’s r values of .205. Moreover, power analysis for multiple regression effects showed that a sample size of 183 with 9 predictors (the most complex analysis we ran) is powered to find Cohen’s f 2 effect sizes as small as .07, which is considered a small effect size 47 (Cohen, 1988). The sample size was thus deemed appropriate to detect practically significant effects.

It should be noted that the data reported here are part of a larger dataset, some of which have been reported on in previous work 21 , 48 . The theoretical questions addressed and the analyses described in this manuscript are novel.

All participants provided written consent, and the University of Western Ontario Ethics Review Board approved all data collection procedures. In their first semester of university, participants completed a battery of questionnaires and cognitive tasks in the lab. Participants have compensated $20 CAD for their time. The order of surveys and cognitive tasks was counterbalanced and randomized across participants. In addition to completing this two-hour lab session, participants also granted the researchers permission to access their de-identified academic transcripts throughout their undergraduate careers by indicating as such on the consent form. These transcripts listed the courses students chose to take and the grades they earned in those courses.

% STEM Courses

The academic transcripts listed all courses students completed throughout their four years at university and the department in which that course was offered. Because the goal of this work is to understand the extent to which math anxiety predicts STEM outcomes, we first categorized different departments as STEM or non-STEM. This was done in two steps. First, traditional science and math departments (e.g., Physics, Mathematics, Engineering, Chemistry) were classified as belonging to the STEM category. Second, for more ambiguous departments (e.g., those in the social sciences, such as Psychology, Economics, Sociology, etc.), the STEM/non-STEM classification was made based on an examination of the content of courses within that department in consultation with university students directly familiar with those courses. The main consideration taken here was whether the courses offered in a given department as a whole involved a substantial amount of math content and/or content and materials about the application of the scientific method. As an illustrative example of these more ambiguous cases, take the two departments Business Administration and Financial Modeling. The content of courses in both departments has to do with theory and practice in business, but Financial Modeling was designated as STEM because of the heavy computational components of many of the courses in that department while Business Administration was designated as non-STEM because its courses did not in general place a large focus on mathematics. For a full list of the departments that participating students took courses in and their STEM/non-STEM designation, see Table S1 . Note that while this process inherently involves a degree of subjectivity, departments were designated as STEM or non-STEM well before we conducted any analyses using this transcript data, and no changes to the STEM/non-STEM designations were made after analyses began.

The ‘% STEM Courses’ measure was computed by summing the number of STEM courses taken by each participant and dividing it by the total number of courses that students took. A proportion was used instead of the raw number of STEM courses to account for variation in the total number of courses, and thus control for the number of non-STEM courses taken by each student. It is useful to note that this latter point is why regression models do not include a control variable ‘% Non-STEM courses’, as % Non-STEM would simply be 1–%STEM.

STEM Grades

For each course taken, transcripts listed the grade the student earned in the course from 0 to 100 points. For each participant, a STEM Grades score was created by computing the average of scores earned in STEM courses.

In some cases, transcript data indicated that students repeated a course they had taken previously, either because they withdrew from the course the first time they took it or because they obtained a poor grade the first time they took it and needed to retake the course to fulfill degree requirements. Of the total of 6211 courses taken by all students in our sample, 52 of those courses (0.8%) were repeated courses, and a total of 34 out of 183 students (18.6%) repeated a course at least once. Controlling for the number of repeated courses students took does not substantially affect any of the key estimates or inferences presented. Hence, to maximize the use of the extant data, we included all grades recorded for a given student on their transcript, regardless of repeats (i.e., when computing the STEM Grades and Non-STEM Grade measures).

Math Anxiety

Math Anxiety was measured using the short Math Anxiety Rating Scale (sMARS 49 ). Participants rated how anxious they would feel in 25 math-related situations (e.g., “Studying for a math test”; “Being given a set of division problems to solve on paper”), which was scored from 0 (Not at all) to 4 (Very much). Math Anxiety scores range from 0 to 100. Cronbach’s α for this measure was .96.

Math Ability

Participants completed difficult mental arithmetic problems adapted from the Kit of Factor-Referenced Cognitive Tests 50 , 51 . Trials included all four basic arithmetic operations: addition (three 2-digit numbers; e.g., 45 + 72 + 87), subtraction (a 2-digit or 3-digit minuend and a 2-digit or 3-digit subtrahend; e.g., 354–87), multiplication (one 2-digit number and one 1-digit number; e.g., 64 × 6), and division (a 1-digit divisor into a 2-digit or 3-digit dividend; e.g., 432 ÷ 9). Problems were open-ended (i.e., not verification); hence, participants responded by typing their answers using the number pad on the keyboard. They were required to calculate the answer mentally—that is, pencil and paper or other devices were not permitted to aid with calculation. As such, the task was relatively difficult for arithmetic (mean accuracy = 81.2%, mean RT = 9.91 s). Operation types were presented in separate blocks, and in each block, participants completed as many problems as they could in 3 min. Participants were not aware that there was a time limit, and the block ended once a participant completed the trial they were at once 3 min had passed (this final trial was omitted from analysis). A math ability score was computed for each participant by summing the total number of problems answered correctly across all four operation types, where higher scores indicate greater math ability. Past work has shown that performance on this task is correlated with performance on several basic numerical tasks (including numerical ordering and numerical comparison tasks 51 ). Internal reliability for this task was computed using participants’ scores for each of the four operation types; Cronbach’s α was .89.

While we acknowledge that mathematics as a whole comprises far more than even the most difficult mental arithmetic task, here we chose a challenging arithmetic task as a measure of objective math ability for several reasons. First, this ensured that all participants would have the requisite knowledge to complete the chosen task (e.g., it is not a given that all students would have taken the necessary course for more specialized math topics, such as geometry or calculus). Second, not all STEM courses will require the same type of specialized math or even specialized math at all. That is, arithmetic is likely to be one of the more universally tapped math skills across a wide range of STEM courses. Finally, prior empirical work has shown that arithmetic is a reliable predictor of more advanced math skills 45 , 46 .

Trait Anxiety

Trait Anxiety was measured using the Trait Anxiety Inventory (TAI 52 ). Participants respond to statements like “I worry too much over something that doesn’t really matter” and “I am ‘calm, cool, and collected’” (reverse scored) on a scale from 1 (Almost never) to 4 (Almost always) based on how they generally feel. The scale contains a total of 20 items, and possible scores range from 20 to 80, where higher scores indicate greater general anxiety. Trait Anxiety was included as a covariate to control for anxiety that is not specific to math. Cronbach’s α for this measure was .93.

Verbal Working Memory

Verbal Working Memory capacity was measured using the commonly used automated reading-span task 53 , 54 . In this task, participants saw a series of sentences and had to judge whether each sentence is sensible (e.g., “Andy was stopped by the policeman because he crossed yellow heaven”). After each sentence, a letter appeared on the screen. After a sequence of 3 to 7 sentences followed by letters, participants recalled the letters they saw in the correct order by clicking them on a new screen that displayed a menu of letters. Participants completed a total of 15 sequences, 3 of each possible sequence length in a randomized order. For each sequence, a participant’s score was determined by multiplying accuracy by length, where accuracy is a binary indicator (1 or 0) of whether all letters were recalled in the correct order, and length is the number of letters participants had to recall in that sequence. A total Verbal Working Memory score was calculated for each participant by summing the scores from each trial. Verbal Working Memory scores range from 0 to 75, where higher scores reflect higher Verbal Working Memory capacity. The Verbal Working Memory task was included as a covariate to control for general cognitive ability.

To control for gender, participants responded to an item asking them to indicate their gender (Male or Female; coded as 0 or 1, respectively).

Non-STEM Grades

For each participant, a non-STEM Grades score was created by computing the average of scores (from 0 to 100 points) earned in non-STEM courses. This allowed us to control for performance in non-STEM courses.

Semesters Absent

At least one semester of transcript data was missing for a subset of 35 participants in the final analytic sample, either because the student took time off from school or left the university. To enable us to account for this in our analysis, we created a ‘Semesters Absent’ control variable that indicates how many semesters of transcript data were missing for a given participant. Note that the results presented in this work do not appreciably change if participants who are missing any transcript data are simply excluded from analyses.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

The data supporting this work can be found at the following link: https://osf.io/bctyg/?view_only=9ce7dd98a8464f1db2af1a40eb0336e7/ .

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Acknowledgements

This work was supported by Banting Postdoctoral Fellowships to I.M.L. and H.M.S. (National Sciences and Engineering Research Council, Canada); University of Western Ontario internal research award to Lyons (Western Research and Faculty of Social Science); Faculty Start-Up Research Funds to I.M.L. (Georgetown University); Alexander Graham Bell Canada Graduate Scholarship to H.M.S. (National Sciences and Engineering Research Council, Canada). CAREER Award to I.M.L. (National Science Foundation, United States, FAIN 2041887). The authors would like to thank Dr. Daniel Ansari for providing resources to support data collection and Michael Slipenkyj, Caitlin Murray, and Ava Cobarrubias for assisting with data entry and management.

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Daker, R.J., Gattas, S.U., Sokolowski, H.M. et al. First-year students’ math anxiety predicts STEM avoidance and underperformance throughout university, independently of math ability. npj Sci. Learn. 6 , 17 (2021). https://doi.org/10.1038/s41539-021-00095-7

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REVIEW article

Mathematics anxiety: what have we learned in 60 years.

• Department of Experimental Psychology, University of Oxford, Oxford, UK

The construct of mathematics anxiety has been an important topic of study at least since the concept of “number anxiety” was introduced by Dreger and Aiken (1957) , and has received increasing attention in recent years. This paper focuses on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We discuss what mathematics anxiety is; how distinct it is from other forms of anxiety; and how it relates to attitudes to mathematics. We discuss the relationships between mathematics anxiety and mathematics performance. We describe ways in which mathematics anxiety is measured, both by questionnaires, and by physiological measures. We discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally, we describe some research on treatment. We conclude with a brief discussion of what still needs to be learned.

Low achievement and low participation in mathematics are matters of concern in many countries; for example, recent concerns in the UK led to the establishment of the National Numeracy organization in 2012. This topic has received increasing focus in recent years, the ever-increasing importance of quantitative reasoning in a variety of educational and occupational situations, ranging from school examinations to management of personal finances.

Some aspects of mathematics appear to be cognitively difficult for many people to acquire; and some people have moderate or severe specific mathematical learning disabilities. But not all mathematical disabilities result from cognitive difficulties. A substantial number of children and adults have mathematics anxiety, which may severely disrupt their mathematical learning and performance, both by causing avoidance of mathematical activities and by overloading and disrupting working memory during mathematical tasks. On the whole, studies suggest that attitudes to mathematics tend to deteriorate with age during childhood and adolescence ( Wigfield and Meece, 1988 ; Ma and Kishor, 1997 ), which has negative implications for mathematical development, mathematics education and adult engagement in mathematics-related activities. Also, while there are nowadays few gender differences in actual mathematical performance in countries that provide equal educational opportunity for boys and girls, females at all ages still tend to rate themselves lower in mathematics and to experience greater anxiety about mathematics than do males. It is important to understand children's and adults' attitudes and emotions with regard to mathematics if we are to remove important barriers to learning and progress in this subject.

Many studies over the years have indicated that many people have extremely negative attitudes to mathematics, sometimes amounting to severe anxiety ( Hembree, 1990 ; Ashcraft, 2002 ; Maloney and Beilock, 2012 ). Mathematics anxiety has been defined as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in … ordinary life and academic situations” ( Richardson and Suinn, 1972 ).

Although, many studies treat mathematics anxiety as a single entity, it appears to consist of more than one component. Wigfield and Meece (1988) found two separate dimensions of mathematics anxiety in sixth graders and secondary school students and found two different dimensions: cognitive and affective, similar to those that had been previously identified in the area of test anxiety by Liebert and Morris (1967) . The cognitive dimension, labeled as “worry,” refers to concern about one's performance and the consequences of failure, and the affective dimension, labeled as “emotionality” refers to nervousness and tension in testing situations and respective autonomic reactions ( Liebert and Morris, 1967 ).

People have been expressing mathematics anxiety for centuries: the verse “Multiplication is vexation … and practice drives me mad” goes back at least to the sixteenth century. From a research perspective, the construct has been an important topic of study at least since the concept of “number anxiety” was introduced by Dreger and Aiken (1957) , and has received increasing attention in recent years, in conjunction with the generally increased focus on mathematical performance.

Although, as will be discussed below, it is unclear to what extent mathematics anxiety causes mathematical difficulties, and to what extent mathematical difficulties and resulting experiences of failure cause mathematics anxiety; there is significant evidence that mathematics anxiety interferes with performance of mathematical tasks, especially those that require working memory. Moreover, whether a person likes or fears mathematics will clearly influence whether they take courses in mathematics beyond compulsory school-leaving age, and pursue careers that require mathematical knowledge ( Chipman et al., 1992 ; Brown et al., 2008 ). Thus, mathematics anxiety is of great importance to the development and use of mathematical skills. It is also important in itself, as a cause of much stress and distress.

