link analysis case study

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Link Prediction in Criminal Networks: A Tool for Criminal Intelligence Analysis

Giulia berlusconi.

1 Università Cattolica del Sacro Cuore and Transcrime, Milano, Italy

Francesco Calderoni

Nicola parolini.

2 MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy

Marco Verani

Carlo piccardi.

3 Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milano, Italy

Conceived and designed the experiments: GB FC NP MV CP. Performed the experiments: GB FC NP MV CP. Analyzed the data: GB FC NP MV CP. Contributed reagents/materials/analysis tools: GB FC NP MV CP. Wrote the paper: GB FC NP MV CP.

Associated Data

All network data are available at Figshare ( https://dx.doi.org/10.6084/m9.figshare.3156067 ).

The problem of link prediction has recently received increasing attention from scholars in network science. In social network analysis, one of its aims is to recover missing links, namely connections among actors which are likely to exist but have not been reported because data are incomplete or subject to various types of uncertainty. In the field of criminal investigations, problems of incomplete information are encountered almost by definition, given the obvious anti-detection strategies set up by criminals and the limited investigative resources. In this paper, we work on a specific dataset obtained from a real investigation, and we propose a strategy to identify missing links in a criminal network on the basis of the topological analysis of the links classified as marginal, i.e. removed during the investigation procedure. The main assumption is that missing links should have opposite features with respect to marginal ones. Measures of node similarity turn out to provide the best characterization in this sense. The inspection of the judicial source documents confirms that the predicted links, in most instances, do relate actors with large likelihood of co-participation in illicit activities.

Introduction

Criminal intelligence analysis aims at supporting investigations, e.g. by producing link charts to identify and target key actors. Law enforcement agencies increasingly use Social Network Analysis (SNA) for criminal intelligence, analyzing the relations among individuals based on information on activities, events, and places derived from various investigative activities [ 1 – 3 ]. SNA provides added value compared to more traditional approaches like link analysis, by enabling in-depth assessment of the internal structure of criminal groups and by providing strategic and tactical advantages. For instance, SNA can inform law enforcement officers in the identification of aliases during large investigations and in the collection of evidence for prosecution [ 2 ]. Furthermore, the network analysis of criminal groups under investigation may help identify effective strategies to achieve network destabilization or disruption [ 3 , 4 ].

Given the sensitiveness and implications of criminal proceedings, criminal intelligence and investigations strive for achieving the most accurate representation of each case. Information gathering and selection are crucial steps, due to the implications of both type I (false positive) and type II (false negative) errors. A number of controls and procedural safeguards are in place to prevent false positives (i.e. wrong accusations). Investigators, prosecutors, and courts routinely deal with irrelevant information by discarding it throughout the proceedings and keeping only material useful to build a case [ 5 ]. Contrarily, the inherently covert nature of criminal activities makes investigations more vulnerable to false negatives (i.e. missing information), with very limited solutions available to the law enforcement agencies due to time and resource constraints.

Missing information is also the main challenge for SNA of criminal networks. Law enforcement data from wiretap or other investigative sources are inevitably incomplete. Criminals often use communication and protection methods to decrease the effectiveness of law enforcement action [ 6 ]. Investigators rely on data-gathering methods, e.g. observations, archives, informants, witnesses, that results in incomplete information and thus a partial vision of the network under investigation [ 5 , 7 – 9 ]. The lack of data generates problems of uncertain information, potentially jeopardizing the effectiveness of the investigations [ 3 ]. In the analysis of criminal networks, missing data can refer to missing nodes and/or missing links [ 7 ].

Missing nodes often depend on the scope and focus of the investigations. In turn, these may affect the specification of network boundaries, i.e. the definition of rules of inclusion of actors and their relations in the network [ 10 – 12 ]. Law enforcement agencies may overlook some important actors, especially if they take precautions against detection [ 5 ]. Research has shown that some skilled criminals assume a strategic position in criminal networks by balancing security and active involvement. Whereas intensive interaction with others normally increases the criminals’ performance, it also affects their visibility and consequently the vulnerability to law enforcement targeting. Some key players (e.g. the boss in a mafia) will avoid direct involvement in the illicit activities to reduce the risk of identification and arrest [ 13 – 15 ]. Nevertheless, the literature points out that even the most skilled criminals may hardly avoid detection in long lasting and intensive investigations, particularly if they have an important role in a criminal group [ 15 ].

Missing links instead refer to the lack of information on the relations between two known criminals. The police may miss meetings, conversations, and plans about criminal activities [ 5 , 16 ]. For instance, criminals may use different telephone lines, according to the nature of the conversation and the interlocutor, and investigators may be able to identify only some of them. The frequent change of mobile phones and SIM cards and the use of particular lines to communicate with high-ranking affiliates may also prevent law enforcement agencies from identifying all conversations among suspects [ 17 ]. This results in incomplete information which may hinder or mislead investigations. Scholars and practitioners in criminology and criminal justice have often acknowledged the problem of missing links [ 5 , 7 , 16 , 18 ]. Yet, studies on the their identification in criminal networks are still rare [ 19 – 21 ]. This is surprising, not only given the significant growth of works on missing links in other fields with the development of a number of different strategies [ 22 – 26 ], but also given that criminal investigations face the problem of missing links almost by definition, due to the scarcity of investigative resources and the anti-detection strategies by criminals [ 20 ].

This paper proposes an innovative strategy to identify possible missing links in a criminal network. It draws from the literature on link prediction and applies it on a unique dataset based on a real investigation. Differently from previous studies, the main assumption is that missing links may have characteristics contrary to those of marginal links discarded during the investigation. Indeed, while some links are ordinarily removed from a criminal network due to their marginality, other links with opposite characteristics may be missing due to lack of information. The analysis thus infers missing links a contrario from the characteristics of marginal links actually removed throughout the proceedings. The possible missing links so detected are highly probable social ties whose existence should be investigated by law enforcement agencies. Their identification during ongoing investigations may support law enforcement agencies in the allocation of scarce investigative resources, especially in the case of large criminal networks, and therefore improve the law enforcement action.

The Oversize dataset

The analysis relies on a unique dataset from operation Oversize, an Italian criminal case against a mafia group. The investigation lasted from 2000 to 2006, and targeted more than 50 suspects involved in international drug trafficking, homicides, and robberies. The trial started in 2007 and lasted until 2009, when the judgment was passed, and the main suspects were convicted with penalties from 5 to 22 years of imprisonment. Most suspects were affiliated to the ‘Ndrangheta, a mafia from Calabria (a southern Italian region) with ramifications in other regions and abroad [ 27 , 28 ].

Contrarily to most empirical studies on criminal networks, which rely on data derived from a single source of information, Oversize’s peculiarity lies in the availability of three networks from three judicial documents corresponding to three different stages of the criminal proceedings [ 16 ]: the wiretap records (WR), the arrest warrant (AW), and the judgment (JU). The wiretap records include all wiretap conversations transcribed by the police and considered relevant at first glance. The arrest warrant contains a selection of the transcripts and other relevant information from informants and other investigative activities (e.g. physical surveillance). The judgment summarizes the trial and includes information from several sources of evidence, including wiretapping and audio surveillance. It is worth mentioning that the documents related to the arrest warrant and judgment are public [ 29 , 30 ], whereas wiretap records are not publicly available because they report private conversations involving people other than suspects (access was obtained by the authors through a special permission). Nonetheless, the three networks, derived from a thorough, exhaustive analysis of the textual judicial documents [ 16 ], can be made public because no personal or sensitive information is reported (see Data Availability Statement).

Most studies on criminal networks focus on one or a small number of case studies, and rely on a single source of information [ 4 , 7 , 16 , 18 , 28 , 31 ], because access to data is difficult to obtain, particularly in the case of wiretap records. The main limitation of a case study approach concerns the external validity of the findings, i.e. the extent to which the results can be generalized beyond the case studies [ 32 ]. The analysis of the Oversize dataset focuses on a single criminal network thus sharing similar limitations on external validity with previous studies. The peculiarity of the dataset (i.e. the availability of three networks) prevents replication on other cases. Yet, it simultaneously constitutes the strength and innovation of the current study because it enables observation of the discarded marginal links and the prediction of possible missing links.

The individuals involved in illicit activities constitute the nodes of the networks, the links indicate a relation between any two actors. We restrict the analysis to the undirected case, i.e. we neglect the directionality of links. The three networks are formally defined by N i = ( V , E i ), i = WR , AW , JU , where V is the set of nodes (the same for all networks, with | V | = 182 nodes) and E i is the set of links of network i . We denote by ( x , y ), with x , y ∈ V , any pair of nodes of network, be they connected by a link, i.e. ( x , y ) ∈ E i , or not. The number c xy of telephone calls recorded between individuals (nodes) ( x , y ) is available for all ( x , y ) ∈ E i . Table 1 summarizes the main statistics of the three networks. We recall that the degree k x of a node x is the number of links incident to x , i.e. the number of neighbor nodes. A node is isolated if k x = 0. The density of the network is the ratio between the number of existing links | E i | and their maximum possible number | V |(| V | − 1)/2.

The networks are simultaneously displayed in Fig 1 . The Oversize networks show some features typical of illicit networks. Many criminal organizations analyzed in the literature exhibit the presence of a core of few highly-connected nodes and a large number of peripheral actors [ 4 , 7 , 28 , 33 – 35 ]. Fig 1 highlights (through node coloring) the result of the k -shell core-periphery analysis [ 36 ]: nodes are partitioned into “concentric” layers (or shells), starting from the periphery and arriving to the core of the network. Each node is assigned to a shell: the 1-shell contains the most peripheral nodes, the 2-shell those which are in the layer immediately more internal, and so on. More in detail, the algorithm for k -shell decomposition can be summarized as follows [ 36 ]: put in the 1-shell (and remove) all nodes with degree k x = 1, and then all nodes having k x ≤ 1 after removal of the former; put in the 2-shell (and remove) all nodes with k x = 2, and then all nodes having k x ≤ 2 after removal of the former; etc. The procedure stops when all nodes have been classified in a k -shell. In the N WR network, 4 shells are identified: they include, from the periphery to the core, 123, 33, 19, and 7 nodes, respectively, thus confirming the presence of a core of few actors and a large number of peripheral individuals.

The links removed in passing from N WR (Wiretap Records) to N AW (Arrest Warrant) ( above ), or from N WR to N JU (Judgement) ( below ), are highlighted in red. Nodes are colored according to their coreness, based on the k -shell analysis of the N WR network: 1 = white (most peripheral), 2 = yellow, 3 = orange, 4 = brown (most central).

Network reduction and marginal links

In passing from N WR to N AW , 58 of the 247 links of N WR are removed (thus E WR ⊃ E AW ) creating 36 isolated nodes. Similarly, in passing from N WR to N JU , 134 links are removed ( E WR ⊃ E JU ) creating 93 isolated nodes. However, the links of N JU are not a subset of those of N AW , i.e. the two reductions are not in cascade. This is normal, as subsequent phases of the criminal proceedings may generate new information, e.g. from witnesses or additional investigative activities.

Fig 1 highlights the links removed in the network reduction processes (i.e. from N WR to N AW , and from N WR to N JU ). The removed links are in most cases associated to a small number of telephone calls ( Fig 2 ). In the original network N WR , the number of calls c xy ranges from 1 to 52, with average value 〈 c xy 〉 = 3.95. On the other hand, the sets of removed links have 〈 c xy 〉 WR → AW = 1.59 (ranging from 1 to 6) and 〈 c xy 〉 WR → JU = 2.53 (from 1 to 20). None of the links with highest number of calls is removed. To substantiate this observation, we repeatedly select at random (for 10 5 repetitions) 58 or 134 links from N WR , namely the same number of links removed, respectively, from N WR to N AW and from N WR to N JU . It turns out (see the right panels in Fig 2 ) that the average number of calls of the links actually removed is extremely small, such that the probability of randomly selecting a smaller value is almost zero in both cases. It can safely be claimed that the link removal process tends to be biased by the intensity of the contacts between individuals, as the links with lower intensity are more likely to be removed.

Left panels : in green, the histogram of the number of calls of the links of N WR . In yellow, the number of calls of the links removed in passing from N WR to N AW ( above , 58 removals), and from N WR to N JU ( below , 134 removals). Right panels : the distribution of the average number of calls of a random sample of 58 links ( above ) or 134 links ( below ) of N WR , compared with the average number of calls (red vertical line) of the links actually removed from N WR to N AW ( above ) and from N WR to N JU ( below ).

The removed links often connect two individuals who had occasional contacts during the two-year investigation. In some cases, they concern pairs of actors who had telephone conversations in a few occasions and for very specific purposes (e.g. the purchase of small quantities of drugs). For instance, n63 (we refer to individuals by means of their anonymized label) was involved in a small number of telephone conversations with different retailers to arrange the purchase of small quantities of drugs in different occasions during the investigation. However, since he was not involved in the trafficking activities, nor in other serious crimes, the links between him and the other alleged criminals were discarded by the police when passing from N WR to N AW . In other occasions, the links removed from the network involved at least one individual who had not been identified by the police. Indeed, 11 out of the 58 links discarded from N WR to N AW involved individuals who participated in (minor) illicit activities and are reported in the judicial documents with the initials “V.M.” (male voice) of “V.F.” (female voice), or with the name or nickname mentioned in the telephone conversations. The same applies to 32 links out of the 134 removed when passing from N WR to N JU .

Other removed links with low intensity concern conversations about issues unrelated to the main illicit activities conducted by the members of the criminal group. Two examples are indicative of this type of links. In one occasion, n40 and n39 discuss about the debts that a third person has towards n39; in another occasion, n49 informs n26 of the arrest of another member of the group. In both cases, the links are formed as a consequence of an occasional communication between two individuals. Such communications may be useful to have a complete picture of the criminal network, but the links did not represent stable communication channels or relations among network members, nor they added any relevant information to the investigation process and they were discarded by the police.

Although it is certainly true that many removals involve peripheral nodes (especially in the N WR to N JU case), the visual inspection of Fig 1 reveals that many removals concern links which are instead connected, on one or both sides, to nodes with medium/large coreness. It cannot be claimed, therefore, that the network reduction is a process trivially involving the network periphery only. On the other end, we already pointed out that the intensity of the contacts (number of telephone calls) seems to be associated with the classification of marginal links by the police (see Fig 2 ). However, this quantity cannot be used for link prediction, since it cannot be associated in a straightforward way to a potential (non detected) link whose likelihood we want to quantify. As a matter of fact, there is no obvious way to associate a “predicted weight” to a predicted (thus non observed) link.