This paper will focus on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We will discuss what mathematics anxiety is, and how distinct it is from other forms of anxiety. We will discuss its relationship to attitudes to mathematics. We will then discuss the relationships between mathematics anxiety and mathematics performance and possible reasons for them. We will then discuss ways in which mathematics anxiety is measured, both by the commonest technique of questionnaires, and by physiological measures. We will then discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally and importantly, we will discuss some implications for treatment. We will conclude with a brief discussion of what still needs to be learned.

Is Mathematics Anxiety Separable from other Forms of Anxiety?

Though, as will be discussed below, mathematics anxiety is closely related to mathematical performance, it cannot be reduced just to a problem with mathematics. It seems to be as much an aspect of “anxiety” as an aspect of “mathematics.” Indeed, before assuming that mathematics anxiety is an entity in its own right, it is necessary to consider relationships between mathematics anxiety and other forms of anxiety, especially test anxiety, and general anxiety. Several studies suggest that mathematics anxiety is more closely related to other measures of anxiety, especially test anxiety, than to measures of academic ability and performance ( Hembree, 1990 ; Ashcraft et al., 1998 ). Such studies typically show correlations of 0.3 and 0.5 between measures of mathematics anxiety and test anxiety.

Mathematics anxiety has also generally been found to correlate with measures of general anxiety; and it is indeed possible that this may serve as a background variable explaining some of the correlation between mathematics anxiety and test anxiety. For example, Hembree (1990) found a mean correlation of 0.35 between the MARS and a measure of general anxiety. In a behavioral genetic study, to be discussed in more detail below, Wang et al. (2014) obtained evidence that genetically based differences in general anxiety contribute to genetic differences in mathematics anxiety.

However, mathematics anxiety cannot be reduced to either test anxiety or general anxiety. Different measures of mathematics anxiety correlate more highly with one another (0.5–0.8) than with test anxiety or general anxiety ( Dew et al., 1983 ; Hembree, 1990 ; review by Ashcraft and Ridley, 2005 ).

People may exhibit performance anxiety not only about tests and examinations, but about a variety of school subjects. Mathematics is usually assumed to elicit stronger emotional reactions, and especially anxiety, than most other academic subjects, but this assumption needs more research ( Punaro and Reeve, 2012 ). Although, the general assumption is that people show much more anxiety and other negative attitudes toward mathematics than other academic subjects, there have not been many studies directly comparing attitudes to mathematics and other subjects.

Certainly anxiety toward other subjects exists, especially when performance in these subjects takes place in front of others. People with dyslexia have been found to exhibit anxiety about literacy ( Carroll et al., 2005 ; Carroll and Iles, 2006 ). It is well-known, that foreign language learning and use, especially by adults, is often inhibited by anxiety ( Horwitz et al., 1986 ; Cheng et al., 1999 ; Wu and Lin, 2014 ). Music students, and even successful musicians, often demonstrate music performance anxiety ( Kenny, 2011 ).

Drawing also elicits performance anxiety and lack of confidence, and there is a decline in confidence with age, which in some ways parallels findings with regard to mathematics. Most young children enjoy drawing, and will often draw spontaneously. Many authors report that interest in drawing seems to decline in most children at or before the transition to secondary school, and many older children and adults will insist that they “can't draw,” even though they had drawn frequently and enthusiastically some years earlier ( Cox, 1989 ; Thomas and Silk, 1990 ; Golomb, 2002 ; but see Burkitt et al., 2010 for somewhat conflicting findings).

Punaro and Reeve (2012) reported a study that directly compared mathematics and literacy anxiety in Australian 9-year-olds and related their anxiety to their actual academic abilities. Although, children expressed anxiety about difficult problems in both mathematics and literacy, worries were indeed greater for mathematics than literacy. Moreover, anxiety about mathematics was related to actual mathematics performance, whereas anxiety about literacy was not related to actual literacy performance. This study would suggest that although mathematics is not the only subject that elicits anxiety, anxiety may indeed be more severe, and possibly affect performance more, for mathematics than for other subjects.

Mathematics Anxiety and Attitudes to Mathematics

Attitudes to mathematics, even negative attitudes, cannot be equated with mathematics anxiety, as the former are based on motivational and cognitive factors, while anxiety is a specifically emotional factor. Nevertheless, attitude measures tend to correlate quite closely with mathematics anxiety. For example, Hembree (1990) found that in school pupils, mathematics anxiety showed a mean correlation of −0.73 with enjoyment of mathematics and −0.82 with confidence in mathematics. In college students, the equivalent mean correlations were a little lower than in schoolchildren, but still very high: −0.47 between mathematics anxiety and enjoyment of mathematics, and −0.65 between mathematics anxiety and confidence in mathematics.

Mathematics anxiety seems to be particularly related to self-rating with regard to mathematics. People who think that they are bad at mathematics are more likely to be anxious. Most studies indicate a negative relationship between mathematics self-concept and mathematics anxiety ( Hembree, 1990 ; Pajares and Miller, 1994 ; Jain and Dowson, 2009 ; Goetz et al., 2010 ; Hoffman, 2010 ).

However, as most of these studies are correlational rather than longitudinal, it is hard once again to establish the direction of causation: does anxiety lead to a lack of confidence in one's own mathematical ability, or does a lack of confidence in one's mathematical ability make one more anxious? Ahmed et al. (2012) carried out a longitudinal study of 495 seventh-grade pupils, who completed self-report measures of both anxiety and self-concept three times over a school year. Structural equation modeling suggested that each characteristic influenced the other over time, but that the effect of self-concept on subsequent anxiety was significantly greater than the effect of anxiety on subsequent self-concept. The details of the results should be taken with some caution, because although the study was longitudinal, it was over a relatively short period (one school year) and also a different pattern might be seen among younger or older children. However, it provides evidence that the relationship between mathematics anxiety and mathematics self-concept is reciprocal: each influences the other.

A closely related construct is self-efficacy. Ashcraft and Rudig (2012) adapted Bandura's (1977) definition of self-efficacy to the topic of mathematics, stating that “self-efficacy is an individual's confidence in his or her ability to perform mathematics and is thought to directly impact the choice to engage in, expend effort on, and persist in pursuing mathematics” (p. 249). It is not precisely the same construct as self-rating, as it includes beliefs about the ability to improve in mathematics, and to take control of one's learning, rather than just about one's current performance; but there is of course significant overlap between the constructs. Studies have demonstrated an inverse relationship between self-efficacy and math anxiety ( Cooper and Robinson, 1991 ; Lee, 2009 ).

Attitudes to mathematics also involve conceptualization of what mathematics is, and it is possible that this is relevant to mathematics anxiety. Many people seem to regard mathematics only as school-taught arithmetic, and may not consider other cultural practices involving numbers as mathematics ( Harris, 1997 ). Also, people may not recognize that arithmetical ability (even without considering other aspects of mathematics) is made up of many components, not just a single unitary ability ( Dowker, 2005 ). This can risk their assumption that if they have difficulty with one component, they must be globally “bad at maths,” thus increasing the risk of mathematics anxiety.

Most studies of mathematics anxiety have not differentiated between different components of mathematics, and it is likely that some components would elicit more anxiety than others and that the correlations between anxiety about different components might not always be very high. Indeed, studies which have looked separately at statistics anxiety and (general) mathematics anxiety in undergraduates have suggested that the two should be seen as separate constructs, and differ in important ways. For example, as will be discussed in the Section Gender and Mathematics Anxiety, most studies suggest that females show more mathematics anxiety than males, but there are no gender differences in statistics anxiety ( Baloğlu, 2004 ).

Prevalence of Mathematics Anxiety

Estimates of the prevalence of mathematics anxiety vary quite widely, and are of course likely to be dependent on the populations being sampled, on the measures used (though many of the studies involve similar measures), and, perhaps especially, on what criteria are used to categorize people as “mathematics anxious.” Most measures of mathematics anxiety assess scores on continuous measures, and there is no clear criterion for how severe the anxiety must be for individuals to be labeled as high in mathematics anxiety.

Richardson and Suinn (1972) estimate that 11% of university students show high enough levels of mathematics anxiety to be in need of counseling. Betz (1978) concluded that about 68% of students enrolled in mathematics classes experience high mathematics anxiety. Ashcraft and Moore (2009) estimated that 17% of the population have high levels of mathematics anxiety. Johnston-Wilder et al. (2014) found that about 30% of a group of apprentices showed high mathematics anxiety, with a further 18% affected to a lesser degree. Chinn (2009) suggested the far lower figure of 2–6% of secondary school pupils in England, which may simply indicate the use of an unusually strict criterion for defining pupils as having high mathematics anxiety. There is no doubt, even when taking the lowest estimates, that it is a very significant problem.

Relationships between Mathematics Anxiety and Mathematics Performance

Numerous studies have shown that emotional factors may play a large part in mathematical performance, with mathematics anxiety playing a particularly large role ( McLeod, 1992 ; Ma and Kishor, 1997 ; Ho et al., 2000 ; Miller and Bichsel, 2004 ; Baloğlu and Koçak, 2006 ). Mathematics anxiety scores correlate negatively with scores on tests of mathematical aptitude and achievement, while usually showing no significant correlation with verbal aptitude and achievement.

One possible reason for the negative association between mathematics anxiety and actual performance is that people who have higher levels of math anxiety are more likely to avoid activities and situations that involve mathematics. Thus, they have less practice ( Ashcraft, 2002 ), which is in itself likely to reduce their fluency and their future mathematical learning.

Mathematics anxiety might also influence performance more directly, by overloading working memory ( Ashcraft et al., 1998 ). Anxious people are likely to have intrusive thoughts about how badly they are doing, which may distract attention from the task or problem at hand and overload working memory resources. It has been found in many studies over the years that general anxiety as a trait is associated with working memory deficits ( Mandler and Sarason, 1952 ; Eysenck and Calvo, 1992 ; Fox, 1992 ; Berggren and Derakhshan, 2013 ). It would appear likely that if anxiety affects working memory, it would have a particularly strong effect on arithmetic, as working memory has been found in many studies to be strongly associated with arithmetical performance, especially in tasks that involve multi-digit arithmetic and/or involve carrying (e.g., Hitch, 1978 ; Fuerst and Hitch, 2000 ; Gathercole and Pickering, 2000 ; Swanson and Sachse-Lee, 2001 ; Caviola et al., 2012 ). Thus, the load that mathematics anxiety and associated ruminations place on working memory could be a plausible explanation for decrements in mathematical performance.

Ashcraft and Kirk (2001) found that people with high maths anxiety demonstrated smaller working memory spans than people with less maths anxiety, especially in tasks that required calculation. In particular, they were much slower and made many more errors than others in tasks where they had to do mental addition at the same time as keeping numbers in memory.

DeCaro et al. (2010) asked adult participants to work out verbally based and spatially based mathematics problems in either low-pressure or high-pressure testing situations. Performance on problems that relied heavily on verbal WM resources was less accurate under high-pressure than under low-pressure tests. Performance on spatially based problems that do not rely heavily on verbal WM was not affected by pressure. Asking some individuals to focus on the problem steps by talking aloud helped to reduce pressure-induced worries and eliminated pressure's negative impact on performance.

While Ashcraft's theory emphasizes the ways in which mathematics anxiety impairs mathematical performance, some researchers such as Núñez-Peña and Suárez-Pellicioni (2014) put more emphasis on how pre-existing mathematical difficulties might cause or increase mathematics anxiety. Poor mathematical attainment may lead to mathematics anxiety, as a result of repeated experiences of failure.

Indeed, it appears that mathematics anxiety is associated not only with performance in high-level calculation skills that require the use of working memory resources, but also with much more basic numerical skills. For example, Maloney et al. (2011) gave high mathematics-anxious (HMA) and low mathematics-anxious (LMA) individuals two variants of the symbolic numerical comparison task. In two experiments, a numerical distance by mathematics anxiety (MA) interaction was obtained, demonstrating that the effect of numerical distance on response times was larger for HMA than for LMA individuals. The authors suggest that HMA individuals have less precise representations of numerical magnitude than their LMA peers; and that this may be primary, and precede the mathematics anxiety. In other words, mathematics anxiety may be associated with low-level numerical deficits that compromise the development of higher-level mathematical skills. Núñez-Peña and Suárez-Pellicioni (2014) also found that people with HMA showed a larger distance effect as well as a larger size effect (longer reaction times to comparisons involving larger numbers) than LMA individuals. Maloney and Beilock (2012) proposed that mathematics anxiety is likely to be due both to pre-existing difficulties in mathematical cognition and to social factors, e.g., exposure to teachers who themselves suffer from mathematics anxiety. Additionally, they proposed that those with initial mathematical difficulties are also likely to be more vulnerable to the negative social influences; and that this may create a vicious circle.

Studies of the relationship between mathematics anxiety and performance also need to take into account that, as stated at the beginning of this paper, mathematics anxiety consists of different components, often termed “cognitive” and “affective.” The cognitive and affective dimensions seem to be differently related to achievement in mathematics. For example, in sixth graders and secondary school students, the affective dimension of math anxiety has found to be more strongly negatively correlated with achievement than the cognitive dimension ( Wigfield and Meece, 1988 ; Ho et al., 2000 ). It also needs to be remembered that, even before considering the non-numerical aspects of mathematics, arithmetic itself is not a single entity, but is made up of many components ( Dowker, 2005 ).

Assessments of Mathematics Anxiety

So far, we have been discussing mathematics anxiety without much reference to the methods used for studying it. However, in order to study mathematics anxiety, it is necessary to find suitable ways of assessing and measuring it. Most measures for assessing mathematics anxiety involve questionnaires and rating scales, and are predominantly used with adolescents and adults. The first such questionnaire to our knowledge is that of Dreger and Aiken (1957) ; and subsequent well-known examples include the Mathematics Anxiety Research Scale or MARS ( Richardson and Suinn, 1972 ) and the Fennema–Sherman Mathematics Attitude Scales ( Fennema and Sherman, 1976 ).

Some questionnaires, mainly including pictorial rating scales, have since been developed for use with primary school children; e.g., the Mathematics Attitude and Anxiety Questionnaire ( Thomas and Dowker, 2000 ; Krinzinger et al., 2007 ; Dowker et al., 2012 ) and the Children's Attitude to Math Scale ( James, 2013 ).

The reliability of mathematics anxiety questionnaires has generally been found to be good, whether measured through inter-rater reliability, test-retest reliability or internal consistency. The test whose psychometric properties have been most frequently assessed is the MARS, in its original form and in various adaptations, and it has been consistently found to be highly reliable (e.g., Plake and Parker, 1982 ; Suinn et al., 1972 ; Levitt and Hutton, 1984 ; Suinn and Winston, 2003 ; Hopko, 2003 ).

Good reliability has also been found for other mathematics anxiety measures such as Betz's (1978) Mathematics Anxiety Scale ( Dew et al., 1984 ; Pajares and Urban, 1996 ) and the Fennema–Sherman scales ( Mulhern and Rae, 1998 ). The mathematics anxiety scales developed specifically for children have also been found to have good reliability, including Thomas and Dowker's (2000) Mathematics Anxiety Questionnaire ( Krinzinger et al., 2007 ); James' (2013) Children's Anxiety in Math Scale; and the scale developed by Vukovic et al. (2013) .

Thus, it is unlikely that any ambiguous or conflicting results in different studies are likely to be due to unreliability of the measures. However, there are potential problems with questionnaire measures as such. In particular, a potential problem with questionnaire measures is that, like all self-report measures, they may be influenced both by the accuracy of respondents' self-perceptions and by their truthfulness in reporting. There are some studies that have attempted to combat this problem by using physiological measures of anxiety when exposed to mathematical stimuli: e.g., heart rate and skin conductance ( Dew et al., 1984 ); cortisol secretion ( Pletzer et al., 2010 ; Mattarella-Micke et al., 2011 ) and especially brain imaging measures ranging from EEG recordings ( Núñez-Peña and Suárez-Pellicioni, 2014 , 2015 ); to functional MRI ( Lyons and Beilock, 2012b ; Young et al., 2012 ; Pletzer et al., 2015 ).

Physiological Measures: Cortisol Secretion

Cortisol secretion is a response to stress ( Hellhammer et al., 2009 ), and therefore might be expected to be higher in people with high levels of mathematics anxiety when presented with mathematical stimuli or activities. Studies do indeed support this view, as well as giving some clues about the interactions between mathematics anxiety and other characteristics.

Pletzer et al. (2010) investigated people's changes in cortisol level in response to the stress of a statistics examination, and the relationship between these changes and their actual examination performance. They were also assessed on a questionnaire measure of mathematics anxiety (a version of the MARS) and on tests of magnitude judgements and arithmetic. With a few exceptions who showed other patterns, most participants either showed an increase in cortisol from the basal level just before the examination, and a decrease afterwards, or a decrease in cortisol from the basal level both before and after the examination. Neither absolute levels or cortisol nor patterns of change in cortisol production correlated with the MARS, with the arithmetical tests, or with performance in the examination itself. However, the cortisol response to the examination did influence the association of other predictor variables and statistics performance. Mathematics anxiety and arithmetic abilities predicted statistics performance significantly in the group who showed an increase in cortisol production before the examination with a subsequent decrease, but not in the group that showed a consistent decrease.

Mattarella-Micke et al. (2011) measured cortisol secretion levels just before and after participants were presented with challenging mathematics problems. They also assessed their working memory. The performance of individuals with low working memory scores was not associated with mathematics anxiety or cortisol secretion. For people with higher working memory scores, those with high mathematics anxiety showed a negative relationship between cortisol secretion and mathematics performance, while those with low mathematics anxiety showed a positive relationship between cortisol secretion and mathematics performance.

Thus, in the studies carried out so far, the relationship between mathematics anxiety and cortisol response are not absolutely straightforward. It appears that the cortisol secretion profile modulates the relationship between mathematics anxiety and mathematics performance, while mathematics anxiety modulates the relationship between cortisol and performance. Thus, there are modulatory relationships between these measures, which are well worth studying further; but no evidence as yet that cortisol response is a good indicator of mathematics anxiety, or should replace traditional questionnaires.

Physiological Measures: What Can Measures of Brain Function Tell us about Mathematics Anxiety?

Attempts at physiological measures of mathematics anxiety have more commonly involved some form of recording of brain function. Dehaene ( 1997 , p. 235) argues that the neuroscience of mathematics can and must involve emotional factors: “…(C)erebral function is not confined to the cold transformation of information according to logical rules. If we are to understand how mathematics can become the subject of so much passion or hatred, we have to grant as much attention to the computations of emotion as to the syntax of reason.” It is, however, only quite recently that we have had the ability to carry out functional brain imaging with sufficient numbers of participants to be able to examine correlations between individual differences in brain function and individual differences in behavioral characteristics. It is even more recently that we have been able to apply functional brain imaging to children.

It is important to remember that finding neural correlates of behavioral characteristics does not mean that the brain characteristics are causing the behavioral characteristics. They are at least as likely to be reflecting the behavioral characteristics. Nevertheless, examining brain-based correlates of mathematics anxiety may give us some clues as to the cognitive characteristics involved, even if it does not tell anything about the direction of causation. They may also give us ways of assessing mathematics anxiety without needing to rely on self-report measures.

Physiological Measures: EEG/ERP

Núñez-Peña and Suárez-Pellicioni (2014 , 2015) carried out both ERP and behavioral measures of numerical processing in people with high and low mathematics anxiety as measured on the MARS questionnaire. In a magnitude comparison test, people with high mathematics anxiety had slower reaction times and showed larger size and distance effects than those with low mathematics anxiety. ERP measures showed that those with high mathematics anxiety showed higher amplitude in frontal areas for both the size and distance effects than did those with low mathematics anxiety: a component which has been proposed to be associated with numerical processing. They also looked at two-digit addition in people with high and low mathematics anxiety. They were presented with correct and incorrect answers to such problems, and asked to say whether each answer was right or wrong. Participants with high mathematics anxiety were significantly slower and less accurate than those with low mathematics anxiety. ERP analysis showed that people with high mathematics anxiety showed a P2 component of larger amplitude than did people with low mathematics anxiety. This component had been previously found to be associated with devoting attentional resources to emotionally negative stimuli. Thus, the studies suggest that people with high mathematics anxiety may be devoting extra attentional resources to their worries, possibly at the expense of task performance, though the direction of causation cannot be determined from a correlational study.

Physiological Measures: Functional MRI

There has been much evidence that stress affects the activation levels of regions of the prefrontal cortex, possibly interfering with the working memory functions associated with this area ( Qin et al., 2009 ). These effects have been shown to be greater in people with high levels of general anxiety as a trait. For example, Bishop (2009) found that, even in the absence of threat stimuli, people with high trait anxiety showed less prefrontal activation in attentional control tasks than people with lower trait anxiety, and this was associated with less efficient performance. Basten et al. (2012) found that high trait anxiety was associated with high activation of the right dorsolateral prefrontal cortex (dLPFC) and left inferior frontal sulcus, which are generally found to be implicated in the goal-directed control of attention, and with strong deactivation of the rostral-ventral anterior cingulate cortex, a key region in the brain's default-mode network. The authors suggested that these activation patterns were likely to be associated with inefficient manipulations in working memory.

Lyons and Beilock (2012a) carried out functional brain imaging studies with adults with high and low mathematics anxiety. The individuals with high mathematics anxiety tended to show less activity in the frontal and parietal areas in anticipating and carrying out mathematical tasks than did less anxious individuals. They also did less well in the mathematical tasks. However, there was a subgroup, that did show strong activation of these areas when anticipating a mathematics task, and these individuals performed much better than those who did not show such activation, and almost as well as those with low mathematics anxiety. This group of individuals also showed high activation during the mathematics task, not so much of the parietal and other cortical areas associated with arithmetic, but of subcortical areas associated with motivation and assessment of risk and reward. The authors suggested that the deficit in performance of individuals with high mathematics anxiety might be determined by their response and interpretation of their anxiety response, instead of the magnitude of those anxiety response or their mathematics skills per se .

Pletzer et al. (2015) carried out an fMRI study of two groups of people, matched for their mathematical performance on tests of magnitude judgment and arithmetic, but differing in levels of mathematics anxiety, as measured by a version of the MARS. Eighteen participants scored high and 18 low on the measure of mathematics anxiety. They underwent fMRI when carrying out two numerical tasks: number comparison and number bisection. For comparison, they were also given brief non-numerical cognitive tasks involving verbal reasoning and mental rotation. The groups did not differ in their brain activation patterns for the non-numerical tasks. In the numerical tasks, they did not differ with regard to the activation of areas known to be involved in number processing, such as the intraparietal sulcus (similar to findings of Lyons and Beilock, 2012a , b ) suggesting that performance deficits of high mathematics anxious individuals were unlikely to be due to lower mathematics skills; but the group with high mathematics anxiety showed more activity in other areas of the brain, especially frontal areas associated with inhibition. This suggests that processing efficiency may be impaired in people with high mathematics anxiety, requiring more effort to inhibit incorrect responses. The differences seemed to occur specifically for items that required magnitude processing, and were not found for items that involved multiplication and could readily be solved by fact retrieval.

Recently, functional brain imaging studies have indicated that 7- to 9-year-old children are already showing some of the same neural correlates of mathematics anxiety as adults. Young et al. (2012) carried out a functional MRI study with 7- to 9-year-old children, and found that mathematics anxiety was associated with high levels of activity in right amygdala regions that are involved in processing negative emotions and reduced activity in posterior parietal and dorsolateral prefrontal cortex regions associated with mathematical problem-solving (the latter finding was in contrast to Pletzer et al., 2015 , Lyons and Beilock, 2012a , b who found no activation differences in these areas). Children with high mathematics anxiety also showed greater functional connectivity between the amygdala and areas in the ventromedial prefrontal cortex that are associated with negative activity was also positively correlated with task activity in two subcortical regions: the right caudate nucleus and left hippocampus, both of which are known to be involved in memory processes. Crucially, these brain activity differences were mainly found, not during the actual mathematics task, but during the cue that preceded it (similar to Lyons and Beilock, 2012b ). Thus, the control processes that influence whether mathematics anxiety will inhibit performance seem to occur at the time of anticipation of the mathematics task, rather than during the task itself.

These studies have led to some interesting proposals about the most effective timing of cognitive treatments for mathematics anxiety. In particular, Lyons and Beilock ( 2012b , p. 2108) have proposed, on the basis of the above-mentioned brain-imaging studies and their own findings (greater activation in areas associated with visceral threat detection and pain perception with higher mathematics anxiety before but not during mathematics performance), that “emotional control processes that act early on the arousal of negative affective responses (e.g., reappraisal) are more effective at mitigating these responses and limiting concomitant performance decrements than explicit suppression of these responses later in the affective process.” As we shall see, this has implications for treatments.

Factors that Influence Mathematics Anxiety: Genetics

So far, we have been discussing the nature and assessment of mathematics anxiety, without much reference to the factors that influence it. One potential factor that has been investigated is genetics. Wang et al. (2014) carried out behavioral genetic studies of mathematics anxiety in a sample of 514 twelve-year-old twin pairs. They were given the Elementary Students version of the MARS as a measure of mathematics anxiety; the Spence Children's Anxiety Scale as a measure of test anxiety; a mathematical problem solving subtest of the Woodcock-Johnson III Tests of Achievement; and a reading comprehension test from the Woodcock Reading Mastery Test. Mathematics anxiety correlated significantly with general anxiety, and also correlated negatively with both mathematical problem solving and reading comprehension, while general anxiety did not correlate significantly with either academic measure. Univariate and multivariate behavioral genetic modeling indicated that genetic factors accounted for about 40% of the variance in mathematics anxiety, with most of the rest being explained by non-shared environmental factors.