In the following, we will assess two topological indicators, namely link betweenness and node similarity, in their ability of characterizing the links which are marginal and thus, a contrario , in predicting the links which have not been detected but are likely to exist (missing links). These two quantities can indeed be used for this exercise, since their value can be naturally associated to a non existing (predicted) link, contrarily to the link weight (i.e. the number of calls). For this analysis, we will work on the unweighed (binary) network, i.e. we will neglect the information on the number of calls, both because we want to assess the predicting capabilities of the pure topological information (e.g. who is in contact with whom), and because the actual benefit of using weights in link prediction is known to be questionable [ 37 ].

Link betweenness

Our first hypothesis is that removed links are characterized by low betweenness. This means that they are redundant in the sense that they connect individuals who are already connected in some way in the network and do not significantly improve the flow of information. Networks are generally composed of subgroups (or communities) connected by one or a few links that bridge between them. “Structural holes”[ 38 ] are non-redundant contacts that lie in a brokerage position between otherwise disconnected components and thus facilitate the exchange of information and ideas. Links connecting different communities have high link betweenness (a generalization of Freeman’s node betweenness [ 39 , 40 ]), since they are crucial to connect different parts of a network. Conversely, within-community links are to some extent redundant and their removal is likely to have little impact on the network. Our first hypothesis is thus tested through the computation of the link betweenness for both removed and non-removed links. We recall that, given a link ( x , y ) ∈ E i connecting nodes x and y , the link betweenness b xy is the number of shortest paths passing through ( x , y ), among those connecting all node pairs ( s , t ) of the network. More precisely:

where B st is the number of (equivalently) shortest paths connecting ( s , t ), and B s t x y is the number of such paths passing through ( x , y ). Betweenness thus emphasizes those links that favor the exchange of information among network members. The first hypothesis thus assumes that marginal links may have low betweenness and this may explain why they were discarded throughout the proceedings.

Node similarity

Our second, alternative hypothesis is based on the literature on link prediction. Several studies have applied different link prediction methods to a number of networks. They show that nodes are more likely to be connected when they are similar and share a number of features [ 22 , 23 ]. According to the second hypothesis, thus, marginal links connect structurally dissimilar nodes, i.e. individuals who occasionally collaborate but are dissimilar in terms of interests, background, and involvement in criminal activities. Therefore, these connections are not crucial for the criminal conducts. The literature proposes several analytical strategies for link prediction, with new methods constantly added, mostly based on measures of node similarity [ 24 – 26 ]. Given the small size of the Oversize networks, such strategies are a viable option, since the exhaustive calculation of similarities for all node pairs is computationally feasible. The hypothesis is that marginal links have low similarity scores and this would explain their removal.

Node similarity approaches attribute a score s xy to all node pairs ( x , y ) and, consequently, induce a ranking of all node pairs. Notice that, if ( x , y ) ∈ E i (the set of links), s xy can be interpreted as a score attributed to the link. Thus, node similarity actually yields a ranking of all the links E i . Among the many possible similarity scores, the simplest one amounts at counting the number of Common Neighbors (CN) of nodes ( x , y ):

where Γ( z ) denotes the set of neighbors of node z . The rationale is that ( x , y ) must have common features, interests, etc., if they have many common acquaintances. Thus it is likely that they are directly connected, or that they will in the near future. Empirical evidences of this assumption have been found in many instances [ 41 , 42 ].

The CN similarity score can be refined in many ways, e.g. by weighting—not simply counting—the number of common neighbors. One of these ways leads to the definition of the Resource Allocation (RA) similarity score:

where k z = |Γ( z )| is the degree of node z . Here, the role of the common neighbor z in connecting ( x , y ) is diluted if z has many connections, since it will have less resources allocated to bridge ( x , y ).

CN and RA are widely used to quantify node similarity. Extensive tests on the capability of a broad set of indicators (including the two above) in solving the link prediction problem, found that CN obtains a very good performance despite its extreme simplicity, whereas RA ranks as one of the best indicators on a large set of benchmark tests [ 24 ].

Fig 3 shows the relationship between the number of calls c xy , the betweenness b xy , and the similarity score s xy , both for the whole network N WR and for the marginal links (here we only consider the reduction N WR to N AW for brevity). The figure reveals that all the removed links collocate among those with low similarity score, whereas we find removed links spread throughout the entire betweenness range. On the basis of this preliminary observation, we now consider the two hypotheses above discussed.

Each blue cross corresponds to a link ( x , y ) ∈ E WR . Red circles highlight the links removed in passing from N WR to N AW . The horizontal axis is truncated to improve readability: only 4 links over 247 have c xy > 20, none of which is removed.

To check the first hypothesis (i.e. the removed links have low betweenness), we compute the betweenness of all links of the network N WR and we compare their statistics to those of the links which are removed in passing to N AW or, respectively, N JU . The results are summarized in Fig 4 . The average betweenness of the links of N WR is 〈 b xy 〉 WR = 249.4, and those of the removed links are not largely dissimilar, namely 〈 b xy 〉 WR → AW = 300.7 and 〈 b xy 〉 WR → JU = 238.0, respectively. Incidentally, some of the removed links have betweenness value of the order of the highest values found in the network (left panels in Fig 4 ). Furthermore, if we repeatedly select at random (for 10 5 repetitions) 58 or, respectively, 134 links to remove (these are the number of links removed from N WR to N AW and, respectively, from N WR to N JU ), we discover that the average betweenness of the links actually removed is by no means anomalously small—in the N WR to N AW case it is even larger than average (right panels in Fig 4 ). This leads to the rejection of our first hypothesis.

Left panels : in green, the histogram of the betweenness of the links of N WR . In yellow, the betweenness of the links removed in passing from N WR to N AW ( above , 58 removals), and from N WR to N JU ( below , 134 removals). Right panels : the distribution of the average betweenness of a random sample of 58 links ( above ) or 134 links ( below ) of N WR , compared with the average betweenness (red vertical line) of the links actually removed from N WR to N AW ( above ) and from N WR to N JU ( below ).

We now move to our second hypothesis (i.e. the removed links connect structurally dissimilar nodes) and adopt a strategy common in the research on missing links, i.e. node similarity. We compute the similarity score s xy (i.e. the similarity of the node pair ( x , y )) of all the links of the network N WR , and we compare their statistics to those of the links which are removed in passing to N AW or, respectively, N JU . The results are summarized in Fig 5 for the CN similarity score ( Eq (2) ). The average score of the links of N WR is 〈 s xy 〉 WR = 0.789, whereas those of the removed links are much smaller, namely 〈 s xy 〉 WR → AW = 0.397 and 〈 s xy 〉 WR → JU = 0.455, respectively. None of the removed links has a score of the order of the highest values found in N WR (left panels in Fig 5 ).

Left panels : in green, the histogram of the score of the links of N WR (247 links). In yellow, the score of the links removed in passing from N WR to N AW ( above , 58 removals), and from N WR to N JU ( below , 134 removals). Right panels : the distribution of the average score of a random sample of 58 links ( above ) or 134 links ( below ) of N WR , compared with the average score (red vertical line) of the links actually removed from N WR to N AW ( above ) and from N WR to N JU ( below ).

To give statistical significance to the above observation, we repeatedly select at random (for 10 5 repetitions) the same number of links removed from N WR to N AW and, respectively, from N WR to N JU (58 or 134 links). The average score of the links actually removed is extremely small, such that the probability of randomly selecting a smaller average score is p < 0.01 in both cases (right panels in Fig 5 ). This means that the link removal process, if assessed in terms of similarity score s xy , appears to be strongly biased towards the links with least score. In this respect, the number of calls c xy and the score s xy associated to links seem to play a similar role in driving the removal process. However, as already pointed out, the former cannot be used for link prediction purposes.

The above results are confirmed if we instead adopt the RA similarity score ( Eq (3) ). Here the average score of the links of N WR is 〈 s xy 〉 WR = 0.124, whereas those of the removed links are 〈 s xy 〉 WR → AW = 0.046 and 〈 s xy 〉 WR → JU = 0.067. Again, the probability of randomly selecting a smaller average score is p < 0.01 in both cases. Therefore, the hypothesis that removed links connect individuals who are structurally dissimilar (i.e. individuals who occasionally collaborate but are different in terms of tasks and involvement in criminal activities) can be accepted. Node similarity scores can thus be adopted to identify missing links within the Oversize network.

Prediction of missing links

Our goal is now to identify the possible missing links in the Oversize network by inferring them a contrario , on the basis of the characteristics of the marginal links (i.e. links removed along the criminal proceedings) identified through the testing of the two hypotheses above. As a matter of fact, given that the link removal process proved to be strongly biased towards the smallest similarity scores, it is reasonable to presume that unobserved links (i.e. pairs of actors) with large similarity scores might be connected by missing links. In other words, if a small similarity between two actors—although connected—reveals the marginality of their link, a large similarity should be indicative of a connection, even when the link was not identified by law enforcement agencies. The procedure of attributing large likelihood of existence to links connecting highly similar nodes is at the basis of network reconstruction in all those fields where the knowledge of the complex set of interactions among agents is admittedly largely incomplete, such as for instance in social [ 12 ] or biological networks [ 43 ].

Let us first consider the CN score, defined by Eq (2) . If we compute the similarity s xy of the 247 links of the network N WR , we find that they range from 0 to 7, with average value 〈 s xy 〉 = 0.789. On the other hand, if we compute s xy for all ( x , y ) ∉ E WR , i.e. for all node pairs not directly connected, we find values ranging from 0 to 5, but a much smaller average 〈 s xy 〉 = 0.123. Indeed, if we exhaustively consider all the combinations of a pair ( x , y ) ∈ E WR with another ( x , y ) ∉ E WR , we find that the latter has a higher s xy than the former in 19.7% of the cases only.

Since s xy is significantly higher for pairs ( x , y ) directly connected, it is reasonable to presume that those pairs ( x , y ) ∉ E WR with extremely large s xy be actually connected by a missing link, i.e. a link existing but not experimentally observed. More precisely, if we set a threshold value S (typically large), we can compute the fraction α (typically small) of existing links ( x , y ) ∈ E WR with s xy ≥ S . If we now take a pair ( x ′, y ′) ∉ E WR such that s x ′ y ′ ≥ S , then the probability that s x ′ y ′ ≥ s xy is larger than 1 − α (i.e. typically large) for whatever ( x , y ) ∈ E WR , namely the predicted link ( x ′, y ′) collocates among the node pairs with higher similarity.

Fig 6 reports the relationship between the similarity threshold S , the number of predicted links N pred , and the link “reliability” 1 − α . In the following we focus our discussion on S = 3, a value which corresponds to 1 − α ≈ 0.90 and to a number of 17 predicted links (among the | V |(| V | − 1)/2 − | E WR | = 16224 pairs non directly connected). It is a reasonable trade off between a too tight ( S = 4, with N pred = 3) and a too loose threshold ( S = 2, with N pred = 100), as the number of predicted links is of the order of roughly one tenth of the existing links. The predicted links are highlighted in Fig 7 . Notice that they mostly connect nodes with large centrality (i.e. k -shell coreness), and thus they could represent important, yet overlooked, relationships among key individuals.

The plot visualizes the relationship between the number of predicted links N pred , the link reliability 1 − α , and the similarity threshold S . The inset replicates the part of the plot with the highest reliability values.

The Oversize network N WR of the Wiretap Records (nodes and links in grey), with the 17 predicted links with largest CN similarity score s xy (in blue). Nodes are colored according to their coreness based on the k -shell analysis (1 = white (most peripheral), 2 = yellow, 3 = orange, 4 = brown (most central)). The two parts of the network most relevant for link prediction are magnified in the bottom.

In the light of that, we carried out a new campaign of analysis of the judicial documents to discover clues of the possible connections among the relevant individuals: the results are discussed below and summarized in Table 2 . It should be emphasized that the absence of the predicted links from the original network N WR essentially means that those connections have not corresponded to a recorded telephone call in the period of investigation (see the Discussion section for an overview of possible motivations). This does not exclude, however, the existence of a social connection of whatever nature, which is crucial to be discovered in order to have the most possible complete picture of the criminal network.

For all predicted links, with the only exception of (n5, n39), the analysis of the judicial documents finds evidence of the likelihood of a social tie.

Node similarity predicts a link between n49 and n27, two of the main traffickers within the criminal network; n49 is the son of the boss and, with his father in jail, he was in charge of the trafficking activities, the management of the criminal group, and the investment of the proceeds of crime in both legal and illegal activities; n27 was heavily involved in the drug trafficking activities; in particular, he was charged with being responsible of the purchase and retail of large quantities of cocaine. Considering their role within the criminal group, it is highly probable that the two knew each other personally and had contacts. Similar considerations apply to the missing link identified between n49 and n48, who was in charge of the wholesale distribution of the drug in the province of Lecco, in the north of Italy. The judicial documents suggest that they collaborated with the mediation of other members of the criminal organization. However, both n49 and n48 lived in the same area and had key roles in the drug distribution chain, increasing the likelihood of a link between the two, as identified by the node similarity scores.

Node similarity also predicts a link between n50 and n160. The former is n49’s brother, also involved in drug trafficking activities. The latter is a fugitive who acted as a broker in the wholesale of drug. His being on the run was favored by n49, who provided constant support to n160. Considering the strong link between n49 and n160, and the close relationship between n49 and n50, it is likely that n50 and n160 also knew each other personally. Another predicted link is the one between n118, who is the wife of n45, and n36. Indeed, n118 is one of the few women suspected of being involved in the illicit activities of the criminal group. She was aware of her husband’s involvement in drug trafficking and her telephone calls discussing drug debts were intercepted by the police. The husband of n118 used to buy cocaine from n36 on behalf of other members of the criminal organization. The two men’s frequent contacts and n118’s involvement in illicit activities indicate that n118 and n36 may have known each other. The likelihood of a link between n13 and n43, also predicted by node similarity measures, is confirmed by a telephone call intercepted by Italian law enforcement agencies during the investigation. No conversations were recorded between the two alleged criminals; however, in June 2004 n13 informed another member of the organization of n43’s arrest, indicating that n13 and n43 knew each other.