It is unlikely that there are genetic factors specific to mathematics anxiety. Rather, the multivariate analyses suggested that mathematics anxiety was influenced by the genetic and environmental risk factors involved in general anxiety, and the genetic factors involved in mathematical problem solving. Thus, mathematics anxiety may result from a combination of negative experiences with mathematics, and predisposing genetic risk factors associated with both mathematical cognition and general anxiety.

Gender and Mathematics Anxiety

One of the factors that has received most study with regard to mathematics anxiety is that of gender. Much recent research indicates that males and females, in countries that provide equal education for both genders, show little or no difference in actual mathematical performance ( Spelke, 2005 ). However, they do indicate that females tend to rate themselves lower and to express more anxiety about mathematics ( Wigfield and Meece, 1988 ; Hembree, 1990 ; Else-Quest et al., 2010 ; Devine et al., 2012 ), though such differences are not huge ( Hyde, 2005 ). Most studies suggest such gender differences only develop at adolescence, and that primary school children do not exhibit gender differences in mathematics anxiety ( Dowker et al., 2012 ; Wu et al., 2012 ; Harari et al., 2013 ) though even in the younger age group boys often rate themselves higher in mathematics than girls do ( Dowker et al., 2012 ). This increased anxiety may come from several sources, including exposure to gender stereotypes, and the influence and social transmission of anxiety by female teachers who are themselves anxious about mathematics ( Beilock et al., 2010 ).

It may also be related to more general differences in anxiety between males and females. Many studies indicate that females tend to show higher levels of trait anxiety and the closely related trait of Neuroticism than males (e.g., Feingold, 1994 ; Costa et al., 2001 ; Chapman et al., 2007 ) and show higher prevalence of clinical anxiety disorders ( McLean et al., 2011 ). They have been found to show greater anxiety than males even in subjects where their actual performance tends to be higher than that of males, such as foreign language learning ( Park and French, 2013 ).

Also, males tend to show more confidence and rate themselves higher in a number of domains than females do (e.g., Beyer, 1990 ; Beyer and Bowden, 1997 ; Jakobsson et al., 2013 ). Thus, it is not surprising that this should also apply to mathematics, and, given the associations between anxiety and self-rating, that it might contribute to gender differences in mathematics anxiety.

However, there is some evidence that gender differences in mathematics anxiety cannot be reduced to gender differences in general academic self-confidence or in test anxiety. Devine et al. (2012) found that mathematics anxiety has an effect on mathematics performance, even after controlling for general test anxiety, in girls but not in boys. They asked 433 British secondary school children in school years 7, 8, and 10 (11-to 15-year-olds) to complete mental mathematics tests and Mathematics Anxiety and Test Anxiety questionnaires. Boys and girls did not differ in mathematics performance; but girls had both higher mathematics anxiety and higher test anxiety. Both girls and boys showed a positive correlation between mathematics anxiety and test anxiety and a negative correlation between mathematics anxiety and mathematics performance. Both boys and girls showed a negative correlation between mathematics anxiety and mathematics performance. However, regression analyses showed that for boys, this relationship disappeared after controlling for general test anxiety. Only girls continued to show an independent relationship between mathematics anxiety and mathematics performance.

By contrast, Hembree (1990) suggested that math anxiety is more negatively related to achievement in males than in females, and some other studies suggested that there are no gender differences in the relationship between mathematics anxiety and performance ( Meece et al., 1990 ; Ma, 1999 ; Wu et al., 2012 ). However, most such studies have not controlled for general test anxiety. Gender effects on the relationship between mathematics anxiety and performance may also depend on whether one is examining the cognitive or affective component of mathematics anxiety, and on what aspects of mathematics are involved. Indeed, Miller and Bichsel (2004) found that mathematics anxiety was more related to basic mathematics scores in males, but to applied mathematics scores in females. More research is needed as to what influences gender differences in both mathematics anxiety itself, and in its influence on performance.

It is unlikely that such gender differences are the result of gender differences in working memory, as on the whole, studies show relatively few gender differences in working memory ( Robert and Savoie, 2006 ) though some studies suggest that males may be better at visuo-spatial working memory and females at verbal working memory ( Robert and Savoie, 2006 ). Intriguingly, Ganley and Vasilyeva (2014) carried out a mediation analysis that suggested that mathematics anxiety seemed to affect visuo-spatial working memory more in female than male college students, and that this led to a greater decrement in mathematics performance. However, since other studies suggest that mathematics anxiety affects verbal more than visuo-spatial working memory ( DeCaro et al., 2010 ), there is still much room for further research here.

One possible explanation for greater mathematics anxiety in females than males is stereotype threat . Stereotype threat occurs in situations where people feel at risk of confirming a negative stereotype about a group to which they belong. In the domain of mathematics anxiety, this usually refers to females being reminded of the stereotype that males are better at mathematics than females, though it can also occur with regard to other stereotypes. For example, Aronson et al. (1999) found that white American men performed less well in mathematics when they were told that Asians tend to perform better in mathematics than white people, than when they were not exposed to this stereotype.

Most of the studies of the effects of stereotype threat on mathematics anxiety are somewhat indirect: they indicate that mathematics performance is worse when people are exposed to stereotype threat, but do not usually include direct measures of mathematics anxiety. While one likely explanation for the effects of stereotype threat is that it increases mathematics anxiety, there are other possibilities: e.g., that participants choose to conform to social expectations. This caution must be borne in mind when considering the evidence about the effects of stereotype threat on performance.

Schmader (2002) and Beilock et al. (2007) found that women performed less well on an arithmetic task if they were told that the researchers were studying why women do more poorly than men. Beilock et al. (2007) noted that, as is often found in studies of mathematics anxiety, the effect only occurred for problems that required the significant use of working memory resources.

Johns et al. (2005) gave participants a mathematics test under three conditions: one without any reference to gender stereotypes; one where they were told that the researchers were studying reasons why women performed less well in mathematics; and one where they were exposed to the same gender stereotype, but also taught explicitly about the nature of stereotype threat in this context, and how it could increase women's anxiety when doing mathematics. Females performed less well than men in the condition where the gender stereotype was presented without explanation, but there were no gender differences either in the condition where no gender stereotype was presented or in the condition where they were taught explicitly about the stereotype threat.

However, the effect of stereotype threat is not always found, especially in children. Ganley et al. (2013) carried out three studies with a total sample of 931 school children ranging from fourth to twelfth grade, and using several different methods from the implicit to the highly explicit to induce stereotype threat. There was no evidence of any effect of stereotype threat on girls' performance in any of these studies. It may be that stereotype threat only exerts an influence in very specific circumstances, or on the other hand that it always occurs and exerts an influence under all circumstances, so that the experimental manipulations exerted no additional effect. It may also be that the importance of stereotype threat has been overestimated at least with regard to children; or that the effects were greater in the past than now, due to changes in social attitudes.

Moreover, it may be that gender stereotypes are affecting not so much mathematics anxiety itself as self-perceptions of mathematics anxiety. Goetz and colleagues gave secondary school pupils questionnaires about mathematics anxiety as a trait , and also about their anxiety as a state during a mathematics class ( Goetz et al., 2013 ; Bieg et al., 2015 ). Both boys and girls tended to report higher trait anxiety than state anxiety, but girls did so to a much greater extent. Girls reported higher trait anxiety than boys in both studies, but higher state anxiety only in one of the studies. One possible conclusion that girls do not in fact experience so much more mathematics anxiety than boys, but that due to gender stereotypes they expect to experience more mathematics anxiety, and this in itself may discourage them from pursuing mathematics activities and courses.

Factors that Affect Mathematics Anxiety: Age

On the whole, mathematics anxiety appears to increase with age during childhood. Most studies suggest that severe mathematics anxiety is uncommon in young children, though some researchers have found significant mathematics anxiety even among early primary school children ( Wu et al., 2012 ). This apparent increase in mathematics anxiety with age is consistent with findings that show that other attitudes to mathematics change with age. Unfortunately, they tend to deteriorate as children get older ( Ma and Kishor, 1997 ; Dowker, 2005 ; Mata et al., 2012 ). Blatchford (1996) found that two-thirds of 11-years-olds rate mathematics as their favorite subject, but that few 16-year-olds do so. Some studies suggest that the deterioration of attitudes begins even before the end of primary school ( Wigfield and Meece, 1988 ).

There are a number of reasons why mathematics anxiety might increase with age: some relating more to the “anxiety” and some more to the “mathematics.” One reason is that general anxiety appears to increase with age during childhood and adolescence could also reflect increases in tendency to general anxiety. For example, it is generally found that the onset of clinical anxiety disorders peaks in early adolescence ( Kiessler et al., 2005 ) though it is possible that such disorders in younger children are under-diagnosed due to lack of clear and appropriate diagnostic methods ( Egger and Angold, 2006 ). It may be that a factor such as increasing intolerance of uncertainty or increasing awareness of social comparison is leading to both increased general anxiety and to increased mathematics anxiety in particular.

Reasons more specifically relating to mathematics may include exposure to other people's negative attitudes to mathematics; to social stereotypes, for example about the general difficulty of mathematics or about supposed gender differences in mathematics; to experiences of failure or the threat of it; and/or to changes in the content of mathematics itself. Arithmetic with larger numbers that make greater demands on working memory, and more abstract non-numerical aspects of mathematics, may arouse more anxiety than the possibly more accessible aspects of mathematics encountered by younger children.

Moreover, the relationships between attitudes and performance may change with age. A meta-analysis by Ma and Kishor (1997) indicated that the relationship between attitudes and performance increases with age. Some studies suggest that among young children, performance is not significantly related to anxiety ( Cain-Caston, 1993 ; Krinzinger et al., 2009 ; Dowker et al., 2012 ; Haase et al., 2012 ), but is more related to liking for mathematics and especially to self-rating. However, different studies give conflicting results; and some studies do show a significant relationship between anxiety and performance in young children ( Dossey et al., 1988 ; Newstead, 1998 ; Wu et al., 2012 ; Ramirez et al., 2013 ; Vukovic et al., 2013 ).

There are at least three possible explanations for the conflicting findings. One is that the results may vary according to the aspect of mathematics anxiety that is being studied. Studies that base their measures on Richardson and Suinn (1972) . Mathematics Rating Scale (MARS) or MARS-Elementary ( Suinn et al., 1988 ) have tended to show such a relationship even in young children ( Wu et al., 2012 ; Vukovic et al., 2013 ), and this could reflect the fact that such measures tend to focus on the affective dimension of mathematics anxiety. Those that have used the Mathematics Anxiety Questionnaire (MAQ) developed by Thomas and Dowker (2000) have tended not to show such a relationship in younger children ( Krinzinger et al., 2007 , 2009 ; Dowker et al., 2012 ; Haase et al., 2012 ; Wood et al., 2012 ), which could reflect the fact that this measure places more emphasis on the cognitive (“worry”) aspect of mathematics. The few studies that have included both dimensions of mathematics anxiety have suggested that performance in young children is related to the affective but not to the cognitive dimension ( Harari et al., 2013 ), whereas studies of older children and adults suggest that performance is related to both, but is more strongly related to the affective dimension ( Wigfield and Meece, 1988 ; Ho et al., 2000 ). More research is needed on how the relationship changes with age between performance and different components of mathematics anxiety.

A second explanation is that mathematics anxiety becomes more closely related to mathematics performance because of changes in working memory. Working memory of course increases with age in childhood ( Henry, 2012 ), which could affect the relationship between anxiety and performance. One study does suggest that the relationship between anxiety and performance is greater in children with higher than lower levels of working memory. Vukovic et al. (2013) carried out a longitudinal study of 113 children, who were followed up from second to third grade. Mathematics anxiety was measured by items from the MARS-Elementary and from Wigfield and Meece's (1988) MAQ. Mathematics anxiety was negatively related to performance in calculation but not geometry. It was also negatively correlated with pupils' improvement from second to third grade, but only for children with higher levels of working memory. This is at first sight surprising given that working memory is generally positively correlated with mathematical performance, and especially in view of the theory that mathematics anxiety impedes performance by overloading working memory. We would suggest that a likely explanation is that among younger elementary school children, only those with high levels of working memory are already using mathematical strategies that depend significantly on working memory, and that therefore these may be the children whose progress is most impeded by mathematics anxiety. This could be one explanation for mathematics anxiety being more correlated with performance more in older than in younger children.

A third possible explanation is cultural. The studies that do show a relationship between mathematics anxiety and achievement among young children tend to be from the USA, though this could of course be a coincidence, and there are at present no obvious reasons why the relationship should be stronger in the USA than elsewhere. Nevertheless, there is evidence more generally for cultural influences on mathematics anxiety.