Other links predicted by the CN similarity score include those forming a closed triad among n40, n53, and n147. The three suspects were involved in the drug retail in the province of Lecco and they used to buy the drug from the same wholesalers. As for n49 and n48, sharing drug distribution channels and operating in the same area justifies high node similarity scores. Nodes n40, n53, and n147 all share a missing link with n48’s boss n19, a drug trafficker involved in the wholesale of cocaine in the province of Lecco. A direct link between n19 and the three retailers was never confirmed by the police; however, the four suspects had trade relationships through n19’s subordinates, including n48, and they may have known each other personally. Two links were also predicted between n19’s assistant n24, and n48 and n147, respectively. The need to balance security and efficiency may have resulted in a division of labor between n19 and n24, with the former dealing cocaine with n48 and—indirectly—n147, and the latter having contacts with other wholesalers and retailers in the Lecco province. The strong relationship between n19 and n24, however, makes the predicted links very likely to have existed in the criminal organization. Another closed triad is formed by predicted links among n28, n26, and n140: as a matter of fact, n28 is n27’s younger brother; his activities included blending and hiding cocaine before its sale. The drug was then distributed by n27 with the help of n26, n140 and other wholesalers. Although no conversations or meetings were recorder among n28, n26, and n140, it is thus likely that they knew each other or had contacts in the past.

Overall, the thorough analysis of the judicial documents allowed us to validate, with a reasonable degree of reliability, 16 out of 17 of the links predicted by the CN similarity scores.

We now move to investigating the predicting capabilities of the RA similarity score, defined by Eq (3) . The relationship between the similarity threshold S , the number of predicted links N pred , and the link “reliability” 1 − α is not only qualitatively, but also quantitatively very similar to that displayed in Fig 6 for the CN score (we omit the figure for the sake of conciseness). In particular, to facilitate a direct comparison with the CN results, we select again a threshold value (in this case S = 0.45) such that 17 links are predicted with a reliability 1 − α ≈ 0.90. It turns out that the links predicted by RA have only a partial overlap with those predicted by CN, since only 5 links out of 17 are designated by both methods. The attempt of validating the 12 new links through the analysis of the judicial documents, however, was not conclusive: no strong evidences were found for them, contrarily to what above described for the CN score.

It seems therefore that the RA similarity score, in this specific case, has a weaker predicting capability than the CN score. With the aim of interpreting this fact, we focus on the 12 links predicted by RA but not by CN: notice that, having selected S = 3 for CN, they necessarily correspond to node pairs having exactly 1 or 2 common neighbors. Non connected pairs, i.e. ( x , y ) ∉ E WR , have a maximum RA score of about s xy = 0.625. In view of Eq (3) , to get a top-ranking RA score it is sufficient to have a common neighbor which is exclusive to the node pair (i.e. a degree 2 node) since this guarantees s xy ≥ 0.5 (only 12 node pairs out of 16224 meet this inequality). This represents a peculiar form of connection, especially if we compare it with the typical scenario of CN top-ranking pairs, which are instead connected by 4 or 5 common neighbors. Fig 8 displays two representative cases of predicted links which are in the top ranking positions for CN and RA, respectively, but are not predicted by the other method. The local network structure appears to be strongly different: in the CN case, the predicted link is immersed in a dense community, contrarily to the RA case. Indeed, if we compute the average clustering coefficient of the nodes connecting the predicted links which are not in common between the two methods, we find c avg = 0.431 for CN and c avg = 0.090 for RA, a clear indication of a different local topology. On the other hand, the local topology around the link predicted by RA suggests that n149 is likely to have the peculiar role of brokering two important subnetworks (notice the large number of neighbors of n9 and n43). If it is so, it is not suprising that no direct connection should exist, as the intermediation is exerted precisely by n149.

The left panel portrays the portion of the N WR network around the link (n19, n147), predicted by the CN score (incidentally, (n13, n43) is also a predicted link). The right panel portrays the portion of network around the link (n9, n43) predicted by the RA score.

To further explore which link prediction methods are appropriate in this specific case, we broaden the scope of the analysis by testing two additional methods, namely the Katz index similarity (e.g., [ 24 ]) and the Structural Perturbation Method (SPM) [ 25 ]. Both of them are global, i.e., the likelihood of a predicted link depends on the entire network. This is not the case for the CN and RA methods, which are based on a similarity score s xy whose value only depends on the local structure of the network around ( x , y ).

Given an undirected, unweighed network with adjacency matrix A , the Katz index defines the similarity of nodes ( x , y ) by

where 0 < β < 1/ λ max ( A ) to ensure convergence. By recalling that ( A k ) xy is the number of paths of length k connecting ( x , y ), and noting that A xy = 0 if the link ( x , y ) does not exist (which is the case when we quantify the likelihood of ( x , y ) for prediction), we interpret Eq (4) as a generalization of the CN score, since it considers the paths of all lengths connecting ( x , y ) instead of those of length 2 only, which are those passing through the common neighbors.

For the network N WR we have λ max ( A ) = 7.07 and thus 0 < β < 0.141. To facilitate the comparison with the results above discussed, we select again the top-17 predicted links according to index Eq (4) . It turns out that the 17 predicted links are the same as those of CN in the range 0 < β < 0.060, while for β = 0.100 the links predicted in common by Katz and CN reduce to 13 (but only 4 in common by Katz and RA). Interestingly, the 4 new links predicted by Katz (they are (n9, n39), (n13, n40), (n24, n40), (n43, n143)) are, in the CN ranking, in the set immediately below the top-17. Most notably, we were able to find in the judicial documents clear evidence of the likelihood of these social ties (we omit the details for brevity). Overall, we can safely claim that the results of the global link prediction method based on Katz similarity are consistent with those of the CN approach and, as such, they depart significantly from those obtained by the RA method.

The SPM considers the set of predicted links as a perturbation of the nominal network (coded by the adjacency matrix A ) which, however, preserves its structural features (see [ 25 ] for details). To quantify the sensitivity to perturbations, a small portion of links are randomly selected and removed, so that we can write A = A R + Δ A with the (symmetric) matrix Δ A containing the removed links. Then A R is decomposed according to its eigenbasis:

where | V | is the number of nodes and λ k and v k are the eigenvalue of A R and the corresponding orthogonal and normalized eigenvector, respectively. The perturbed matrix is obtained as

which can be interpreted as an approximation of A in a linear expansion based on A R . In practice, A ˜ will be obtained as the average of many instances of Eq (6) , each one computed for a different random removal Δ A . Finally, the predicted links ( x , y ) are those with largest A ˜ x y among the node pairs non connected in the original network, i.e., those with A xy = 0.

If we apply the SPM to the adjacency matrix A of the network N WR , we find a set of top-17 predicted links which overlaps with that of the CN method by 11 to 14 links, according to parametrization (number of random removals and fraction of removed links). The links in common with RA, instead, are never more than 4. In all instances, the new links predicted by SPM turn out to be, in the CN ranking, in the set immediately below the top-17. As for the Katz index described above, the results of the SPM prediction are largely consistent with those of the CN approach and, on the contrary, depart significantly from those obtained by the RA method.

To summarize the results of the link prediction analysis, we have found three different methods (one local, CN, and two global, Katz index and SPM) whose results are largely overlapping. Most notably, these results find significant validation in the judicial documentation, since they correspond to social ties not included in wiretap records but nonetheless very likely to exist. On the other hand, the fourth method, RA, does not seem an appropriate tool for link prediction in this specific case: its results are divergent with respect to the other methods and, moreover, its predicted links cannot be validated through the available documents. Of course, the most general question on which other methods, among the many available [ 22 – 26 , 44 ], are appropriate in this specific context remains open. However, our analysis indicates that a few methods able to provide reliable predictions do exist. Among them, CN should certainly be appreciated for its conceptual simplicity and easy computability.

The rejection of the first hypothesis, according to which marginal (i.e. discarded) links are those with low betweenness, has some interesting implications. From a network analysis standpoint, it is a fact that the criminal justice system discarded as marginal a number of links with high betweenness. This may appear surprising, as these links connected not only peripheral nodes but also nodes with medium-high coreness. Thus, they may appear to bridge the “structural holes” within the criminal group [ 38 ]. In fact, a careful analysis reveals that links with high betweenness include a few occasional contacts or communications unrelated to the illicit activities. Despite their apparent bridging function, from a criminal intelligence standpoint these links are marginal. Overall, we must conclude that link betweenness proved to be unable to discriminate between marginal and important links in the criminal network.

The second hypothesis, based on node similarity, performed definitely better in the identification of marginal links. The link removal process independently conducted by the criminal justice system focused on links with low similarity, whereas in all instances it considered as relevant those links with high similarity. This demonstrates that node similarity matters beyond the merely topological analysis, as we have evidence that it is also naturally embedded in the activities of the law enforcement agencies.

The specific nature of the criminal case and the design of the study prevent an exhaustive and conclusive verification of the predicted links. In this study, instead, it is possible to verify the prediction through independent analysis of the judicial sources. The information of the case shows that social ties corresponding to the predicted links are, in almost all instances, very likely to have existed in the criminal organization, although undetected by investigators and thus not annotated in the Oversize networks. Reasons for overlooking predicted links include suspects’ use of communication and protection methods, investigators’ limited time and resources, and reliance on imperfect data-gathering methods (e.g. covert observations, informants, witnesses)[ 5 , 7 – 9 ]. It is also worth noting that strong empirical evidence from wiretaps or other investigative sources must be available to include a link between any two suspects in the judicial documents. Investigators may have suspected some of the predicted links without being able to demonstrate their actual existence. At the same time, since criminals face a trade-off between efficiency and security, they may have deployed several security strategies against law enforcement surveillance, thus impeding the detection of their interactions [ 13 , 15 ].

Conclusions

Previous studies suggest that various fields of law enforcement may benefit from SNA: identification of suitable targets for network destabilization and prediction of the impact of their removal; detection of aliases through the analysis of actors with similar patterns of connections; and identification of potential defectors according to their position in the network [ 2 , 45 ]. In this paper, we show how SNA may support criminal intelligence analysis and ongoing investigations by identifying missing links among suspects.

This study demonstrated that node similarity, already applied in different fields for link prediction, can identify possible missing links also in criminal networks, when information is noisy or incomplete almost by definition. The criminal justice system deploys a number of guarantees against false positives such as incorrect accusations and interactions unrelated to criminal conducts. Conversely, effective strategies to prevent false negatives, such as missing information, are scarce. Due to constrained data collection resources, law enforcement agencies may indeed miss some actors and links, with negative consequences on intelligence and investigation activities. This applies to drug trafficking networks, such as the Oversize network, as well as to other types of covert networks including street gangs and terrorist groups. These criminal organizations can all be conceived as networks of relations among co-offenders based on kinship or criminal collaboration. Since the social network approach to crime focuses on the relationships among co-offenders rather than, e.g. their illicit activities [ 46 ], SNA can be used to analyze any type of criminal networks, from small and flexible groups of collaborating criminals to more structured organizations.

Node similarity measures helped identify the characteristics of the links independently removed throughout the criminal proceedings: the removal process was strongly biased towards the links with least node similarity score. This provided support to the hypothesis that links discarded by the investigators throughout the criminal proceedings connect individuals that are structurally dissimilar, i.e. they link individuals who occasionally collaborate but are dissimilar in terms of tasks and involvement in criminal activities. Therefore, the removed links are not crucial for the criminal conducts. Consequently, node similarity enabled prediction of links that are likely to exist, but that were undetected by the police. Missing links were inferred a contrario from the characteristics of removed links, on the assumption that pairs of unconnected actors with large node similarity scores were likely connected by missing links, but for several reasons went unnoticed by law enforcement agencies. Content analysis of the judicial sources independently corroborates the likelihood of predicted links. Moreover, the comparative analysis of different similarity scores reveals that not all of them have the same predictive capability: we argue that the reason lies in the different topological properties they highlight.

In conclusion, the results show that node similarity measures can inform ongoing criminal investigations. On one hand, the independent link reduction conducted by the law enforcement agencies confirms node similarity as an important property of relevant links. On the other hand, link prediction may point out where to direct the scarce investigative resources for more effective investigations or even uncover relevant patterns overlooked by law enforcement authorities, especially in the case of investigations targeting large networks or criminal organizations with sophisticated communication and protection methods. Besides their practical implications, the results extend the prediction of missing links to a field largely neglected so far.

Funding Statement

The Polisocial Award program is the only funding source and it supports the authors NP and MV. No other fund was available. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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Using Link Analysis To Define Data Relationships In Investigations

Clarifying The Who Behind The What And When

Today’s digital investigations are being powered by  link analysis . Link analysis is an analytical process whereby data points, often referred to as “nodes”, are used to identify relationships and connections between disparate data sources. The power behind link analysis and its rapid adoption in today’s era of big data is that it enables data visualization, data clustering, charting, timelining and more through data aggregation. When it comes to the copious amounts of data that can be acquired throughout the course of a legal investigation, the process is invaluable to identify patterns and context between a vast number of seemingly disconnected data sources.

Subruta Paul, in his 2013 article entitled, “ On Some Aspects of Link Analysis and Informal Network in Social Network Platform ” explains different linking types, which include explicit links and aggregate links. Explicit links are those that are created between nodes which correspond to a specific defined entity. One example, as provided by Paul, is a phone call. When a phone call is placed, there is a defined link between the originating phone number and the destination phone number. When all of these phone calls between two specific phone numbers are combined, it results in an aggregate link, representing all of the placed calls.

Leveraging explicit and aggregate link analysis is invaluable to digital investigators seeking to establish contextual relationships and behavior patterns.

Leveraging explicit and aggregate link analysis is invaluable to digital investigators seeking to establish contextual relationships and behavior patterns. Explicit linking, beyond that of just the phone numbers themselves, can be taken a step further helping to define the behavior of the individual being investigated, providing further context. Let’s explore this concept.

If we gathered data from someone’s smartphone in the course of an investigation, we can examine the call log and extrapolate all calls placed and received by that specific device. The phone number of the device can then be explicitly linked to an individual via the  IMSI  (International Mobile Subscriber Identity), defining the relationship between the user and the phone. We can then aggregate the data as well as the underlying metadata, including things like call duration and the date of each of the calls. Given this additional explicit link, we can now identify the phone numbers that this individual contacted the most or engaged with for the longest period of time.

This example extends itself to a plethora of other potential explicit links. The individual’s phone may have geolocation artifacts, text messages, app data, transactions and even connected device data (often referred to as the Internet of Things or “IoT”) recorded in its device history. Performing link analysis on these additional nodes by linking the phone number, the device’s  IMEI  (International Mobile Equipment Identity), or the user’s IMSI can result in a cornucopia of links to examine.

Our example barely scratches the surface of how using link analysis to identify explicit links and aggregation of data for analysis can aid an investigation. This type of analysis can establish context, and even possibly intent. This is where the power of tools like  ESI Analyst  can help refine an investigation by demonstrating a series of events in a timeline, showing their relationships to a given individual or set of actors. The power of link analysis is a proven and effective tool that enables robust data visualization and, most importantly, a clear and comprehensive understanding of the data being analyzed. If you would like to learn more, please reach out and  arrange a demonstration  today.  

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Data visualization for fraud detection tools

The fraud detection visualization challenge.

Fraud management has changed massively in recent years, with the advance of digital technologies and AI creating new opportunities and techniques for fraudsters to commit crime faster, and with more agility.

To detect and investigate it effectively, you need to see connections – between people, accounts, transactions, and dates – and understand complex sequences of events.

That means analyzing a lot of data.

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The visualization-AI intelligence cycle

A successful fraud investigation follows the visualization-AI intelligence cycle, combining the different strengths of visual analytics, AI and human reasoning.

Detection: AI software uses machine learning and pattern recognition to make recommendations and raise alerts.

Investigation: Interactive graph visualization presents insights in a way that’s easy for human investigators to navigate, analyze, and gain actionable intelligence.

Prevention: Investigators use what they’ve learned to inform the next set of queries and rules they feed into the system.

As patterns of fraud are detected, analysts can use the new insight to update and improve their automated systems.

Detecting fraud

Fraud detection is an increasingly automated process, as analysts are often looking for familiar patterns of activity. They automatically score each case or transaction, and assign it to a category – often using machine learning to process events.

The increase in scams means a higher volume of alerts fall into the ‘unsure’ category. No matter how advanced automated fraud detection is today, a flagged transaction needs fast analytical expertise from a human investigator. Visual graph and timeline analysis makes that possible.

Here’s a visual graph analysis chart showing a vehicle insurance claim that’s been flagged for review. Nodes represent claims, vehicles, people, and addresses. An automatic hierarchy layout makes it easy to spot dependencies.

An unusual connection stands out right away: the witness, Everett Page, shares an address with Walter Stewart, who has a previous claim relating to the same vehicle involved in this incident.

This is enough for the analyst to flag this claim for deeper investigation.

Timeline visualization adds a time dimension, making it easy to understand the sequence in which events unfolded.

This dataset contains a record of credit card transactions. We can easily pick out those which are disputed (in red) and identify the patterns around them.

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Investigating fraud

More complex cases, for example those that might involve coordinated fraud rings and organized crime, require more complex human involvement. Here, link analysis and timeline visualizations are investigation tools. They present larger volumes of data for investigators to navigate and turn into actionable intelligence.

Understanding patterns of fraud relies on the analyst’s domain knowledge and investigative skills, which are both enhanced with visual analysis.

This fictional but typical dataset includes links between nodes representing policies, policyholder details, insurance claims, vehicle damage, doctors, witnesses, and mechanics. When you visualize a lot of cases at once, it’s easy to pick out ordinary claims – they’re the Y-shaped structures dotted around the chart – from the more complex, potentially fraudulent claims.

Timeline visualization makes it easy to see how the relationships between traders developed through time.

In this insider trading example, we see Shany Keebler buying shares just before a big profit announcement. Combine that with communications data and unusual patterns start to emerge.

Timeline analysis for insider trading investigation

Preventing fraud

The third stage of the visualization-AI intelligence cycle is prevention – where data science teams use new information to train their models. It’s also an opportunity to close loopholes or vulnerabilities in the system.

Here, link analysis provides an overview of investigation outputs and operational data from multiple silos.

Armed with a single intuitive view, data scientists can uncover patterns and trends, and recommend model and process changes to prevent future scams.

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What Is a Case Study? How to Write, Examples, and Template

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How to write a case study

Case study template, case study examples, types of case studies, what are the benefits of case studies , what are the limitations of case studies , case study vs. testimonial.

In today's marketplace, conveying your product's value through a compelling narrative is crucial to genuinely connecting with your customers.

Your business can use marketing analytics tools to understand what customers want to know about your product. Once you have this information, the next step is to showcase your product and its benefits to your target audience. This strategy involves a mix of data, analysis, and storytelling. Combining these elements allows you to create a narrative that engages your audience. So, how can you do this effectively?

What is a case study? 

A case study is a powerful tool for showcasing a business's success in helping clients achieve their goals. It's a form of storytelling that details real-world scenarios where a business implemented its solutions to deliver positive results for a client.

In this article, we explore the concept of a case study , including its writing process, benefits, various types, challenges, and more.

Understanding how to write a case study is an invaluable skill. You'll need to embrace decision-making – from deciding which customers to feature to designing the best format to make them as engaging as possible.  This can feel overwhelming in a hurry, so let's break it down.

Step 1: Reach out to the target persona

If you've been in business for a while, you have no shortage of happy customers. But w ith limited time and resources, you can't choose everyone.  So, take some time beforehand to flesh out your target buyer personas. 

Once you know precisely who you're targeting, go through your stable of happy customers to find a buyer representative of the audience you're trying to reach. The closer their problems, goals, and industries align, the more your case study will resonate.

What if you have more than one buyer persona? No problem. This is a common situation for companies because buyers comprise an entire committee. You might be marketing to procurement experts, executives, engineers, etc. Try to develop a case study tailored to each key persona. This might be a long-term goal, and that's fine. The better you can personalize the experience for each stakeholder, the easier it is to keep their attention.  

Here are a few considerations to think about before research:

• Products/services of yours the customer uses (and how familiar they are with them)
• The customer's brand recognition in the industry
• Whether the results they've achieved are specific and remarkable
• Whether they've switched from a competitor's product/service
• How closely aligned they are with your target audience

These items are just a jumping-off point as you develop your criteria.  Once you have a list, run each customer through it to determine your top targets. Approach the ones on the top (your "dream" case study subjects) and work your way down as needed.

Who to interview

You should consider interviewing top-level managers or executives because those are high-profile positions. But consider how close they are to your product and its results.

Focusing on an office manager or engineer who uses your product daily would be better. Look for someone with a courtside view of the effects.

The ways to request customer participation in case studies can vary, but certain principles can improve your chances:

• Make it easy for customers to work with you, respecting their valuable time. Be well-prepared and minimize their involvement.
• Emphasize how customers will benefit through increased publicity, revenue opportunities, or recognition for their success. 
• Acknowledge their contributions and showcase their achievements.
• Standardizing the request process with a script incorporating these principles can help your team consistently secure case study approvals and track performance.

Step 2: Prepare for the interview

Case study interviews are like school exams. The more prepared you are for them, the better they turn out. Preparing thoroughly also shows participants that you value their time. You don't waste precious minutes rehashing things you should have already known. You focus on getting the information you need as efficiently as possible.

You can conduct your case study interview in multiple formats, from exchanging emails to in-person interviews. This isn't a trivial decision.  As you'll see in the chart below, each format has its unique advantages and disadvantages. 

You'll also have to consider who will ask and answer the questions during your case study interview. It's wise to consider this while considering the case study format.  The number of participants factors into which format will work best. Pulling off an in-person interview becomes much harder if you're trying to juggle four or five people's busy schedules. Try a video conference instead.

Before interviewing your case study participant, it is crucial to identify the specific questions that need to be asked.  It's essential to thoroughly evaluate your collaboration with the client and understand how your product's contributions impact the company. 

Remember that structuring your case study is akin to crafting a compelling narrative. To achieve this, follow a structured approach:

• Beginning of your story. Delve into the customer's challenge that ultimately led them to do business with you. What were their problems like? What drove them to make a decision finally? Why did they choose you?
• The middle of the case study.  Your audience also wants to know about the experience of working with you. Your customer has taken action to address their problems. What happened once you got on board?
• An ending that makes you the hero.  Describe the specific results your company produced for the customer. How has the customer's business (and life) changed once they implemented your solution?

Sample questions for the case study interview

If you're preparing for a case study interview, here are some sample case study research questions to help you get started:

• What challenges led you to seek a solution?
• When did you realize the need for immediate action? Was there a tipping point?
• How did you decide on the criteria for choosing a B2B solution, and who was involved?
• What set our product or service apart from others you considered?
• How was your experience working with us post-purchase?
• Were there any pleasant surprises or exceeded expectations during our collaboration?
• How smoothly did your team integrate our solution into their workflows?
• How long before you started seeing positive results?
• How have you benefited from our products or services?
• How do you measure the value our product or service provides?

Step 3: Conduct the interview

Preparing for case study interviews can be different from everyday conversations. Here are some tips to keep in mind:

• Create a comfortable atmosphere.  Before diving into the discussion, talk about their business and personal interests. Ensure everyone is at ease, and address any questions or concerns.
• Prioritize key questions.  Lead with your most crucial questions to respect your customer's time. Interview lengths can vary, so starting with the essentials ensures you get the vital information.
• Be flexible.  Case study interviews don't have to be rigid. If your interviewee goes "off script," embrace it. Their spontaneous responses often provide valuable insights.
• Record the interview.  If not conducted via email, ask for permission to record the interview. This lets you focus on the conversation and capture valuable quotes without distractions.

Step 4: Figure out who will create the case study

When creating written case studies for your business, deciding who should handle the writing depends on cost, perspective, and revisions.

Outsourcing might be pricier, but it ensures a professionally crafted outcome. On the other hand, in-house writing has its considerations, including understanding your customers and products. 

Technical expertise and equipment are needed for video case studies, which often leads companies to consider outsourcing due to production and editing costs. 

Tip: When outsourcing work, it's essential to clearly understand pricing details to avoid surprises and unexpected charges during payment.

Step 5: Utilize storytelling

Understanding and applying storytelling elements can make your case studies unforgettable, offering a competitive edge. 

Source: The Framework Bank

Every great study follows a narrative arc (also called a "story arc"). This arc represents how a character faces challenges, struggles against raising stakes, and encounters a formidable obstacle before the tension resolves.

In a case study narrative, consider:

• Exposition. Provide background information about the company, revealing their "old life" before becoming your customer.
• Inciting incident. Highlight the problem that drove the customer to seek a solution, creating a sense of urgency.
• Obstacles (rising action). Describe the customer's journey in researching and evaluating solutions, building tension as they explore options.
• Midpoint. Explain what made the business choose your product or service and what set you apart.
• Climax. Showcase the success achieved with your product.
• Denouement. Describe the customer's transformed business and end with a call-to-action for the reader to take the next step.

Step 6: Design the case study

The adage "Don't judge a book by its cover" is familiar, but people tend to do just that quite often!

A poor layout can deter readers even if you have an outstanding case study. To create an engaging case study, follow these steps:

• Craft a compelling title. Just like you wouldn't read a newspaper article without an eye-catching headline, the same goes for case studies. Start with a title that grabs attention.
• Organize your content. Break down your content into different sections, such as challenges, results, etc. Each section can also include subsections. This case study approach divides the content into manageable portions, preventing readers from feeling overwhelmed by lengthy blocks of text.
• Conciseness is key. Keep your case study as concise as possible. The most compelling case studies are precisely long enough to introduce the customer's challenge, experience with your solution, and outstanding results. Prioritize clarity and omit any sections that may detract from the main storyline.
• Utilize visual elements. To break up text and maintain reader interest, incorporate visual elements like callout boxes, bulleted lists, and sidebars.
• Include charts and images. Summarize results and simplify complex topics by including pictures and charts. Visual aids enhance the overall appeal of your case study.
• Embrace white space. Avoid overwhelming walls of text to prevent reader fatigue. Opt for plenty of white space, use shorter paragraphs, and employ subsections to ensure easy readability and navigation.
• Enhance video case studies. In video case studies, elements like music, fonts, and color grading are pivotal in setting the right tone. Choose music that complements your message and use it strategically throughout your story. Carefully select fonts to convey the desired style, and consider how lighting and color grading can influence the mood. These elements collectively help create the desired tone for your video case study.

Step 7: Edits and revisions

Once you've finished the interview and created your case study, the hardest part is over. Now's the time for editing and revision. This might feel frustrating for impatient B2B marketers, but it can turn good stories into great ones.

Ideally, you'll want to submit your case study through two different rounds of editing and revisions:

• Internal review. Seek feedback from various team members to ensure your case study is captivating and error-free. Gather perspectives from marketing, sales, and those in close contact with customers for well-rounded insights. Use patterns from this feedback to guide revisions and apply lessons to future case studies.
• Customer feedback. Share the case study with customers to make them feel valued and ensure accuracy. Let them review quotes and data points, as they are the "heroes" of the story, and their logos will be prominently featured. This step maintains positive customer relationships.

Case study mistakes to avoid

• Ensure easy access to case studies on your website.
• Spotlight the customer, not just your business.
• Tailor each case study to a specific audience.
• Avoid excessive industry jargon in your content.

Step 8: Publishing

Take a moment to proofread your case study one more time carefully. Even if you're reasonably confident you've caught all the errors, it's always a good idea to check. Your case study will be a valuable marketing tool for years, so it's worth the investment to ensure it's flawless. Once done, your case study is all set to go!

Consider sharing a copy of the completed case study with your customer as a thoughtful gesture. They'll likely appreciate it; some may want to keep it for their records. After all, your case study wouldn't have been possible without their help, and they deserve to see the final product.

Where you publish your case study depends on its role in your overall marketing strategy. If you want to reach as many people as possible with your case study, consider publishing it on your website and social media platforms. 

Tip: Some companies prefer to keep their case studies exclusive, making them available only to those who request them. This approach is often taken to control access to valuable information and to engage more deeply with potential customers who express specific interests. It can create a sense of exclusivity and encourage interested parties to engage directly with the company.

Step 9: Case study distribution

When sharing individual case studies, concentrate on reaching the audience with the most influence on purchasing decisions

Here are some common distribution channels to consider:

• Sales teams. Share case studies to enhance customer interactions, retention , and upselling among your sales and customer success teams. Keep them updated on new studies and offer easily accessible formats like PDFs or landing page links.
• Company website. Feature case studies on your website to establish authority and provide valuable information to potential buyers. Organize them by categories such as location, size, industry, challenges, and products or services used for effective presentation.
• Events. Use live events like conferences and webinars to distribute printed case study copies, showcase video case studies at trade show booths, and conclude webinars with links to your case study library. This creative approach blends personal interactions with compelling content.
• Industry journalists. Engage relevant industry journalists to gain media coverage by identifying suitable publications and journalists covering related topics. Building relationships is vital, and platforms like HARO (Help A Reporter Out) can facilitate connections, especially if your competitors have received coverage before.