Culture, Nationality, and Mathematics Anxiety

Some aspects of attitudes to mathematics seem to be common to many countries and cultures: e.g., the tendency for young children to like mathematics, and for attitudes to deteriorate with age ( Ma and Kishor, 1997 ; Dowker, 2005 ). However, different countries differ not only in actual mathematics performance, but also in liking mathematics; in whether mathematics is attributed more to ability or effort; and how much importance is attributed to mathematics ( Stevenson et al., 1990 ; Askew et al., 2010 ).

Some of these differences could affect mathematics anxiety, though the direction is not completely predictable. Children in high-achieving countries could be low in mathematics anxiety because they are doing well (and/or may do well because they are not impeded by mathematics anxiety). On the other hand, they could be high in mathematics anxiety, because such countries often attach high importance to mathematics and to academic achievement in general, making failure more threatening; and because such children are likely to be comparing themselves with high-achieving peers, rather than with lower-achieving children in other countries. Lee (2009) investigated mathematics anxiety scores in a variety of countries and found that the relationship between a country's overall mathematics achievement level, and the average level of mathematics anxiety among children in that country, was not consistent. Children in high-achieving Asian countries, such as Korea and Japan, tended to demonstrate high mathematics anxiety; while those in high-achieving Western European countries, such as Finland, the Netherlands, Liechtenstein, and Switzerland tended to demonstrate low mathematics anxiety. At present, the reason for these differences is not clear. They may be related to the fact that pressure to do well in examinations is probably significantly greater in Asian countries (e.g., Tan and Yates, 2011 ). They could also be related to some as yet undetermined specific aspects of the educational systems or curricula.

Another possible reason could involve cultural or ethnic differences either in willingness to admit to mathematics anxiety, or in the nature of the relationship between mathematics anxiety and mathematics performance. Several studies have suggested that ethnic minority students express more positive attitudes to mathematics than white pupils both in the USA ( Catsambis, 1994 ; Lubienski, 2002 ) and in the UK ( National Audit Office, 2008 ), which did not conform to actual differences in performance. However, the meta-analysis of Ma (1999) showed no ethnic differences with regard to the relationship between anxiety and performance.

There is overwhelming evidence that both the socio-economic status of individuals and the economic position of countries have a very large influence on mathematical participation and achievement (e.g., Chiu and Xihua, 2008 ), However, there has been little research specifically on the influence of socio-economic status on mathematics anxiety or attitudes to mathematics; and the research that has been done does not suggest a very strong SES effect on these variables ( Jadjewski, 2011 ).

Potential Treatments of Mathematics Anxiety

Research has already told us a lot about the nature of emotions and attitudes toward mathematics. So far, it tells us less about how such attitudes can be modified, and how mathematics anxiety may be treated, or, ideally, prevented. It is likely that early interventions for children with mathematical difficulties may go some way toward preventing a vicious spiral, where mathematical difficulties cause anxiety, which causes further difficulties with mathematics. Parents and teachers could attempt to model positive attitudes to mathematics and avoid expressing negative ones to children. This may, however, be difficult if the parents or teachers are themselves highly anxious about mathematics. There could be greater media promotion of mathematics as interesting and important. However, much more research is needed on the effectiveness of different strategies for improving attitudes to mathematics. In such research, it must be taken into account, both that mathematics has many components and that different strategies might be effective with different components; and that improving attitudes to mathematics means not only reducing anxiety and other negative emotions toward mathematics, but increasing positive emotions toward mathematics.

Treatments of already-established mathematics anxiety may involve both mathematics interventions as such, and treatments for anxiety such as systematic desensitization and cognitive behavior therapy. So far, no miracle cure seems to be in sight. However, there are new methods, based on recent research findings that appear to be promising.

In particular, researchers have recently attempted to use findings about the cognitive aspects of mathematics anxiety, and about cognitive treatments of anxiety more generally, to develop techniques involving reappraisal of the anxiety-provoking situation. A few recent studies suggest that instructing people to reappraise the nature and consequences of mathematics anxiety may reduce the negative effects, breaking a vicious circle, whereby people feel that their anxiety will worsen their performance or is a signal of inability to carry out the tasks. Johns et al. (2008) and Jamieson et al. (2010) found that informing people that arousal could actually improve performance led to better mathematics performance than in a control condition.

Beilock and colleagues have developed a promising intervention for mathematics anxiety that amounts to “writing out” the negative affect and worry ( Ramirez and Beilock, 2011 ; Park et al., 2014 ). The researchers drew on previous findings that writing about traumatic and highly emotional events lowered ruminating behavior in individuals with clinical depression ( Smyth, 1998 ). A possible mechanism for this could be that writing enables a form of reappraisal that interrogates the need to worry in the first place. This in turn frees working memory resources consumed by worrying, which can be deployed toward task performance. Ramirez and Beilock (2011) tested this proposition both in a laboratory environment and also in a high-stakes field experiment (i.e., an exam). Both the laboratory and field experiments showed that writing about one's worries before academic performance significantly improved performance compared to a control condition (e.g., writing about untested exam material). An exam can be stressful for anyone taking it. Most interesting, therefore, was the finding that 10 min of expressive writing before an exam was only beneficial for individuals with high test anxiety, compared to control writing. Individuals with low test anxiety did not experience any particular benefits from expressive writing. The authors attribute this to the extent to which individuals with high and low test anxiety differ in worrying about exams. Individuals with lower test anxiety, who presumably worry less, would therefore write about fewer worries during an expressive writing exercise. In other words, there is simply less worry that needs to be “written out” for individuals with low test anxiety, in contrast to individuals with high mathematics anxiety. The potential of this kind of intervention to facilitate a level playing field during exams is potentially large. Indeed, students in the expressive condition outperformed those in the control condition by 6%. In letter grades, the expressive condition students earned a B+ on average, while those in the control condition earned a B–. Could this kind of intervention be useful for mathematics anxiety? The same group of authors has suggested that this may be the case. In a recent paper, Park et al. (2014) explored the influence of expressive writing on the link between mathematics anxiety and mathematics performance. Parallel to the Ramirez and Beilock (2011) results, Park et al. (2014) found that expressive writing ameliorated performance on tasks of modular arithmetic (specially developed working memory-intensive mathematics problems) in high mathematics anxiety individuals compared to a control writing task. As stated earlier in this paper, one of the central tenets of current theories of mathematics anxiety is that the negative emotional state and associated ruminations absorb working memory resources necessary for task completion. Expressive writing seems to disrupt the negative emotional cognitions, and allows individuals to engage with the mathematical tasks rather than the attendant anxiety. Unlike Ramirez and Beilock (2011) , Park et al. (2014) did not test these propositions in the field with an actual mathematics exam. Therefore, the benefit of expressive writing on mathematics examination performance remains a presumption in need of verification. However, a note of cautious optimism is permissible, given both the promising results from the earlier field experiments as well as evidence of higher performance on working memory-intensive problems reported in Park et al. (2014) . Future research can easily investigate this possibility, as the only requirement is that proctors instruct students to engage in a writing task 10 min before the start of an exam.

Recently, the potential of cognitive tutoring to intervene with mathematics anxiety has been explored. Supekar et al. (2015) examined whether an intensive, 8-week one-on-one math-tutoring programme, MathWise that was developed by Fuchs et al. (2013) to improve mathematical skills could remediate math anxiety of children aged 7–9 years old. Children underwent three sessions of 40–50 min mathematics tutoring per week. They reported math anxiety levels using the Scale for Early Mathematics Anxiety ( Wu et al., 2012 ) and were scanned using fMRI before and after training. During scanning, children performed on an arithmetic problem-solving task (Addition task) and number-identification (Control task). This study found that tutoring reduced math anxiety scores and remediated aberrant functional responses and connectivity in emotion-related circuits associated with the basolateral amygdala in children with high mathematics anxiety, but not those with low mathematics anxiety. In particular, they found that children with greater tutoring-associated decreases in their amygdala activity showed higher reductions in mathematics anxiety. The authors proposed that similar to models of exposure-based therapy for anxiety disorders, sustained exposure to mathematical stimuli could reduce mathematics anxiety, possibly through modulating the role of the amygdala. Together, this study showed that a relatively short and intensive one-on-one cognitive tutoring could remediate mathematics anxiety through modulation of neural functions.

As highlighted by Sokolowski and Necka (2016) however, interpretations of these findings should consider that since children were categorized through the extreme group approach (into high or low math-anxious using a median-split of pre-test SEMA scores) and were not recruited on the basis of their math anxiety levels, it is possible that children with nearly average SEMA scores might have been included in the high math anxious group (which is typically defined, for example by Ashcraft and Kirk (2001) , as the highest 20% of this population). Such classification might affect the interpretations of “aberrant neural responses” attributed to children with high mathematics anxiety. Nonetheless, Supekar et al. (2015) provided a proof-of-concept that behavioral interventions with simultaneous neural, social and cognitive assessments could contribute to our understanding of the relationship between individual differences and efficacy of interventions.

Another potential form of treatment, which is just beginning to be explored, involves non-invasive brain stimulation. Non-invasive brain stimulation techniques are used by researchers to modulate neural activity on broad areas of the cortex. Transcranial electrical stimulation (tES) has emerged as a painless technique in which mild electrical currents are applied to the scalp and can be used to both upregulate and downregulate neuronal activity underneath the cortex.

Might such a technique be useful as an intervention for mathematics anxiety? As stated above, some brain imaging research has examined the neurophysiological signatures of mathematics anxiety. These include abnormal amygdala activation ( Young et al., 2012 ) associated with fear processing, activation of the dorsoposterior insula, associated with pain perception ( Lyons and Beilock, 2012a ), and hypoactivation of regions in the frontoparietal network such as the dorsolateral prefrontal cortex, associated with both cognitive control of negative emotions and with mathematical performance ( Lyons and Beilock, 2012b ). Transcranial electrical stimulation enables researchers to modulate cortical activity in regions that may facilitate greater emotional control over the negative emotional response to mathematical stimuli, thereby improving performance. Transcranial direct current stimulation (tDCS) is the most widely used form of tES. tDCS is a non-invasive and painless neuromodulation technique wherein a low direct current, usually between 1 and 2 mA, is transmitted into cortical tissue through scalp-electrodes ( Nitsche et al., 2008 ; Cohen Kadosh, 2013 ; Krause and Cohen Kadosh, 2014 ). The electrical signals in tDCS alter neuronal polarization, thereby manipulating the probability that the targeted neurons will fire; typically, anodal stimulation is known to facilitate neural firing, while cathodal stimulation inhibits neuronal firing of the stimulated cortical region ( Nitsche and Paulus, 2000 ). In sham (placebo) stimulation, a burst of current is provided and turned-off, generating the same physical sensations as real stimulation (e.g., mild itching, burning, tingling, or stinging), but producing no change in cortical excitability. This serves as a reliable blinding method, and participants are generally unable to distinguish between real and sham stimulation ( Gandiga et al., 2006 ). The brain region usually targeted in emotion-related tDCS research is the dorsolateral prefrontal cortex (dlPFC), which is implicated in working memory and affective regulation ( Peña-Gómez et al., 2011 ), and is closely involved in the response and control of stress ( Cerqueira et al., 2008 ).

Sarkar et al. (2014) investigated the effects of tDCS to the dlPFC on mathematics anxiety. High mathematics anxiety individuals received 1 mA of tDCS for 30 min (or 30 s, in the placebo condition) to their left and right dorsolateral prefrontal cortices to enhance cognitive control over the negative emotional response elicited by mathematical stimuli. A low mathematics anxiety group received the same treatment. Sarkar et al. (2014) also examined changes in salivary cortisol, mentioned above as a possible physiological measure of anxiety. Anodal and cathodal stimulation were applied to the left and right dlPFC, respectively. In their study, Sarkar et al. (2014) found that, compared to sham stimulation, real tDCS lowered reaction times in the arithmetic decision task for individuals with high mathematics anxiety. They found the opposite pattern for low mathematics anxiety participants, who were slower in real compared to sham stimulation. The cortisol changes mirrored the behavioral changes. Compared to sham stimulation, high mathematics anxiety participants showed a decline in salivary cortisol concentrations from pre- to post-test during real tDCS. For the low mathematics anxiety group, salivary cortisol concentrations declined from pre-test to post-test only during sham tDCS, but not during real stimulation. This suggests tDCS might be able to alleviate the stress associated with mathematics anxiety, thereby improving mathematical performance in individuals with high mathematics anxiety. It is still necessary to be cautious about this possibility for several reasons. Firstly, as discussed above, the relationship between cortisol secretion and mathematics anxiety may not be totally straightforward. Secondly, the ecological validity of such intervention (e.g., as regards the training design and the practicality of using tDCS outside the laboratory) remains to be improved ( Cohen Kadosh, 2014 ; Looi et al., 2016 ). In the context of mathematics anxiety, further research is needed to examine whether tDCS could enhance performance for individuals with high mathematics anxiety in real-life settings and examinations (e.g., high-stakes situations). Given that the arithmetic decision task used by Sarkar et al. (2014) only required participants to decide whether very basic mathematical equations were true or false (e.g., 8 × 2 = 16, true or false), future studies could adopt more complex, realistic tasks. Thirdly, the improvement on such tasks was to the degree of ~50 ms, significant in a laboratory context but hardly relevant to the types of situations where mathematics anxiety is most relevant. Since behavioral studies mostly observe the influence of mathematics anxiety on difficult maths tasks (see Artemenko et al., 2015 for a recent review) and tES appears to be more effective during difficult tasks ( Popescu et al., 2016 ), future studies could investigate whether improvements of individuals with mathematics anxiety would be greater during more difficult tasks. Fourthly, since the dlPFC is involved in many functions, it is as yet unclear exactly which of these functions was crucially affected here: in particular, whether tDCS affected performance by influencing its role in emotional processing, or working memory, or both. Fifthly, the findings suggest that such treatments would need to be targeted to people who are high in mathematics anxiety, and that their indiscriminate application to people with lower mathematics anxiety might actually impair performance. Hence, research that examines the mechanisms of such effects (positive or negative; short- or long-term) is needed ( Bestmann et al., 2015 ). Finally, behavioral effects are influenced by the parameters of tDCS. For example, while Sarkar et al. (2014) showed that tDCS applied during mathematical tasks benefited those with high mathematics anxiety and impaired performance of those with low mathematics anxiety, it remains to be investigated whether changing the parameters of stimulation (e.g., applying stimulation before or after mathematical tasks) would yield different behavioral outcomes (for a review of other factors, see Looi and Cohen Kadosh, 2015 ). Thus, these findings are merely the first, though a promising step in the development of tES as a potential intervention for mathematics anxiety.