Want to learn more about Marketing Analytics Software? Explore Marketing Analytics products.

It can seem daunting to transform the information you've gathered into a cohesive narrative.  We’ve created a versatile case study template that can serve as a solid starting point for your case study.

With this template, your business can explore any solutions offered to satisfied customers, covering their background, the factors that led them to choose your services, and their outcomes.

The template boasts a straightforward design, featuring distinct sections that guide you in effectively narrating your and your customer's story. However, remember that limitless ways to showcase your business's accomplishments exist.

To assist you in this process, here's a breakdown of the recommended sections to include in a case study:

• Title.  Keep it concise. Create a brief yet engaging project title summarizing your work with your subject. Consider your title like a newspaper headline; do it well, and readers will want to learn more. 
• Subtitle . Use this section to elaborate on the achievement briefly. Make it creative and catchy to engage your audience.
• Executive summary.  Use this as an overview of the story, followed by 2-3 bullet points highlighting key success metrics.
• Challenges and objectives. This section describes the customer's challenges before adopting your product or service, along with the goals or objectives they sought to achieve.
• How product/service helped.  A paragraph explaining how your product or service addressed their problem.
• Testimonials.  Incorporate short quotes or statements from the individuals involved in the case study, sharing their perspectives and experiences.
• Supporting visuals.  Include one or two impactful visuals, such as graphs, infographics, or highlighted metrics, that reinforce the narrative.
• Call to action (CTA).  If you do your job well, your audience will read (or watch) your case studies from beginning to end. They are interested in everything you've said. Now, what's the next step they should take to continue their relationship with you? Give people a simple action they can complete. 

Case studies are proven marketing strategies in a wide variety of B2B industries. Here are just a few examples of a case study:

• Amazon Web Services, Inc.  provides companies with cloud computing platforms and APIs on a metered, pay-as-you-go basis. This case study example illustrates the benefits Thomson Reuters experienced using AWS.
• LinkedIn Marketing Solutions combines captivating visuals with measurable results in the case study created for BlackRock. This case study illustrates how LinkedIn has contributed to the growth of BlackRock's brand awareness over the years. 
• Salesforce , a sales and marketing automation SaaS solutions provider, seamlessly integrates written and visual elements to convey its success stories with Pepe Jeans. This case study effectively demonstrates how Pepe Jeans is captivating online shoppers with immersive and context-driven e-commerce experiences through Salesforce.
• HubSpot offers a combination of sales and marketing tools. Their case study demonstrates the effectiveness of its all-in-one solutions. These typically focus on a particular client's journey and how HubSpot helped them achieve significant results.

There are two different types of case studies that businesses might utilize:

Written case studies 

Written case studies offer readers a clear visual representation of data, which helps them quickly identify and focus on the information that matters most. 

Printed versions of case studies find their place at events like trade shows, where they serve as valuable sales collateral to engage prospective clients.  Even in the digital age, many businesses provide case studies in PDF format or as web-based landing pages, improving accessibility for their audience. 

Note: Landing pages , in particular, offer the flexibility to incorporate rich multimedia content, including images, charts, and videos. This flexibility in design makes landing pages an attractive choice for presenting detailed content to the audience.

Written case study advantages

Here are several significant advantages to leveraging case studies for your company:

• Hyperlink accessibility.  Whether in PDF or landing page format, written case studies allow for embedded hyperlinks, offering prospects easy access to additional information and contact forms.
• Flexible engagement.  Unlike video case studies, which may demand in-person arrangements, written case studies can be conducted via phone or video streaming, reducing customer commitment and simplifying scheduling.
• Efficient scanning . Well-structured written case studies with a scannable format cater to time-strapped professionals. Charts and callout boxes with key statistics enhance the ease of information retrieval.
• Printable for offline use.  Written case studies can be effortlessly printed and distributed at trade shows, sales meetings, and live events. This tangible format accommodates those who prefer physical materials and provides versatility in outreach, unlike video content, which is less portable.

Written case study disadvantages

Here are some drawbacks associated with the use of case studies:

• Reduced emotional impact.  Written content lacks the emotional punch of live video testimonials, which engage more senses and emotions, making a stronger connection.
• Consider time investment.  Creating a compelling case study involves editing, proofreading, and design collaboration, with multiple revisions commonly required before publication.
• Challenges in maintaining attention.  Attention spans are short in today's ad-saturated world. Using graphics, infographics, and videos more often is more powerful to incite the right emotions in customers.

Video case studies

Video case studies are the latest marketing trend. Unlike in the past, when video production was costly, today's tools make it more accessible for users to create and edit their videos. However, specific technical requirements still apply.

Like written case studies, video case studies delve into a specific customer's challenges and how your business provides solutions. Yet, the video offers a more profound connection by showcasing the person who faced and conquered the problem.

Video case studies can boost brand exposure when shared on platforms like YouTube. For example, Slack's engaging case study video with Sandwich Video illustrates how Slack transformed its workflow and adds humor, which can be challenging in written case studies focused on factual evidence.

Source : YouTube

This video case study has garnered nearly a million views on YouTube.

Video case study advantages

Here are some of the top advantages of video case studies. While video testimonials take more time, the payoff can be worth it. 

• Humanization and authenticity.  Video case studies connect viewers with real people, adding authenticity and fostering a stronger emotional connection.
• Engaging multiple senses.  They engage both auditory and visual senses, enhancing credibility and emotional impact. Charts, statistics, and images can also be incorporated.
• Broad distribution.  Videos can be shared on websites, YouTube, social media, and more, reaching diverse audiences and boosting engagement, especially on social platforms.

Video case study disadvantages

Before fully committing to video testimonials, consider the following:

• Technical expertise and equipment.  Video production requires technical know-how and equipment, which can be costly. Skilled video editing is essential to maintain a professional image. While technology advances, producing amateurish videos may harm your brand's perception.
• Viewer convenience.  Some prospects prefer written formats due to faster reading and ease of navigation. Video typically requires sound, which can be inconvenient for viewers in specific settings. Many people may not have headphones readily available to watch your content.
• Demand on case study participants.  On-camera interviews can be time-consuming and location-dependent, making scheduling challenging for case study participants. Additionally, being on screen for a global audience may create insecurities and performance pressure.
• Comfort on camera.  Not everyone feels at ease on camera. Nervousness or a different on-screen persona can impact the effectiveness of the testimonial, and discovering this late in the process can be problematic.

Written or video case studies: Which is right for you?

Now that you know the pros and cons of each, how do you choose which is right for you?

One of the most significant factors in doing video case studies can be the technical expertise and equipment required for a high level of production quality. Whether you have the budget to do this in-house or hire a production company can be one of the major deciding factors.

Still, written or video doesn't have to be an either-or decision. Some B2B companies are using both formats. They can complement each other nicely, minimizing the downsides mentioned above and reaching your potential customers where they prefer.

Let's say you're selling IT network security. What you offer is invaluable but complicated. You could create a short (three- or four-minute) video case study to get attention and touch on the significant benefits of your services. This whets the viewer's appetite for more information, which they could find in a written case study that supplements the video.

Should you decide to test the water in video case studies, test their effectiveness among your target audience. See how well they work for your company and sales team. And, just like a written case study, you can always find ways to improve your process as you continue exploring video case studies.

Case studies offer several distinctive advantages, making them an ideal tool for businesses to market their products to customers. However, their benefits extend beyond these qualities. 

Here's an overview of all the advantages of case studies:

Valuable sales support

Case studies serve as a valuable resource for your sales endeavors. Buyers frequently require additional information before finalizing a purchase decision. These studies provide concrete evidence of your product or service's effectiveness, assisting your sales representatives in closing deals more efficiently, especially with customers with lingering uncertainties.

Validating your value

Case studies serve as evidence of your product or service's worth or value proposition , playing a role in building trust with potential customers. By showcasing successful partnerships, you make it easier for prospects to place trust in your offerings. This effect is particularly notable when the featured customer holds a reputable status.

Unique and engaging content

By working closely with your customer success teams, you can uncover various customer stories that resonate with different prospects. Case studies allow marketers to shape product features and benefits into compelling narratives. 

Each case study's distinctiveness, mirroring the uniqueness of every customer's journey, makes them a valuable source of relatable and engaging content. Storytelling possesses the unique ability to connect with audiences on an emotional level, a dimension that statistics alone often cannot achieve. 

Spotlighting valuable customers

Case studies provide a valuable platform for showcasing your esteemed customers. Featuring them in these studies offers a chance to give them visibility and express your gratitude for the partnership, which can enhance customer loyalty . Depending on the company you are writing about, it can also demonstrate the caliber of your business.

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It's important to consider limitations when designing and interpreting the results of case studies. Here's an overview of the limitations of case studies:

Challenges in replication

Case studies often focus on specific individuals, organizations, or situations, making generalizing their findings to broader populations or contexts challenging. 

Time-intensive process

Case studies require a significant time investment. The extensive data collection process and the need for comprehensive analysis can be demanding, especially for researchers who are new to this method.

Potential for errors

Case studies can be influenced by memory and judgment, potentially leading to inaccuracies. Depending on human memory to reconstruct a case's history may result in variations and potential inconsistencies in how individuals recall past events. Additionally, bias may emerge, as individuals tend to prioritize what they consider most significant, which could limit their consideration of alternative perspectives.

Challenges in verification

Confirming results through additional research can present difficulties. This complexity arises from the need for detailed and extensive data in the initial creation of a case study. Consequently, this process requires significant effort and a substantial amount of time.

While looking at case studies, you may have noticed a quote. This type of quote is considered a testimonial, a key element of case studies.

If a customer's quote proves that your brand does what it says it will or performs as expected, you may wonder: 'Aren't customer testimonials and case studies the same thing?' Not exactly.

Testimonials are brief endorsements designed to establish trust on a broad scale. In contrast, case studies are detailed narratives that offer a comprehensive understanding of how a product or service addresses a specific problem, targeting a more focused audience. 

Crafting case studies requires more resources and a structured approach than testimonials. Your selection between the two depends on your marketing objectives and the complexity of your product or service.

Case in point!

Case studies are among a company's most effective tools. You're  well on your way to mastering them.

Today's buyers are tackling much of the case study research methodology independently. Many are understandably skeptical before making a buying decision. By connecting them with multiple case studies, you can prove you've gotten the results you say you can. There's hardly a better way to boost your credibility and persuade them to consider your solution.

Case study formats and distribution methods might change as technology evolves. However, the fundamentals that make them effective—knowing how to choose subjects, conduct interviews, and structure everything to get attention—will serve you for as long as you're in business. 

We covered a ton of concepts and resources, so go ahead and bookmark this page. You can refer to it whenever you have questions or need a refresher.

Dive into market research to uncover customer preferences and spending habits.

Kristen McCabe

Kristen’s is a former senior content marketing specialist at G2. Her global marketing experience extends from Australia to Chicago, with expertise in B2B and B2C industries. Specializing in content, conversions, and events, Kristen spends her time outside of work time acting, learning nature photography, and joining in the #instadog fun with her Pug/Jack Russell, Bella. (she/her/hers)

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Research Writing and Analysis

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Writing a Case Study

What is a case study?

A Case study is: 

• An in-depth research design that primarily uses a qualitative methodology but sometimes​​ includes quantitative methodology.
• Used to examine an identifiable problem confirmed through research.
• Used to investigate an individual, group of people, organization, or event.
• Used to mostly answer "how" and "why" questions.

What are the different types of case studies?

Note: These are the primary case studies. As you continue to research and learn

about case studies you will begin to find a robust list of different types. 

Who are your case study participants?

What is triangulation ? 

Validity and credibility are an essential part of the case study. Therefore, the researcher should include triangulation to ensure trustworthiness while accurately reflecting what the researcher seeks to investigate.

How to write a Case Study?

When developing a case study, there are different ways you could present the information, but remember to include the five parts for your case study.

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• Library Catalogue

Finding case studies

On this page, introduction, finding cases, sample cases, developing and analysing cases.

"Case studies" can mean examples from organizations provided simply to illustrate a point or descriptions of organizational situations designed to be interpreted and analyzed by a learner. The resources below provide a mix of all types of case studies.

This guide also includes some resources that will be of more use to students (e.g., the tips on finding case studies in databases) and other resources that instructors will find useful (e.g., the links to case clearinghouses).

If you don't find what you need here, don't hesitate to ask for help .

  New!  We've recently added another 600+ new cases to our Sage Business Cases resource! 

Try searching the SFU Library catalogue  and include ( case study OR case studies OR cases ) as part of your search. Check out these sample searches:

("case study" OR "case studies" OR cases) AND "organizational behavior"

("case study" OR "case studies" OR cases) AND "strategic management"

("case study" OR "case studies" OR cases) AND "project management"

Also try an Advanced Search  in which you look for case studies in the Subject field, combined with your specific need (entrepreneurship? strategy?) as a Keyword. Add case* in the Title field as well to increase your chance of getting books that contain large numbers of cases. You can also start by  searching for books that have cases in the title AND " case studies" in the subject .

In the SFU Library catalogue, try searching for theses & graduating projects by SFU Business students. Such publications often involve specific case studies. Try searching the catalogue  again, but this time combine the word theses (plural) with your topic. See these sample searches for example theses AND "electronic commerce"  // theses AND "electronic arts" .  Also, try Dissertations and Theses Abstracts and Index  for theses completed elsewhere. See our guide to Finding University Theses and Projects from Simon Fraser and Other Universities for more suggestions.

• In Business Source Complete enter your search terms, then either check off the Document Type Case study or include the Subject Case studies as part of your search.
• CBCA Fulltext Business offers similar ways of finding case studies: either choose the Document Type (click on More Search Options) Case study or include the Subject Case studies as part of your search.
• See the Sample cases area below for some specific journals focusing on business cases.

Websites & databases

Most cases sold by places such as Harvard or the Richard Ivey School of Business are not available via the library. You usually need to pay directly for such cases unless you are an instructor seeking cases to consider for use in a class. If you are a student and a case has been assigned as a reading in your class, check with your instructor to see if the case might have been pre-purchased for all members of your class.