So What Remains to be Understood?

During the last 60 years, we have acquired a much greater understanding of the phenomenon of mathematics anxiety. We have learned more about its correlation with mathematics performance, and for example how working memory may be involved in this. We have learned more about how it changes with age. We have learned more about its relationship to social stereotypes, especially with regard to gender. We have learned something about neural correlates of mathematics anxiety. We have learned something about possible ways to treat mathematics anxiety.

Thus, we have learned a significant amount about many specific aspects of mathematics anxiety. Our biggest need for further learning may involve not so much any specific aspect, as the ways in which the aspects relate to one another. How do the social aspects relate to the neural aspects? How do either or both of these relate to changes with age? How might appropriate treatment be related to age and to the social and cognitive characteristics of the individuals? And of course the perennial “chicken and egg” question: does mathematics anxiety lead to poorer performance, or does poor performance, with its resulting experiences of failure, lead to poorer performance ( Carey et al., 2015 )? Many more interdisciplinary, longitudinal and intervention studies will be needed to answer these questions. An ultimate goal of such research is to integrate findings from across the behavioral, cognitive and biological dimensions of this construct in order to produce a fuller description of mathematics anxiety as a trait that varies between individuals.

There are also more specific aspects of mathematics anxiety that need a lot more study. For example, although there has been a great deal of research on social influences on mathematics anxiety, most of this has involved one particular type of influence: gender stereotyping. Other influences also need more investigation. In particular, there needs to be more investigation of the role of pressures by parents and teachers for school achievement. This is especially true in view of the increasing importance of both mathematics as such and of academic qualifications in today's society; and in view of the increasing concern of governments in several countries about raising academic standards. The question arises of whether and at what point an increasing emphasis on mathematical achievement might have the negative and potentially counterproductive effect of increasing mathematics anxiety; and how this might be prevented. In this context, there needs to be more research on exactly how mathematics anxiety is related to motivation, and, in particular, whether there are differences in the relationships of intrinsic and extrinsic motivation to anxiety ( Gottfried, 1982 ; Lepper, 1988 ; Ryan and Pintrich, 1997 ).

We hope that long before another 60 years have passed, research will have led to a greater understanding of mathematics anxiety, which will enable us to develop interventions and educational methods that will greatly reduce its incidence.

Author Contributions

All authors listed, have made substantial, direct, and intellectual contribution to the work, and approved it for publication.

We thank the Nuffield Foundation for financial support.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Keywords: mathematics anxiety, working memory, gender, stereotype threat, cognitive reappraisal, transcranial direct current stimulation (tDCS)

Citation: Dowker A, Sarkar A and Looi CY (2016) Mathematics Anxiety: What Have We Learned in 60 Years? Front. Psychol. 7:508. doi: 10.3389/fpsyg.2016.00508

Received: 06 August 2015; Accepted: 24 March 2016; Published: 25 April 2016.

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Copyright © 2016 Dowker, Sarkar and Looi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Ann Dowker, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

Current Trends in Math Anxiety Research: a Bibliometric Approach

• Published: 14 October 2023
• Volume 22 , pages 1345–1362, ( 2024 )

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• Ilija Milovanović 1  

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The aim of this study was to investigate current trends in research of math anxiety (MA) through bibliometric perspective. Three main clusters were formed based on author keywords: cognitive correlates (working memory, attention, numerical cognition, mental arithmetic), psychological factors and effects (self-concept and self-efficacy, motivation, confidence, attitudes), and educational context (PISA, measurement, gender differences, math achievement, math education, assessment). Analysis of the index keywords revealed somewhat different organization with two dominant clusters: the experimental cluster in which the most frequent are psychophysiological measures and terms and the correlational cluster in which the topics of MA psychosocial factors are most represented. The map of bibliographic coupling showed several relatively separated groups of authors with different focus in cited references. However, a map of co-citation of authors revealed closeness of these separated groups, with Beilock, S. L. and Ashcraft, M. H. by far the most-cited authors in this field.

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Radević, L., Milovanović, I. Current Trends in Math Anxiety Research: a Bibliometric Approach. Int J of Sci and Math Educ 22 , 1345–1362 (2024). https://doi.org/10.1007/s10763-023-10424-4

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Spotlight on math anxiety

Silke luttenberger.

1 Institute for Educational Sciences and Educational Research, University of Teacher Education Styria, Graz, Austria

Sigrid Wimmer

2 Educational Psychology Unit, Institute of Psychology, University of Graz, Graz, Austria, [email protected]

Manuela Paechter

Anxiety disorders are some of the most widespread mental health issues worldwide. In educational settings, individuals may suffer from specific forms of test and performance anxiety that are connected to a knowledge domain. Unquestionably, the most prominent of these is math anxiety. Math anxiety is a widespread problem for all ages across the globe. In the international assessments of the Programme for International Student Assessment (PISA) studies, a majority of adolescents report worry and tension in math classes and when doing math. To understand how math anxiety takes effect, it has to be regarded as a variable within an ensemble of interacting variables. There are antecedents that facilitate the development of math anxiety. They concern environmental factors such as teachers’ and parents’ attitudes toward their students’ and children’s ability in math, societal stereotypes (eg, on females’ math abilities), or personal factors such as traits or gender. These antecedents influence a number of variables that are important in learning processes. Math anxiety interacts with variables such as self-efficacy or motivation in math, which can intensify or counteract math anxiety. Outcomes of math anxiety concern not only performance in math-related situations, they can also have long-term effects that involve efficient (or not-so-efficient) learning as well as course and even vocational choices. How can math anxiety be counteracted? A first step lies in its correct diagnosis. Questionnaires for the assessment of math anxiety exist for all age groups, starting at primary education level. Help against math anxiety can be offered on different levels: by educational institutions, by teachers and a change in instructional approaches, by parents, or by the affected person. However, much more research is needed to develop effective measures against math anxiety that are tailored to an individual’s characteristics and needs.

This overview on math anxiety pursues the following aims:

• To describe the phenomenon of math anxiety, including information on its prevalence and on how it differs from other forms of anxiety.
• To explain which variables (antecedents) influence the occurrence of math anxiety, which variables interact with it, and what are the (educational) outcomes of math anxiety. These different types of variables are sorted and structured in a framework on math anxiety.
• To introduce instruments for the measurement of math anxiety in different age groups.
• To describe possible means to prevent or reduce math anxiety.

Introduction

Anxiety disorders are some of the most widespread mental health-care problems worldwide. 1 In a 2006 literature review including more than 40 studies from different countries, prevalence rates for anxiety disorders were nearly 17% (taking into consideration the major types such as generalized anxiety disorder, obsessive–compulsive disorder, panic disorder, phobia, posttraumatic stress disorder, and social anxiety disorder). 2 Compared to men, women have higher prevalence rates across all anxiety-disorder categories. Moreover, anxiety disorders involve not only adults. They are also the most common mental health problems experienced by young people. 3

In educational settings, anxiety can have detrimental effects on learners. It involves feelings in specific situations, such as examinations, as well as overall learning, and even lifelong academic and vocational development. Along with more overarching anxiety disorders, individuals may suffer from specific forms of test and performance anxiety that are connected to a knowledge domain. Clearly, the most prominent of these disorders is math anxiety. 4

Math anxiety is a widespread, worldwide problem affecting all age groups. Approximately 93% of adult US-Americans indicate that they experience some level of math anxiety. 4 Estimations are that approximately 17% of the US-American population suffers from high levels of math anxiety. 5 In a sample of adolescent apprentices in the United Kingdom, approximately 30% of the study participants reported high math anxiety, and a further 18% were at least somewhat affected by it. 6 The most extensive set of data is provided by the Programme for International Student Assessment (PISA) studies. In its 2012 assessments, across the 34 participating Organisation for Economic Co-operation and Development (OECD) countries, 59% of the 15- to 16-year-old students reported that they often worry math classes will be difficult for them; 33% reported that they get very tense when they have to complete math homework; and another 31% stated they get very nervous doing math problems. 7

Math anxiety has been mainly investigated in educational settings, and research has seldom been linked to clinical research on anxiety disorders. In the diagnostic systems for mental disorders – the Diagnostic and Statistical Manual of Mental Disorders (DSM) 8 and the International Classification of Diseases (ICD) 9 – it is not included as a separate category, but would rather be subsumed under generalized anxiety disorder or social anxiety disorder. 1 Many individuals who claim to be affected by math anxiety probably would not meet the DSM criteria for an anxiety disorder. Yet, research shows that math anxiety affects individuals of all ages in academic situations as well as in their academic success and well-being. Moreover, math anxiety is distinct from anxieties in other subjects or general test anxiety; for example, research on anxiety in related subjects such as math and statistics shows that, to a large degree, math anxiety and statistics anxiety are independent of each other and have different effects on learners. 10

Math anxiety has been defined as feelings of apprehension and increased physiological reactivity when individuals deal with math, such as when they have to manipulate numbers, solve mathematical problems, or when they are exposed to an evaluative situation connected to math. 10 – 12 Many studies and measurement instruments assume at least two assessment-related dimensions of math anxiety: anxiety experienced when taking a test, and anxiety experienced in the classroom. 11 , 13 Math anxiety experienced in the classroom may also include a sub-facet related to the fear of math teachers. 14 Other studies add the numerical anxiety content-related dimension to test and classroom math anxiety. This describes anxiety that occurs when undertaking math operations and manipulating numbers. 15 , 16 Some researchers further differentiate math anxiety according to different situations in which math tasks are encountered, such as homework in math or mathematical tasks in daily life. 17 Although theories and measurement instruments vary considerably in the differentiation of math anxiety, nearly all of them agree on three facets found within it: test, classroom, and numerical anxiety.

Math anxiety describes an enduring, habitual type of anxiety and can be understood as a trait which represents a fairly stable characteristic of an individual and that influences how an individual feels in, perceives, and evaluates specific situations. 10 Math-anxious individuals experience increased levels of anxiety in math-related situations. State math anxiety manifests itself on an emotional, cognitive, and physiological level and leads to outcomes such as decreases in achievement. On an emotional level, individuals suffer from feelings of tension, apprehension, nervousness, and worry. 1 , 18 On a cognitive level, math anxiety compromises the functioning of working memory (as described in greater detail further). 19 – 21

On a physiological level, the symptoms of math anxiety include increased heart rate, clammy hands, upset stomach, and lightheadedness. 4 Math anxiety and its feelings of tension, or assumptions that students may feel their heart beating faster when confronted with mathematical problems, have been objectively verified. 22 Previous research has compared students’ physiological reactivity while completing math tasks compared to those when completing anagrams. 23 Students with high levels of math anxiety showed greater increases in cardiovascular reactivity when solving mathematical tasks than students with low levels of math anxiety, implying a higher level of strain due to math anxiety.

Neurocognitive research suggests that math anxiety and its affective responses are related to the fear and pain network in the brain. 24 On a neural level, two networks represent the emotionality of math anxiety: the pain network involving the insula 25 and the fear network centered around the amygdala. 26 In functional MRI studies, activity in the insula’s pain network can be observed when math-anxious individuals face a math task. 25 Interestingly, not the task itself, but its anticipation correlates with pain-related activity. In a study focusing on the fear network, 26 highly math-anxious children showed hyperactivity and an abnormal connectivity in the right basolateral amygdala, suggesting that the effects of math anxiety on these networks are age dependent. 24

A framework of math anxiety

Math anxiety takes immediate effect in math-related situations such as examinations or in the classroom. However, it influences individuals over the course of their academic and vocational lives. To understand the influence of math anxiety on learning and learners’ academic development, it should be regarded as one variable within an ensemble of environment-related and person-related variables that interact together.