Sage Business Cases A global and diverse collection of case studies designed to help students see theoretical business concepts put into practice. This collection is available to all SFU students, instructors, and alumni. See this blog post for further details.

Harvard Business School Cases Harvard's cases are available for direct purchase from the HBR Store .  Qualified and registered instructors  can access Harvard's Educator site to preview cases and access Teaching Notes and other supporting materials. Also see below for a discussion on how to find a small number of HBS cases in the Harvard Business Review.

The Case Centre (formerly the European Case Clearing House) "[T]he largest single source . . . of management case studies in the world. We hold and distribute all cases produced by the world's best-known management teaching establishments, as well as case studies in many languages produced by individual authors from almost every corner of the globe." Search for a case, then click on the link for an "inspection copy" (if available) and follow the links to register as a faculty member.

Richard Ivey School of Business - Cases Faculty can register to preview cases. Note that we have several books in the Ivey Casebook Series .

Financial Times The FT contains a short series of Business School Teaching Cases (2022-present), as well as an older series of   Management Case Studies (2010-2014). In addition, many of the articles not listed in the "case study" sections of the FT site may work well as class discussion starters. See, for instance, Equinor: A case study on the trouble with greening oil and gas companies . Note that SFU's FT access is active to June 2025, with discussions about ongoing funding in progress. See this post for details on accessing FT articles.

Cases online via the Harvard Business Review 

Try searching for Harvard Business Review in the Publication Name field in Business Source Complete, then checking the box to limit your search to the Document Type " case study."  Add in other terms to focus your search. 

Note that only a very small subset of all Harvard Business School (HBS) cases are published in the HBR.  The majority of Harvard's business cases are sold only to individuals and classes, not to libraries for use by the entire institution.

Journals that feature case studies

• Journal of Information Technology Teaching Cases : provides "suitable, contemporary case materials for teaching topics in the organisation and management of information systems and on the social consequences of information technology." Note that this is a spin-off journal from the Journal of Information Technology which used to publish such cases. 
• International Journal of Case Studies in Management : Cases from 2003-2012 available via our CBCA database.
• International Journal of Management Cases : The IJMC is the official journal of the CIRCLE Research Centre. CIRCLE (Centre for International Research Consumers, Locations and their Environments) is a virtual research group in over 70 universities.
• Allied Academies International Conference: Proceedings of the International Academy for Case Studies (IACS)
• Journal of the International Academy for Case Studies : Presents classroom teaching cases, with instructor's notes, on any subject which might be taught in a Business School.
• Business Case Journal , Journal of Critical Incidents , and Journal of Case Studies : All from the Society for Case Research
• Asian Case Research Journal : Cases on Asian companies & MNCs operating in Asia-Pacific. No access to the most recent 12 months.
• Journal of Case Research in Business & Economics

Other online sources for cases

• CaseBase & CaseBase2: Case Studies in Global Business : Covers business case studies focused on issues in emerging markets and emerging industries across the globe.
• Business Ethics Case Studies : A few cases from Business Ethics Canada - St. Mary's University
• The Case Centre (formerly the European Case Clearinghouse) offers a selection of free cases .
• Business Gateway : Case studies from Scotland on starting and running a small business.
• The Times 100 : Free business case studies on real life companies. 
• Acadia Institute of Case Studies (Acadia University): Most studies are focused on small business and entrepreneurship and include teaching notes. Some of them even include short videos. Permission is granted for educational use. Note that the AICS site appears to be currently inaccessible, so we've linked to the Web Archive version of their site as of late 2019.
• Company-specific case studies: Intended as examples of how customers have used or could use their products: IBM , Intel , and LANSA .
• Advertising Educational Foundation: Case histories : "Case histories give you an inside look at the steps advertising agencies and advertisers take to create a campaign and how effective it can be. Case histories show the preceding issue/problem, the response and the outcome. Creative is included."
• MarketLine cases in Business Source : Mostly strategic analysis cases featuring large, global companies.
• Open Case Studies : An interdisciplinary collection of cases from UBC that are licensed to allow others to revise and reuse them. Very few of the cases are explicitly categorized as "business," but many of the cases on topics such as Conservation may be useful in a business context.

  An example of case analysis that might give you a sense of what's expected/possible: 

In 1989, the journal Interfaces published an HBS case and asked its readers to submit their analyses. Those analyses were then compiled into two subsequent articles, providing a useful example of the many ways business issues could be viewed and resolved.

Initial case : Porteus, E. L. (1989). The Case Analysis Section: National Cranberry Cooperative . Interfaces, 19 (6), 29–39. https://doi-org.proxy.lib.sfu.ca/10.1287/inte.19.6.29 (Note: this case has been revised multiple times. If it is assigned in your class, make sure you are using the most current revision, mostly likely only available via HBS.)

Analyses:  #1: Porteus, E. L. (1993). Case Analysis: Analyses of the National Cranberry Cooperative -- 1. Tactical Options . Interfaces, 23 (4), 21–39. https://doi-org.proxy.lib.sfu.ca/10.1287/inte.23.4.21

#2: Porteus, E. L. (1993). Case Analysis: Analyses of the National Cranberry Cooperative -- 2. Environmental Changes and Implementation . Interfaces, 23 (6), 81–92. https://doi-org.proxy.lib.sfu.ca/10.1287/inte.23.6.81

• Rotterdam School of Management: CDC Case Writing Training Material Valuable advice to aspiring case writers via a 4-part series in our Sage Business Cases database.
• Learning and researching with case studies : a student companion for business and management research (2024 ebook)
• Why teach with cases? : reflections on philosophy and practice (2022 ebook)
• The ultimate guide to compact cases : case research, writing, and teaching   (2022 ebook)
• Writing, Teaching, and Using Cases : A January 2014 presentation by Leyland Pitt and Michael Parent (both of SFU). Michael and Leyland led a full-day workshop with a focus on case teaching.
• The case writing workbook : a guide for faculty and students : "Designed as an individualized workshop to assist case authors to structure their writing..."
• Guide for Contributors: Tips for Writing Cases : From the publishers of our SAGE Business Cases (SBC) database. Also see the SBC's  Author Guidelines .
• Learning Effectively with Case Studies: A Conversation between a Professor and a Former MBA Student
• The case study companion : teaching, learning and writing business case studies : All angles in one recent (2021) ebook!
• The Case Writer's Toolkit :  "... to help writers visualise concepts, signpost ideas, break down complex information and apply techniques in a practical manner."
• A Brief Guide to Case Teaching : A free guide from The Case Centre
• Teaching with Cases : A Practical Guide : "... focuses on practical advice for instructors that can be easily implemented. It covers how to plan a course, how to teach it, and how to evaluate it."
• Teaching & Authoring Tools : Part of the Ivey Cases site, this page offers documents and videos to help you create your own cases, as well as lists of additional resources.
• Application of a Case Study Methodology by Winston Tellis: (The Qualitative Report, Volume 3, Number 3, September, 1997). This academic article covers the social science methodologies involved in designing, conducting and analysing a case study. It also features a detailed bibliography.
• The Art and Craft of Case Writing (3rd ed. 2012): "[A] practical, comprehensive, and multidisciplinary guide that blends an informal, workshop-style with solid theory and practice." Includes a section on video, multimedia, and Internet cases.
• Basics of Developing Case Studies : Part of the Free Management Library , this site has some basic information on how to develop a case study, as well as links to some sample cases.
• A Guide to Case Analysis : Focus is on how to analyse company cases when learning strategic management techniques. (Depending on your browser settings, you may need to right click this link and open it in a new tab or download it.)
• Case Studies: Overview  (from Cengage): Covers both analysing and writing a case study from the perspective of a business student. From the same publisher: A student's guide to analysing case studies .
• Case Analysis Guide : Developed by a publisher to support students using a Strategic Management text, but applicable in many other situations.
• Short videos on how to approach a case study by the author of the Case Study Handbook: A Student's Guide
• Videos: What is the Case Method? : from The Case Centre

Also, try the subject heading " Case method " in the SFU Library catalogue for books on using the case method in your classes. Suggested sample case method books:

• Encyclopedia of case study research ( print )
• Case study research: design and methods (4th edition, 2009; print )
• Case study research: principles and practices ( online or  print )
• Case writing for executive education: a survival guide ( print )

You might also want to try checking an index of education articles such as ERIC : start with the subject heading (or Descriptor) Case Method (Teaching Technique) .  Alternatively, try our Education Source database using Case method (Teaching) as your subject search term. 

How to Write a Case Study Analysis

Step-By-Step Instructions

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When writing a business case study analysis , you must first have a good understanding of the case study . Before you begin the steps below, read the business case carefully, taking notes all the while. It may be necessary to read the case several times to get all of the details and fully grasp the issues facing the group, company, or industry.

As you are reading, do your best to identify key issues, key players, and the most pertinent facts. After you are comfortable with the information, use the following step-by-step instructions (geared toward a single-company analysis) to write your report. To write about an industry, just adapt the steps listed here to discuss the segment as a whole.

Step 1: Investigate the Company’s History and Growth

A company’s past can greatly affect the present and future state of the organization. To begin, investigate the company’s founding, critical incidents, structure, and growth. Create a timeline of events, issues, and achievements. This timeline will come in handy for the next step. 

Step 2: Identify Strengths and Weaknesses

Using the information you gathered in step one, continue by examining and making a list of the value creation functions of the company. For example, the company may be weak in product development but strong in marketing. Make a list of problems that have occurred and note the effects they have had on the company. You should also list areas where the company has excelled. Note the effects of these incidents as well.

You're essentially conducting a partial SWOT analysis to get a better understanding of the company's strengths and weaknesses. A SWOT analysis involves documenting things like internal strengths (S) and weaknesses (W) and external opportunities (O) and threats (T). 

Step 3: Examine the External Environment

The third step involves identifying opportunities and threats within the company’s external environment. This is where the second part of the SWOT analysis (the O and the T) comes into play. Special items to note include competition within the industry, bargaining powers, and the threat of substitute products. Some examples of opportunities include expansion into new markets or new technology. Some examples of threats include increasing competition and higher interest rates.

Step 4: Analyze Your Findings

Using the information in steps 2 and 3, create an evaluation for this portion of your case study analysis. Compare the strengths and weaknesses within the company to the external threats and opportunities. Determine if the company is in a strong competitive position, and decide if it can continue at its current pace successfully.

Step 5: Identify Corporate-Level Strategy

To identify a company’s corporate-level strategy, identify and evaluate the company’s mission , goals, and actions toward those goals. Analyze the company’s line of business and its subsidiaries and acquisitions. You also want to debate the pros and cons of the company strategy to determine whether or not a change might benefit the company in the short or long term.​

Step 6: Identify Business-Level Strategy

Thus far, your case study analysis has identified the company’s corporate-level strategy. To perform a complete analysis, you will need to identify the company’s business-level strategy. (Note: If it is a single business, without multiple companies under one umbrella, and not an industry-wide review, the corporate strategy and the business-level strategy are the same.) For this part, you should identify and analyze each company’s competitive strategy, marketing strategy, costs, and general focus.

Step 7: Analyze Implementations

This portion requires that you identify and analyze the structure and control systems that the company is using to implement its business strategies. Evaluate organizational change, levels of hierarchy, employee rewards, conflicts, and other issues that are important to the company you are analyzing.

Step 8: Make Recommendations

The final part of your case study analysis should include your recommendations for the company. Every recommendation you make should be based on and supported by the context of your analysis. Never share hunches or make a baseless recommendation.

You also want to make sure that your suggested solutions are actually realistic. If the solutions cannot be implemented due to some sort of restraint, they are not realistic enough to make the final cut.

Finally, consider some of the alternative solutions that you considered and rejected. Write down the reasons why these solutions were rejected. 

Step 9: Review

Look over your analysis when you have finished writing. Critique your work to make sure every step has been covered. Look for grammatical errors , poor sentence structure, or other things that can be improved. It should be clear, accurate, and professional.

Business Case Study Analysis Tips

Keep these strategic tips in mind:

• Know the case study ​backward and forward before you begin your case study analysis.
• Give yourself enough time to write the case study analysis. You don't want to rush through it.
• Be honest in your evaluations. Don't let personal issues and opinions cloud your judgment.
• Be analytical, not descriptive.
• Proofread your work, and even let a test reader give it a once-over for dropped words or typos that you no longer can see.
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Case Study Analysis: Examples + How-to Guide & Writing Tips

A case study analysis is a typical assignment in business management courses. The task aims to show high school and college students how to analyze a current situation, determine what problems exist, and develop the best possible strategy to achieve the desired outcome.

Many students feel anxious about writing case analyses because being told to analyze a case study and provide a solution can seem like a big task. That is especially so when working with real-life scenarios. However, you can rest assured writing a case analysis paper is easier than you think. Just keep reading this article and you will find case study examples for students and the advice provided by Custom-writing experts!

• 👣 Main Steps
• 🕵 Preparing the Case

🔬 Analyzing the Case

• 📑 Format & Structure
• 🙅 Things to Avoid
• 🏁 Conclusion

🔗 References

👣 writing a case study analysis: main steps.

Business management is built on case analysis. Every single economic result shows that the methods and instruments employed were either well-timed and expedient, in the event of success, or not, in case of failure. These two options indicate whether the strategy is efficient (and should be followed) or requires corrections (or complete change). Such an approach to the case study will make your writing piece more proficient and valuable for the reader. The following steps will direct your plan for writing a case study analysis.

Step 1: Preliminary work

• Make notes and highlight the numbers and ideas that could be quoted.
• Single out as many problems as you can, and briefly mark their underlying issues. Then make a note of those responsible. In the report, you will use two to five of the problems, so you will have a selection to choose from.
• Outline a possible solution to each of the problems you found. Course readings and outside research shall be used here. Highlight your best and worst solution for further reference.

Step 2: Drafting the Case

• Provide a general description of the situation and its history.
• Name all the problems you are going to discuss.
• Specify the theory used for the analysis.
• Present the assumptions that emerged during the analysis, if any.
• Describe the detected problems in more detail.
• Indicate their link to, and effect on, the general situation.
• Explain why the problems emerged and persist.
• List realistic and feasible solutions to the problems you outlined, in the order of importance.
• Specify your predicted results of such changes.
• Support your choice with reliable evidence (i.e., textbook readings, the experience of famous companies, and other external research).
• Define the strategies required to fulfill your proposed solution.
• Indicate the responsible people and the realistic terms for its implementation.
• Recommend the issues for further analysis and supervision.

Step 3: Finalizing the Case

Like any other piece of writing, a case analysis requires post-editing. Carefully read it through, looking for inconsistencies and gaps in meaning. Your purpose is to make it look complete, precise, and convincing.

🕵 Preparing a Case for Analysis

Your professor might give you various case study examples from which to choose, or they may just assign you a particular case study. To conduct a thorough data analysis, you must first read the case study. This might appear to be obvious. However, you’d be surprised at how many students don’t take adequate time to complete this part.

Read the case study very thoroughly, preferably several times. Highlight, underline, flag key information, and make notes to refer to later when you are writing your analysis report.

If you don’t have a complete knowledge of the case study your professor has assigned, you won’t conduct a proper analysis of it. Even if you make use of a business case study template or refer to a sample analysis, it won’t help if you aren’t intimately familiar with your case study.

You will also have to conduct research. When it comes to research, you will need to do the following:

• Gather hard, quantitative data (e.g. 67% of the staff participated in the meeting).
• Design research tools , such as questionnaires and surveys (this will aid in gathering data).
• Determine and suggest the best specific, workable solutions.

It would be best if you also learned how to analyze a case study. Once you have read through the case study, you need to determine the focus of your analysis. You can do this by doing the following:

Compare your chosen solutions to the solutions offered by the experts who analyzed the case study you were given or to online assignments for students who were dealing with a similar task. The experts’ solutions will probably be more advanced than yours simply because these people are more experienced. However, don’t let this discourage you; the whole point of doing this analysis is to learn. Use the opportunity to learn from others’ valuable experience, and your results will be better next time.

If you are still in doubt, the University of South Carolina offers a great guide on forming a case study analysis.

📑 Case Analysis Format & Structure

When you are learning how to write a case study analysis, it is important to get the format of your analysis right. Understanding the case study format is vital for both the professor and the student. The person planning and handing out such an assignment should ensure that the student doesn’t have to use any external sources .

In turn, students have to remember that a well-written case analysis provides all the data, making it unnecessary for the reader to go elsewhere for information.

Regardless of whether you use a case study template, you will need to follow a clear and concise format when writing your analysis report. There are some possible case study frameworks available. Still, a case study should contain eight sections laid out in the following format:

• Describe the purpose of the current case study;
• Provide a summary of the company;
• Briefly introduce the problems and issues found in the case study
• Discuss the theory you will be using in the analysis;
• Present the key points of the study and present any assumptions made during the analysis.
• Present each problem you have singled out;
• Justify your inclusion of each problem by providing supporting evidence from the case study and by discussing relevant theory and what you have learned from your course content;
• Divide the section (and following sections) into subsections, one for each of your selected problems.
• Present a summary of each problem you have identified;
• Present plausible solutions for each of the problems, keeping in mind that each problem will likely have more than one possible solution;
• Provide the pros and cons of each solution in a way that is practical.
• Conclusion . This is a summary of your findings and discussion.
• Decide which solution best fits each of the issues you identified;
• Explain why you chose this solution and how it will effectively solve the problem;
• Be persuasive when you write this section so that you can drive your point home;
• Be sure to bring together theory and what you have learned throughout your course to support your recommendations.
• Provide an explanation of what must be done, who should take action, and when the solution should be carried out;
• Where relevant, you should provide an estimate of the cost in implementing the solution, including both the financial investment and the cost in terms of time.
• References. While you generally do not need to refer to many external sources when writing a case study analysis, you might use a few. When you do, you will need to properly reference these sources, which is most often done in one of the main citation styles, including APA, MLA, or Harvard. There is plenty of help when citing references, and you can follow these APA guidelines , these MLA guidelines , or these Harvard guidelines .
• Appendices. This is the section you include after your case study analysis if you used any original data in the report. These data, presented as charts, graphs, and tables, are included here because to present them in the main body of the analysis would be disruptive to the reader. The University of Southern California provides a great description of appendices and when to make use of them.

When you’ve finished your first draft, be sure to proofread it. Look not only for potential grammar and spelling errors but also for discrepancies or holes in your argument.

You should also know what you need to avoid when writing your analysis.

🙅 Things to Avoid in Case Analysis

Whenever you deal with a case study, remember that there are some pitfalls to avoid! Beware of the following mistakes:

• Excessive use of colloquial language . Even though it is a study of an actual case, it should sound formal.
• Lack of statistical data . Give all the important data, both in percentages and in numbers.
• Excessive details. State only the most significant facts, rather than drowning the reader in every fact you find.
• Inconsistency in the methods you have used . In a case study, theory plays a relatively small part, so you must develop a specific case study research methodology.
• Trivial means of research . It is critical that you design your own case study research method in whatever form best suits your analysis, such as questionnaires and surveys.

It is useful to see a few examples of case analysis papers. After all, a sample case study report can provide you with some context so you can see how to approach each aspect of your paper.

👀 Case Study Examples for Students

It might be easier to understand how a case study analysis works if you have an example to look at. Fortunately, examples of case studies are easy to come by. Take a look at this video for a sample case study analysis for the Coca-Cola Company.

If you want another example, then take a look at the one below!

Business Case Analysis: Example

CRM’s primary focus is customers and customer perception of the brand or the company. The focus may shift depending on customers’ needs. The main points that Center Parcs should consider are an increase in customer satisfaction and its market share. Both of these points will enhance customer perception of the product as a product of value. Increased customer satisfaction will indicate that the company provides quality services, and increased market share can reduce the number of switching (or leaving) customers, thus fostering customer loyalty.

Case Study Topics

• Equifax case study: the importance of cybersecurity measures. 
• Study a case illustrating ethical issues of medical research.
• Examine the case describing the complications connected with nursing and residential care.
• Analyze the competitive strategy of Delta Airlines .
• Present a case study of an ethical dilemma showing the conflict between the spirit and the letter of the law.  
• Explore the aspects of Starbucks’ marketing strategyin a case study.  
• Research a case of community-based clinic organization and development.
• Customer service of United Airlines: a case study .
• Analyze a specific schizophrenia case and provide your recommendations.
• Provide a case study of a patient with hyperglycemia.
• Examine the growth strategy of United Healthcare.
• Present a case study demonstrating ethical issues in business.
• Study a case of the 5% shareholding rule application and its impact on the company.
• Case study of post-traumatic stress disorder .
• Analyze a case examining the issues of cross-cultural management .
• Write a case study exploring the ethical issues the finance manager of a long-term care facility can face and the possible reaction to them.
• Write a case study analyzing the aspects of a new president of a firm election.
• Discuss the specifics of supply chain management in the case of Tehindo company.
• Study a case of a life crisis in a family and the ways to cope with it.
• Case study of Tea Leaves and More: supply chain issues.   
• Explore the case of ketogenic diet implementation among sportspeople.  
• Analyze the case of Webster Jewelry shop and suggest some changes.  
• Examine the unique aspects of Tea and More brand management.  
• Adidas case study: an ethical dilemma .
• Research the challenges of Brazos Valley Food Bank and suggest possible solutions.  
• Describe the case of dark web monitoring for business.  
• Study a case of permissive parenting style .
• Case study of Starbucks employees.
• Analyze a case of workplace discrimination and suggest a strategy to avoid it.
• Examine a case of the consumer decision-making process and define the factors that influence it.
• Present a case study of Netflix illustrating the crucial role of management innovation for company development.  
• Discuss a case describing a workplace ethical issue and propose ways to resolve it.
• Case study of the 2008 financial crisis: Graham’s value investing principles in the modern economic climate.
• Write a case study analyzing the harmful consequences of communication issues in a virtual team.
• Analyze a case that highlights the importance of a proper functional currency choice. 
• Examine the case of Hitachi Power Systems management.  
• Present a case study of medication research in a healthcare facility.
• Study the case of Fiji Water and the challenges the brand faces.  
• Research a social problem case and suggest a solution.
• Analyze a case that reveals the connection between alcohol use and borderline personality disorder.
• Transglobal Airline case study: break-even analysis.
• Examine the case of Chiquita Brands International from the moral and business ethics points of view.
• Present a case study of applying for Social Security benefits. 
• Study the case of a mass hacker attack on Microsoft clients and suggest possible ways to prevent future attacks.
• Case study of leadership effectiveness. 
• Analyze a case presenting a clinical moral dilemma and propose ways to resolve it. 
• Describe the case of Cowbell Brewing Company and discuss the strategy that made them successful.
• Write a case study of WeWork company and analyze the strengths and weaknesses of its strategy.
• Case study of medical ethical decision-making.
• Study the case of The Georges hotel and suggest ways to overcome its managerial issues.

🏁 Concluding Remarks

Writing a case study analysis can seem incredibly overwhelming, especially if you have never done it before. Just remember, you can do it provided you follow a plan, keep to the format described here, and study at least one case analysis example.

If you still need help analyzing a case study, your professor is always available to answer your questions and point you in the right direction. You can also get help with any aspect of the project from a custom writing company. Just tackle the research and hand over the writing, write a rough draft and have it checked by a professional, or completely hand the project off to an expert writer.

Regardless of the path you choose, you will turn in something of which you can be proud!

✏️ Case Study Analysis FAQ

Students (especially those who study business) often need to write a case study analysis. It is a kind of report that describes a business case. It includes multiple aspects, for example, the problems that exist, possible solutions, forecasts, etc.

There should be 3 main points covered in a case study analysis:

• The challenge(s) description,
• Possible solutions,
• Outcomes (real and/or foreseen).

Firstly, study some examples available online and in the library. Case study analysis should be a well-structured paper with all the integral components in place. Thus, you might want to use a template and/or an outline to start correctly.

A case study analysis is a popular task for business students. They typically hand it in the format of a paper with several integral components:

• Description of the problem
• Possible ways out
• Results and/or forecasts

Students sometimes tell about the outcome of their research within an oral presentation.

• Case Study: Academia
• Windows of vulnerability: a case study analysis (IEEE)
• A (Very) Brief Refresher on the Case Study Method: SAGE
• The case study approach: Medical Research Methodology
• Strengths and Limitations of Case Studies: Stanford University
• A Sample APA Paper: Radford University
• How to Write a Case Study APA Style: Seattle PI
• The Case Analysis: GVSU
• How to Outline: Purdue OWL
• Incorporating Interview Data: UW-Madison Writing Center
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Organizing Your Social Sciences Research Paper: Writing a Case Study

• Purpose of Guide
• Design Flaws to Avoid
• Independent and Dependent Variables
• Glossary of Research Terms
• Narrowing a Topic Idea
• Broadening a Topic Idea
• Extending the Timeliness of a Topic Idea
• Academic Writing Style
• Choosing a Title
• Making an Outline
• Paragraph Development
• Executive Summary
• The C.A.R.S. Model
• Background Information
• The Research Problem/Question
• Theoretical Framework
• Citation Tracking
• Content Alert Services
• Evaluating Sources
• Reading Research Effectively
• Primary Sources
• Secondary Sources
• Tiertiary Sources
• What Is Scholarly vs. Popular?
• Qualitative Methods
• Quantitative Methods
• Using Non-Textual Elements
• Limitations of the Study
• Common Grammar Mistakes
• Writing Concisely
• Avoiding Plagiarism
• Footnotes or Endnotes?
• Further Readings
• Annotated Bibliography
• Dealing with Nervousness
• Using Visual Aids
• Grading Someone Else's Paper
• Types of Structured Group Activities
• Group Project Survival Skills
• Multiple Book Review Essay
• Reviewing Collected Essays
• Writing a Case Study
• About Informed Consent
• Writing Field Notes
• Writing a Policy Memo
• Writing a Research Proposal
• Bibliography

The term case study refers to both a method of analysis and a specific research design for examining a problem, both of which are used in most circumstances to generalize across populations. This tab focuses on the latter--how to design and organize a research paper in the social sciences that analyzes a specific case.

A case study research paper examines a person, place, event, phenomenon, or other type of subject of analysis in order to extrapolate  key themes and results that help predict future trends, illuminate previously hidden issues that can be applied to practice, and/or provide a means for understanding an important research problem with greater clarity. A case study paper usually examines a single subject of analysis, but case study papers can also be designed as a comparative investigation that shows relationships between two or among more than two subjects. The methods used to study a case can rest within a quantitative, qualitative, or mixed-method investigative paradigm.

Case Studies . Writing@CSU. Colorado State University; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010 ; “What is a Case Study?” In Swanborn, Peter G. Case Study Research: What, Why and How? London: SAGE, 2010.

How to Approach Writing a Case Study Research Paper

General information about how to choose a topic to investigate can be found under the " Choosing a Research Problem " tab in this writing guide. Review this page because it may help you identify a subject of analysis that can be investigated using a single case study design.