Based on findings from learning and instruction and research on moderating and mediating variables of math anxiety, 10 , 21 the following figure presents a framework for understanding math anxiety and its effects. It distinguishes between different types of variables:

• (Educational) outcome variables such as performance, learning behaviors, or choices are influenced by math anxiety. 5 , 10 They have a long-term effect on the further development of math anxiety and related variables.
• Antecedents that influence the occurrence of math anxiety. These antecedents may be environment related, and include culture, the characteristics of educational systems, as well as parents’ and teachers’ attitudes toward math and their students and children. 27 Furthermore, antecedents of math anxiety may be person related and include aspects such as trait anxiety or gender. 10 , 13
• Variables that interact reciprocally with math anxiety. In this context, self-efficacy, self-concept, and motivation in math are described. These variables interact in the immediate learning process with each other. Furthermore, they influence each other on a long range. Together with math anxiety, these variables influence outcome variables. 7 , 10

Outcomes of math anxiety

According to Figure 1 , math anxiety influences various outcome variables, the most important of which are introduced here.

A framework for understanding math anxiety.

Math anxiety and performance

Studies on performance mainly focus on students in secondary education and university students. In contrast, our literature review found fewer studies in primary education.

Studies in secondary education (grades 6–12) nearly always find negative relationships between anxiety and performance in math which are mainly measured as points in achievement tests or as grades. Ashcraft and Krause write: “The story told by the correlations is sad indeed. The higher one’s math anxiety, the lower one’s math learning, mastery, and motivation”. 28

Meta-analyses and studies with samples from different school grades confirm this and give an insight into the relationship, mostly by means of correlation: in a 1990 meta-analysis with seven studies and students in grades 5–12, correlations varied between r =−0.18 and r =−0.47. 29 A study in the same year with students in grades 7–9 reported correlations of r =−0.20. 30 A meta-analysis in 1999 with 26 studies and all grades in secondary education found correlations between r =−0.12 and r =−0.47. 31 Data from the PISA studies with 15- to 16-year olds confirm these results on an international level. Within and across countries, math anxiety correlates negatively with PISA math task achievement. This relationship remained stable over several assessment periods. 7 , 32

These correlations between math anxiety and performance point at significant relationships that vary considerably in their size. Correlations of r =−0.18 mean a shared variance between math anxiety and performance of only 3.24%; values of r =−0.47 mean 22.09% shared variance, which is a rather large amount of shared variance. Altogether, these figures suggest that math anxiety can only explain a part of task performance (yet, partly, a considerable one), and is one variable within an ensemble of several others.

The studies in primary education yield results similar to the ones in secondary education. In a meta-analysis with three studies in upper elementary education, correlations between various facets of math anxiety and performance ranged from r =−0.19 to r =−0.49. 31 This means a shared variance between 3.61% and 24.01%. Math anxiety in early grades, such as Grade 2, influences math performance not only in the same grade but also in subsequent grades. 33 However, it is unclear whether, in primary education, mathematical knowledge, in general, or only specific aspects of mathematical knowledge are affected by math anxiety. In three studies in lower primary education, in grades 1 and 2, math anxiety had a stronger effect on mathematical reasoning and knowledge of concepts than on numerical operations and counting skills. 34 – 36 In contrast, in studies in upper elementary education, math anxiety was negatively related to achievement on tasks measuring different types of knowledge, conceptual knowledge, and where the application of mathematical operations were concerned. 31 Furthermore, different facets of math anxiety seem to contribute differently to math performance in primary education. 37 , 38 Altogether, more investigations are needed for this age group.

Research with university students shows rather ambiguous results. In a 1990 meta-analysis, correlations varied between r =0.02 and r =0.57. 29 In a study with freshmen psychology students, correlations of r =−0.21 for course anxiety and r =−0.33 for math test anxiety and grades in the final school year were found. 10 Again, the correlations are significant, although shared variance ranges between only 4.41% and 10.89%.

Math anxiety, performance, and effects on working memory

According to the Attentional Control Theory, efficient cognitive processing depends on two attentional systems: a top–down, goal-driven system that is influenced by current goals and expectations, and a stimulus-driven system that is influenced by the salient stimuli of the environment. 39 , 40 Anxiety disrupts the balance between these two systems, causing the stimulus-driven system to become dominant, thus reducing the capacity to focus on task-relevant, instead of threat-related, information. This imbalance is connected to impairments in cognitive processing so that it becomes more difficult to resist the disruption of interference from task-irrelevant stimuli and to focus on task-relevant stimuli. 41 , 42

Working-memory impairments involve specific aspects of mathematical proficiency, especially accuracy and procedural fluency. Whereas accuracy refers to the correctness of task solutions and the number of errors, fluency refers to the ability to apply procedures efficiently, within a short amount of time, and with minimal effort. Fluency depends on practice and includes the establishment of work routines. As such, fluency indicates familiarity with mathematical problems. Math anxiety appears to influence fluency more strongly than accuracy. Students with lower math anxiety are more efficient and complete more digits correctly per minute on mathematical tasks (with operations such as addition, subtraction, multiplication, division, and linear equations) than students with higher degrees of math anxiety. 43 These assumptions, however, were verified for only adult students and not for children or adolescents who may be less fluent in mathematical task processing.

Math anxiety not only impairs genuine mathematical cognitive processes, but overarching cognitive processes that depend on fluency as well. In a study with undergraduate psychology students, students with medium or high math anxiety were impaired in their reading processes when the text was related to math. 42 Similarly, specific declines in working-memory capacity were found when a computation task was administered, albeit not when participants worked on verbally based tasks. 28 , 41 Math anxiety compromises reading speed as well as errors in task solving, although it depletes memory resources only for performance in math-related tasks, not in other domains. Recent research suggest that cognitive processes of forgetting math content are related to math anxiety. 44

Math anxiety and learning behaviors, especially procrastination

Math anxiety not only has direct effects on task performance, but influences long-term learning as well. Students with high levels of math anxiety are prone to a variety of adverse learning behaviors: they invest less time and effort in learning, organize their learning environment less efficiently, and devote less concentration and attention to a learning session. 10 Moreover, math-anxious students tend to avoid math-related situations and courses and more frequently exhibit procrastination behavior. 45 Academic procrastination makes students postpone their involvement with academic tasks such as homework or preparation for examinations. In math, the acquisition of knowledge and skills and the development of fluency in carrying out tasks depends strongly on constant practice. Procrastination, therefore, has significant effects, setting off a vicious cycle when math-anxious students avoid preparing for math, perform below expectations in examinations, and probably develop even higher levels of math anxiety as a result. 46

Math anxiety and academic and vocational choices

Math-anxious students take fewer math courses and avoid elective math coursework as early as secondary school. 5 , 28 These choices influence the further development of knowledge and skills as well as attitudes and self-estimations as they relate to math. Consequently, at a later age, students with high levels of math anxiety regard themselves as less able in math and expect to do badly in exams. Math-anxious students (often females) avoid enrollment not only in math courses but also in related fields such as science, technology, and engineering. 30 , 47

In a 1992 investigation with female freshmen college students, math anxiety was related to career interests and enrollment in courses in different disciplinary fields. 48 Students were asked how likely it would be for them to choose a career in various fields and how happy they would be in the respective field. Math anxiety proved to be crucial when it came to exclusion from a career in science and engineering; here, interest and math anxiety had antagonistic effects. Interest in science and engineering were mostly associated with low levels of math anxiety and contributed positively to considering a career in these domains. Math anxiety and interest were more important for the students’ career decisions than their knowledge of math, as measured by SAT (Scholastic Assessment Test) scores. 48

Antecedents of math anxiety

Antecedents of math anxiety can be divided into personal and environmental characteristics. Personal antecedents refer to the individual (eg, prior knowledge, trait anxiety, or gender), whereas environmental antecedents include aspects such as educational or cultural values or the influence of other significant people in their own life.

Significant people like teachers or parents

Teachers, parents, and other important adults serve as role models and influence children with their own attitudes toward math. 27 , 49 Teachers may spread the myth that math ability is inborn, and success depends on giftedness. In addition, they may emphasize that achievement in math depends on effort and persistence. In primary education, teachers have an especially significant influence, transferring their own anxiety in math to their students. 49 , 50 Female elementary school teachers influence girls in particular; the teacher’s level of math anxiety influences the achievement of the girls in their classes as well as the beliefs the girls maintain about their own mathematical abilities. 51 , 52 Moreover, school teachers foster math anxiety if they exhibit their own negative attitudes toward math in the classroom. 53 In contrast, teachers support positive attitudes in math if they provide encouragement, emphasize that mistakes are also a part of successful learning, and if they appeal to their students’ motivation and sense of self-efficacy and self-concept, for example, via accurate judgments of student performance and an accurate, yet self-assuring, feedback. 54

Parents shape their children’s educational values and self-assessments by their own attitudes toward math. Parents’ beliefs about their child’s ability have strong impacts on his or her self-assessment. These beliefs do not necessarily rely on objective assessments because parents may maintain stereotypical evaluations. 55 , 56 Parents’ attributions toward math serve as a frame of reference, meaning that they may transfer their own math anxiety to their children. Mothers, in particular, influence their daughters’ attitudes toward math, self-assessments, and math anxiety. 27

Culture and educational systems

According to the PISA studies, the level of math anxiety on the one side and the strength of the correlation between math-anxiety, self-assessments in math abilities, and performance on the other side differ across countries. 7 , 32 , 57 Specific differences exist between Asian and Western European countries. Students in Asian countries, especially Korea, Japan, and Thailand, report low values on math self-concepts and self-efficacy and high math anxiety, whereas students in Western European countries such as Austria, Germany, Liechtenstein, Sweden, and Switzerland show high math self-efficacy and self-concept and low math anxiety. Asian students tend to set high goals and evaluate themselves according to strict standards. Additionally, they perceive their parents and themselves to be less satisfied with their school performance compared to non-Asian students. 32 , 58 All of these elements contribute to high anxiety and low self-concept and self-efficacy. But when it comes to math anxiety, the European countries show a stronger association between math anxiety and performance than Asian countries. However, in all countries, math anxiety correlates (yet, to different degrees) with achievement on the PISA math tasks. 32

Gender and stereotypes

Studies on math anxiety in secondary and tertiary education nearly always find higher levels of math anxiety in female, than in male, students. 11 , 59 – 61 Gender inequalities seem to vary between the different facets of math anxiety. Women score higher on math test anxiety than men. At least in university education, the results for the content-related facets such as numerical anxiety are more ambiguous; here, studies display greater disagreement on gender differences. Some studies find gender differences for all facets of math anxiety 10 , 13 whereas, in other studies, women score higher than men on test anxiety but men score higher on numerical anxiety. 62 Here, more fine-tuned research on gender differences in the different facets of math anxiety seems necessary.

Studies in secondary education confirm a gender bias in math anxiety. 60 With basically all facets of math anxiety, girls score higher than boys. This holds true for all grades. 12 , 59 , 63 In a majority of PISA study countries, 7 girls (aged 15–16) scored higher than boys on test, classroom, and numerical anxiety. Interestingly, gender differences in math anxiety were widest in countries that have comparatively low levels of math anxiety. 32

To prevent math anxiety at an early age, it would be important to know at which age gender differences come into being. Research on younger children, however, provides no clear picture. In a 2012 study, children between the ages of 7.5 and 9.4 years were asked how worried/relaxed they are about working on math tasks, about math tests, or understand ing the teacher in a math class. No gender differences were found for this sample. 64 This result was confirmed in studies in different countries and with different age groups: with a sample of 136 children between 7 and 10 years and measures of numerical, homework/classroom, and test anxiety in Germany; 17 with a sample of 8-year-old children and measures of classroom and test anxiety in the Netherlands; 65 with a sample of 6- to 7-year-olds and measures of worry in the United States; 34 and with a sample of 7- to 9-year-olds and an overall measure of math anxiety also in the United States. 66 In contrast, in a recent study in 2017 with samples of British children aged 8–9, girls scored higher on numerical and test anxiety. 12 Although the majority of studies speak against gender differences in primary education, the results still are not clear-cut. Studies nearly exclusively use a cross-sectional design. There is a need for long-term studies in which the development of gender differences in math anxiety can be observed over children’s formative years.

A large part of gender differences in math anxiety can be attributed to stereotypes about females’ abilities in math (as well as in science, technology, and engineering). 55 , 59 Girls internalize stereotypes about lower abilities in math and regard themselves as being less gifted than boys. These kinds of self-depreciatory assessments influence learning behaviors as well as math anxiety. In assessment situations, the internalized stereotype affects the perception of task difficulty and is related to increased strain and tension as well as decreased performance. 55 , 67 Over the course of childhood and adolescence, self-depreciatory assessment and anxiety lead to avoidance of math, harmful learning behaviors, and lower performance. 57 , 61

In addition to these effects, studies suggest that at least a smaller part of gender differences is due to hereditary influences. In their twin studies with comparisons of females and males, Malanchini et al 68 observed differences but sex only accounted for between 1.3% and 5.5% of the variance. This result, together with the research results described earlier, speaks for a large influence of individuals’ environment and stereotypes concerning girls’ and women’s aptitude in math, with a smaller influence of sex.

Genetic dispositions

Studies with monozygotic and dizygotic twins suggest that math anxiety has a genetic component, too. 68 , 69 The hereditary contribution to math anxiety can be investigated by comparisons of monozygotic and dizygotic twins. Monozygotic twins share 100% and dizygotic twins only 50% of their segregating alleles. A study with 12-year-old 69 as well as one with 19- to 20-year-old twin pairs 68 showed a moderate hereditary contribution to math anxiety, with environmental influences explaining the rest of the variance. Individuals with a hereditary disposition are more likely to develop math anxiety. However, more research is needed as the role of the genetic influence in comparison to the influence of family and school environment is still unclear.

A disposition that has a high comorbidity with math anxiety is dyscalculia. When children have weaknesses in mathematical skills and experience difficulties and negative feedback, they often develop math anxiety, too. Approximately 1–6% of children are assumed to suffer from dyscalculia. 70 They need specific interventions and support that considers their specific handicaps as well as math anxiety. However, an analysis of treatments for this group would go beyond the scope of this article with its focus on individuals with mainly unimpaired math skills.

General anxiety proneness

General anxiety proneness can be described as the habitual tendency to perceive stressful situations as threatening. 1 , 10 , 18 , 71 Endler and Kocovski 72 also use the term “trait anxiety”. General anxiety proneness describes relatively stable individual differences in general proneness to anxiety. 18 Therefore, a domain-specific form of anxiety should be related to general anxiety proneness. In a meta-analysis with samples of children and young adults, general and math anxiety correlated significantly with coefficients ranging from r =0.24 to r =0.54. 29 However, the strength of the relationship differs for the various facets of math anxiety; test and classroom anxiety pertaining to math are more closely related to general anxiety proneness than numerical anxiety. 10 Studies of the hereditary influence on general anxiety and math anxiety show that both types of anxiety have a small degree of shared, but a larger degree of unshared, components. 68 , 69

Variables in reciprocal interaction with math anxiety

Figure 1 suggests that math anxiety reciprocally interacts with other variables in math-related situations. The most important variables are introduced further.

Self-efficacy and self-concept

With regard to math, self-efficacy describes the belief of a person that, through their own action and effort, one can successfully perform in math. 7 The self-concept is related to self-efficacy, but is more focused on beliefs in academic domains. 73 It describes an individual’s beliefs in his or her competence in comparison to a standard of knowledge, to other learners’ knowledge, or an assessment of a person’s own development in an academic domain. 73

Overall, self-efficacy and self-concept in math are positively related to performance and negatively to math anxiety; the PISA studies demonstrate this quite impressively for all participating countries. 7 However, the self-concept is not an accurate reflection of actual competence in a domain, but instead, is influenced by stereotypes. 55 Self-concept, anxiety, and performance in math influence each other in the long term. High performance may boost self-concept and decrease anxiety, whereas a higher self-concept and lower anxiety levels inspire motivation in learning and reduce negative learning behaviors such as procrastination. 10 , 73 , 74

Prior knowledge

Lack of knowledge or the inability to understand mathematical concepts strongly contribute to math anxiety. 4 According to the Reciprocal Theory, 70 poor performance triggers math anxiety, and math anxiety leads to poor performance in a task-related situation. As described earlier, math anxiety is related to cognitive processing deficits in the working memory and, consequently, to poor performance and poor uptake of knowledge in task-related situations. 29

Furthermore, math anxiety prevents long-term learning and knowledge acquisition in math: learners with math anxiety avoid math-related courses and tasks over the course of time. In situations where processing mathematical content cannot be avoided, they show decreases in cognitive reflection on the task at hand. 75 Shorter and more shallow contact with math then leads to low levels of knowledge and skills.

Motivation can be described as an individual preference and a positively experienced, situation-specific state when working on a task. Students with higher motivation in a subject invest more time and effort in learning and performance and apply more effective learning strategies. 74 While motivation describes the tendency to approach, anxiety describes the tendency to avoid a task or a situation.

Very few studies however investigate the interaction between motivation, math anxiety, and performance. Against this background, Wang et al 76 doubt the numerous research results which assume a direct linear, negative correlation between math anxiety and performance. Research on state anxiety and performance on complex tasks mostly assumes a curvilinear relationship according to the Yerkes–Dodson law. Here, an intermediate level of stress produces optimal performance, whereas extremely low and high levels of stress produce poor performance. It seems that intrinsic motivation changes the relationship between math anxiety and performance. In studies with children and adults, a linear, negative correlation between math anxiety and performance was found for learners with low levels of motivation and a curvilinear correlation for learners with high levels of motivation in math. 76 For learners with high intrinsic motivation, a moderate degree of math anxiety may have beneficial effects.

Findings on the long-term effects of anxiety and learning behaviors support this notion. Anxiety may induce the motivation to avoid failure and its negative consequences. If the consequences of failure are severe (eg, dropping out of a course), and if students believe that there is a chance for success, math anxiety induces them to invest effort and time and strengthens positive effort motivation. Math anxiety, the expectation of success, and motivation interact with each other. 10 , 33 , 74

Assessment of math anxiety

In both education and research, it is necessary to assess math anxiety and compare different individuals’ levels of it. Math anxiety is nearly exclusively assessed using questionnaires with rating scales; this is done for all age groups.

The two most widely used math anxiety questionnaires for adults are, without question, the Mathematics Anxiety Rating Scale (MARS) and its short version, the Revised Mathematics Anxiety Rating Scale (R-MARS). 16 , 77 The items describe different situations applying math: studying for a math test, taking an exam, processing math in a daily-life situation, etc. Individuals assess the level of anxiety in the respective situation on a Likert scale. Both questionnaires distinguish different facets of math anxiety according to the type of situation: test anxiety, math course anxiety, computation anxiety, anxiety to apply math in daily life, and fear of math teachers. 62 Different types of validity were assessed positively: content validity as rated by experts, structural validity by an examination of the factorial structure, and criterion-related validity by the relationship to grades, to performance on standardized math tests, and to states of anxiety in math-related situations. 11 , 62 , 77 , 78 The MARS is one of the most comprehensive questionnaires concerning the inclusion of different facets of math anxiety. Shorter questionnaires mostly focus only on math test anxiety and numerical anxiety – for example, the Abbreviated Math Anxiety Scale (AMAS). 11 , 13

Questionnaires for students in secondary education are often variations of the instruments for adults. An example is the MARS-E (elementary form) for children grades 4 onwards, which means age 10 to adolescence. 79 The items describe situations in school and children’s daily life. As with the version for adults, children and adolescents assess the level of anxiety they experience in their respective situations.

Questionnaires for younger children need to correspond to the respective developmental level including reading skills. Most questionnaires attempt to do this by using items with very concrete math-related situations from children’s daily life and rating scales with illustrative icons like smileys (for an overview, see Ganley and McGraw 14 ). However, it can be discussed whether these adaptations adequately reflect children’s level of understanding.

An innovative questionnaire for children aged 7–10 is the Mathematics Anxiety Interview (MAI). 17 Here, children look at pictures of math-related situations and receive a corresponding text description. They then assess their emotional, cognitive, physiological reactions and behaviors in the situation on a Likert scale, which means how excited they feel in such a situation, how worried they are, how strongly their heart beats, or whether they would like to escape from the situation. The children, furthermore, assess their overall anxiety in the situation. To our knowledge, the MAI is the only questionnaire with this kind of fine-tuned assessment of the different types of possible reactions to anxiety.

Our literature review found only one questionnaire for even younger children aged 6–8. Aarnos and Perkkilä developed a test in which children describe their feelings with regard to pictures with or without mathematical content. Furthermore, children are asked to draw pictures which are evaluated by content analysis. 80 , 81 While this kind of assessment requires no reading skills, the reliability of its evaluation does, in fact, pose a problem.

Altogether, questionnaires vary with regard to the age group and the facets of math anxiety they measure. While some take a narrow approach and include only a few facets, others include a wide range of math anxiety aspects. Nearly all questionnaires (with the exception of the MAI) rely on a global assessment of anxiety. Questionnaires vary with regard to how precisely they focus on math anxiety. Some measure not only math anxiety but, under the umbrella of math anxiety, they even subsume concepts that are related to math anxiety while measuring different concepts such as self-concept. 14 , 82

Implications for practice, means to prevent or reduce math anxiety

In light of the severe impairments to individuals’ lives, the question arises of how math anxiety can be prevented or at least alleviated. Measures may aim to directly reduce math anxiety or to counteract math anxiety by strengthening an individual’s positive assessments and attitudes or by supporting efficient learning. Measures against math anxiety can be taken by educational institutions, teachers, parents, or the affected person.

At the institutional level, curricular strategies against math anxiety may be implemented. Various colleges already offer courses against math anxiety wherein students learn techniques to overcome barriers in learning math and handle their fear of the subject. 83 Educational institutions may also provide the opportunity to take tests several times and give test-anxious students an emotional safety net. Even if students do not use a retest, the opportunity itself eases strain. 83 , 84 Some institutions attempt to reduce math anxiety by improving students’ knowledge, for example, by introductory math courses for freshmen. 85

Teachers may choose instructional strategies that enhance students’ interest and motivation, for example, by relating math to students’ lives and to daily-life situations. 4 Math instruction and tasks should be attractive to both males and females and, thus, prevent the formation of stereotypes. Similar advice involves the use of hands-on devices and manipulatives in learning. 4 , 83 Such instructional measures may enhance motivation, self-efficacy, and self-concept, as well as success, and counteract math anxiety as a result. Math anxiety can be reduced by the development of a positive yet realistic self-concept in math – all while keeping in mind that improvements in students’ self-concept will be short-lived without enhancing knowledge acquisition and improving achievement.

In exams, teachers may introduce anxiety-reducing measures such as using humorous examination tasks, or dividing the learning contents into several smaller examinations instead of one extensive examination. 21 Given that pressure enhances math anxiety and its effects in examinations, teachers should set enough time for math examinations and avoid time constraints. 86

Parents may support their children in developing a positive self-concept and preventing the development of math anxiety by, for example, providing adequate feedback or praise to achievement in math, by maintaining realistic expectations for their children’s success in math, or by showing how math is used in positive ways, such as in sports, hobbies, home repair, etc. 4

Learners can protect themselves against the development of math anxiety by different means. These involve the realistic attribution of success and failure to one’s abilities or effort and the development of a positive yet realistic self-concept. Learners should focus more on past successes than failures, and believe in their abilities instead of doubting them. 4 Other measures concern positive learning behaviors, for example, leaving enough study time for repetition of the material to be mastered, allotting enough time to study, and avoiding procrastination. 4 , 21 , 74 In math-related situations, students may use relaxation techniques to alleviate their anxiety level. 4 , 87 Another means for reducing exam anxiety is reappraisal, which means a change in a situation’s evaluation and its potentially threatening characteristics over to more positive attributes. 88 , 89

However, our research review on interventions to math anxiety showed a limited range of studies. Studies on the topic need a more systematic approach. Presently, studies focus on different outcomes of math anxiety, on different age groups; they mostly investigate various smaller interventions over a short time period. For the advancement of interventions on math anxiety, a clinimetric framework with a joint understanding and description of the phenomenon itself, of rating scales, and indexes for measurement of math anxiety as well as for success of interventions would be helpful.

In both research and practice, it has been acknowledged on an international level that math anxiety poses a severe problem over entire life spans. The effects of math anxiety on performance have been widely investigated, and its negative impact has been acknowledged. Issues, however, still remain with regard to math anxiety that need further investigation.

One concerns the temporal development of math anxiety and (methodologically) the need for long-term investigations. There is still a lack of research on the question of how math anxiety develops in childhood and how it becomes established over time. More knowledge on this question could help prevent math anxiety at an early age. Long-term studies that cover a formative phase in children’s development are advisable.

Another issue concerns the relationship between math anxiety and moderating variables. As could be shown for intrinsic motivation, moderating variables may change the relationship between math anxiety and performance; when learners experienced intrinsic motivation, moderate levels of math anxiety had a positive influence on performance. Here, methodological and statistical approaches are needed that take into consideration the reciprocal interaction of an ensemble of variables.

Lastly, as it was pointed out in the last section, research on math anxiety would very much profit from a more standardized clinimetric approach and joint agreements of researchers and practitioners on how to define and measure math anxiety.

As shown, there are numerous possibilities for the support of math-anxious individuals and reducing math anxiety. More knowledge on the development of math anxiety and its interaction with other variables will be important in supporting math-anxious individuals. Ideally, countermeasures should ultimately be offered that are tailored specifically to each individual’s personality, knowledge, and needs.

The authors report no conflicts of interest in this work.