However, identifying a case to investigate involves more than choosing the research problem . A case study encompasses a problem contextualized around the application of in-depth analysis, interpretation, and discussion, often resulting in specific recommendations for action or for improving existing conditions. As Seawright and Gerring note, practical considerations such as time and access to information can influence case selection, but these issues should not be the sole factors used in describing the methodological justification for identifying a particular case to study. Given this, selecting a case includes considering the following:

• Does the case represent an unusual or atypical example of a research problem that requires more in-depth analysis? Cases often represent a topic that rests on the fringes of prior investigations because the case may provide new ways of understanding the research problem. For example, if the research problem is to identify strategies to improve policies that support girl's access to secondary education in predominantly Muslim nations, you could consider using Azerbaijan as a case study rather than selecting a more obvious nation in the Middle East. Doing so may reveal important new insights into recommending how governments in other predominantly Muslim nations can formulate policies that support improved access to education for girls.
• Does the case provide important insight or illuminate a previously hidden problem? In-depth analysis of a case can be based on the hypothesis that the case study will reveal trends or issues that have not been exposed in prior research or will reveal new and important implications for practice. For example, anecdotal evidence may suggest drug use among homeless veterans is related to their patterns of travel throughout the day. Assuming prior studies have not looked at individual travel choices as a way to study access to illicit drug use, a case study that observes a homeless veteran could reveal how issues of personal mobility choices facilitate regular access to illicit drugs. Note that it is important to conduct a thorough literature review to ensure that your assumption about the need to reveal new insights or previously hidden problems is valid and evidence-based.
• Does the case challenge and offer a counter-point to prevailing assumptions? Over time, research on any given topic can fall into a trap of developing assumptions based on outdated studies that are still applied to new or changing conditions or the idea that something should simply be accepted as "common sense," even though the issue has not been thoroughly tested in practice. A case may offer you an opportunity to gather evidence that challenges prevailing assumptions about a research problem and provide a new set of recommendations applied to practice that have not been tested previously. For example, perhaps there has been a long practice among scholars to apply a particular theory in explaining the relationship between two subjects of analysis. Your case could challenge this assumption by applying an innovative theoretical framework [perhaps borrowed from another discipline] to the study a case in order to explore whether this approach offers new ways of understanding the research problem. Taking a contrarian stance is one of the most important ways that new knowledge and understanding develops from existing literature.
• Does the case provide an opportunity to pursue action leading to the resolution of a problem? Another way to think about choosing a case to study is to consider how the results from investigating a particular case may result in findings that reveal ways in which to resolve an existing or emerging problem. For example, studying the case of an unforeseen incident, such as a fatal accident at a railroad crossing, can reveal hidden issues that could be applied to preventative measures that contribute to reducing the chance of accidents in the future. In this example, a case study investigating the accident could lead to a better understanding of where to strategically locate additional signals at other railroad crossings in order to better warn drivers of an approaching train, particularly when visibility is hindered by heavy rain, fog, or at night.
• Does the case offer a new direction in future research? A case study can be used as a tool for exploratory research that points to a need for further examination of the research problem. A case can be used when there are few studies that help predict an outcome or that establish a clear understanding about how best to proceed in addressing a problem. For example, after conducting a thorough literature review [very important!], you discover that little research exists showing the ways in which women contribute to promoting water conservation in rural communities of Uganda. A case study of how women contribute to saving water in a particular village can lay the foundation for understanding the need for more thorough research that documents how women in their roles as cooks and family caregivers think about water as a valuable resource within their community throughout rural regions of east Africa. The case could also point to the need for scholars to apply feminist theories of work and family to the issue of water conservation.

Eisenhardt, Kathleen M. “Building Theories from Case Study Research.” Academy of Management Review 14 (October 1989): 532-550; Emmel, Nick. Sampling and Choosing Cases in Qualitative Research: A Realist Approach . Thousand Oaks, CA: SAGE Publications, 2013; Gerring, John. “What Is a Case Study and What Is It Good for?” American Political Science Review 98 (May 2004): 341-354; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Seawright, Jason and John Gerring. "Case Selection Techniques in Case Study Research." Political Research Quarterly 61 (June 2008): 294-308.

Structure and Writing Style

The purpose of a paper in the social sciences designed around a case study is to thoroughly investigate a subject of analysis in order to reveal a new understanding about the research problem and, in so doing, contributing new knowledge to what is already known from previous studies. In applied social sciences disciplines [e.g., education, social work, public administration, etc.], case studies may also be used to reveal best practices, highlight key programs, or investigate interesting aspects of professional work. In general, the structure of a case study research paper is not all that different from a standard college-level research paper. However, there are subtle differences you should be aware of. Here are the key elements to organizing and writing a case study research paper.

I.  Introduction

As with any research paper, your introduction should serve as a roadmap for your readers to ascertain the scope and purpose of your study . The introduction to a case study research paper, however, should not only describe the research problem and its significance, but you should also succinctly describe why the case is being used and how it relates to addressing the problem. The two elements should be linked. With this in mind, a good introduction answers these four questions:

• What was I studying? Describe the research problem and describe the subject of analysis you have chosen to address the problem. Explain how they are linked and what elements of the case will help to expand knowledge and understanding about the problem.
• Why was this topic important to investigate? Describe the significance of the research problem and state why a case study design and the subject of analysis that the paper is designed around is appropriate in addressing the problem.
• What did we know about this topic before I did this study? Provide background that helps lead the reader into the more in-depth literature review to follow. If applicable, summarize prior case study research applied to the research problem and why it fails to adequately address the research problem. Describe why your case will be useful. If no prior case studies have been used to address the research problem, explain why you have selected this subject of analysis.
• How will this study advance new knowledge or new ways of understanding? Explain why your case study will be suitable in helping to expand knowledge and understanding about the research problem.

Each of these questions should be addressed in no more than a few paragraphs. Exceptions to this can be when you are addressing a complex research problem or subject of analysis that requires more in-depth background information.

II.  Literature Review

The literature review for a case study research paper is generally structured the same as it is for any college-level research paper. The difference, however, is that the literature review is focused on providing background information and  enabling historical interpretation of the subject of analysis in relation to the research problem the case is intended to address . This includes synthesizing studies that help to:

• Place relevant works in the context of their contribution to understanding the case study being investigated . This would include summarizing studies that have used a similar subject of analysis to investigate the research problem. If there is literature using the same or a very similar case to study, you need to explain why duplicating past research is important [e.g., conditions have changed; prior studies were conducted long ago, etc.].
• Describe the relationship each work has to the others under consideration that informs the reader why this case is applicable . Your literature review should include a description of any works that support using the case to study the research problem and the underlying research questions.
• Identify new ways to interpret prior research using the case study . If applicable, review any research that has examined the research problem using a different research design. Explain how your case study design may reveal new knowledge or a new perspective or that can redirect research in an important new direction.
• Resolve conflicts amongst seemingly contradictory previous studies . This refers to synthesizing any literature that points to unresolved issues of concern about the research problem and describing how the subject of analysis that forms the case study can help resolve these existing contradictions.
• Point the way in fulfilling a need for additional research . Your review should examine any literature that lays a foundation for understanding why your case study design and the subject of analysis around which you have designed your study may reveal a new way of approaching the research problem or offer a perspective that points to the need for additional research.
• Expose any gaps that exist in the literature that the case study could help to fill . Summarize any literature that not only shows how your subject of analysis contributes to understanding the research problem, but how your case contributes to a new way of understanding the problem that prior research has failed to do.
• Locate your own research within the context of existing literature [very important!] . Collectively, your literature review should always place your case study within the larger domain of prior research about the problem. The overarching purpose of reviewing pertinent literature in a case study paper is to demonstrate that you have thoroughly identified and synthesized prior studies in the context of explaining the relevance of the case in addressing the research problem.

III.  Method

In this section, you explain why you selected a particular subject of analysis to study and the strategy you used to identify and ultimately decide that your case was appropriate in addressing the research problem. The way you describe the methods used varies depending on the type of subject of analysis that frames your case study.

If your subject of analysis is an incident or event . In the social and behavioral sciences, the event or incident that represents the case to be studied is usually bounded by time and place, with a clear beginning and end and with an identifiable location or position relative to its surroundings. The subject of analysis can be a rare or critical event or it can focus on a typical or regular event. The purpose of studying a rare event is to illuminate new ways of thinking about the broader research problem or to test a hypothesis. Critical incident case studies must describe the method by which you identified the event and explain the process by which you determined the validity of this case to inform broader perspectives about the research problem or to reveal new findings. However, the event does not have to be a rare or uniquely significant to support new thinking about the research problem or to challenge an existing hypothesis. For example, Walo, Bull, and Breen conducted a case study to identify and evaluate the direct and indirect economic benefits and costs of a local sports event in the City of Lismore, New South Wales, Australia. The purpose of their study was to provide new insights from measuring the impact of a typical local sports event that prior studies could not measure well because they focused on large "mega-events." Whether the event is rare or not, the methods section should include an explanation of the following characteristics of the event: a) when did it take place; b) what were the underlying circumstances leading to the event; c) what were the consequences of the event.

If your subject of analysis is a person. Explain why you selected this particular individual to be studied and describe what experience he or she has had that provides an opportunity to advance new understandings about the research problem. Mention any background about this person which might help the reader understand the significance of his/her experiences that make them worthy of study. This includes describing the relationships this person has had with other people, institutions, and/or events that support using him or her as the subject for a case study research paper. It is particularly important to differentiate the person as the subject of analysis from others and to succinctly explain how the person relates to examining the research problem.

If your subject of analysis is a place. In general, a case study that investigates a place suggests a subject of analysis that is unique or special in some way and that this uniqueness can be used to build new understanding or knowledge about the research problem. A case study of a place must not only describe its various attributes relevant to the research problem [e.g., physical, social, cultural, economic, political, etc.], but you must state the method by which you determined that this place will illuminate new understandings about the research problem. It is also important to articulate why a particular place as the case for study is being used if similar places also exist [i.e., if you are studying patterns of homeless encampments of veterans in open spaces, why study Echo Park in Los Angeles rather than Griffith Park?]. If applicable, describe what type of human activity involving this place makes it a good choice to study [e.g., prior research reveals Echo Park has more homeless veterans].

If your subject of analysis is a phenomenon. A phenomenon refers to a fact, occurrence, or circumstance that can be studied or observed but with the cause or explanation to be in question. In this sense, a phenomenon that forms your subject of analysis can encompass anything that can be observed or presumed to exist but is not fully understood. In the social and behavioral sciences, the case usually focuses on human interaction within a complex physical, social, economic, cultural, or political system. For example, the phenomenon could be the observation that many vehicles used by ISIS fighters are small trucks with English language advertisements on them. The research problem could be that ISIS fighters are difficult to combat because they are highly mobile. The research questions could be how and by what means are these vehicles used by ISIS being supplied to the militants and how might supply lines to these vehicles be cut? How might knowing the suppliers of these trucks from overseas reveal larger networks of collaborators and financial support? A case study of a phenomenon most often encompasses an in-depth analysis of a cause and effect that is grounded in an interactive relationship between people and their environment in some way.

NOTE:   The choice of the case or set of cases to study cannot appear random. Evidence that supports the method by which you identified and chose your subject of analysis should be linked to the findings from the literature review. Be sure to cite any prior studies that helped you determine that the case you chose was appropriate for investigating the research problem.

IV.  Discussion

The main elements of your discussion section are generally the same as any research paper, but centered around interpreting and drawing conclusions about the key findings from your case study. Note that a general social sciences research paper may contain a separate section to report findings. However, in a paper designed around a case study, it is more common to combine a description of the findings with the discussion about their implications. The objectives of your discussion section should include the following:

Reiterate the Research Problem/State the Major Findings Briefly reiterate the research problem you are investigating and explain why the subject of analysis around which you designed the case study were used. You should then describe the findings revealed from your study of the case using direct, declarative, and succinct proclamation of the study results. Highlight any findings that were unexpected or especially profound.

Explain the Meaning of the Findings and Why They are Important Systematically explain the meaning of your case study findings and why you believe they are important. Begin this part of the section by repeating what you consider to be your most important or surprising finding first, then systematically review each finding. Be sure to thoroughly extrapolate what your analysis of the case can tell the reader about situations or conditions beyond the actual case that was studied while, at the same time, being careful not to misconstrue or conflate a finding that undermines the external validity of your conclusions.

Relate the Findings to Similar Studies No study in the social sciences is so novel or possesses such a restricted focus that it has absolutely no relation to previously published research. The discussion section should relate your case study results to those found in other studies, particularly if questions raised from prior studies served as the motivation for choosing your subject of analysis. This is important because comparing and contrasting the findings of other studies helps to support the overall importance of your results and it highlights how and in what ways your case study design and the subject of analysis differs from prior research about the topic.

Consider Alternative Explanations of the Findings It is important to remember that the purpose of social science research is to discover and not to prove. When writing the discussion section, you should carefully consider all possible explanations for the case study results, rather than just those that fit your hypothesis or prior assumptions and biases. Be alert to what the in-depth analysis of the case may reveal about the research problem, including offering a contrarian perspective to what scholars have stated in prior research.

Acknowledge the Study's Limitations You can state the study's limitations in the conclusion section of your paper but describing the limitations of your subject of analysis in the discussion section provides an opportunity to identify the limitations and explain why they are not significant. This part of the discussion section should also note any unanswered questions or issues your case study could not address. More detailed information about how to document any limitations to your research can be found here .

Suggest Areas for Further Research Although your case study may offer important insights about the research problem, there are likely additional questions related to the problem that remain unanswered or findings that unexpectedly revealed themselves as a result of your in-depth analysis of the case. Be sure that the recommendations for further research are linked to the research problem and that you explain why your recommendations are valid in other contexts and based on the original assumptions of your study.

V.  Conclusion

As with any research paper, you should summarize your conclusion in clear, simple language; emphasize how the findings from your case study differs from or supports prior research and why. Do not simply reiterate the discussion section. Provide a synthesis of key findings presented in the paper to show how these converge to address the research problem. If you haven't already done so in the discussion section, be sure to document the limitations of your case study and needs for further research.

The function of your paper's conclusion is to: 1)  restate the main argument supported by the findings from the analysis of your case; 2) clearly state the context, background, and necessity of pursuing the research problem using a case study design in relation to an issue, controversy, or a gap found from reviewing the literature; and, 3) provide a place for you to persuasively and succinctly restate the significance of your research problem, given that the reader has now been presented with in-depth information about the topic.

Consider the following points to help ensure your conclusion is appropriate:

• If the argument or purpose of your paper is complex, you may need to summarize these points for your reader.
• If prior to your conclusion, you have not yet explained the significance of your findings or if you are proceeding inductively, use the conclusion of your paper to describe your main points and explain their significance.
• Move from a detailed to a general level of consideration of the case study's findings that returns the topic to the context provided by the introduction or within a new context that emerges from your case study findings.

Note that, depending on the discipline you are writing in and your professor's preferences, the concluding paragraph may contain your final reflections on the evidence presented applied to practice or on the essay's central research problem. However, the nature of being introspective about the subject of analysis you have investigated will depend on whether you are explicitly asked to express your observations in this way.

Problems to Avoid

Overgeneralization One of the goals of a case study is to lay a foundation for understanding broader trends and issues applied to similar circumstances. However, be careful when drawing conclusions from your case study. They must be evidence-based and grounded in the results of the study; otherwise, it is merely speculation. Looking at a prior example, it would be incorrect to state that a factor in improving girls access to education in Azerbaijan and the policy implications this may have for improving access in other Muslim nations is due to girls access to social media if there is no documentary evidence from your case study to indicate this. There may be anecdotal evidence that retention rates were better for girls who were on social media, but this observation would only point to the need for further research and would not be a definitive finding if this was not a part of your original research agenda.

Failure to Document Limitations No case is going to reveal all that needs to be understood about a research problem. Therefore, just as you have to clearly state the limitations of a general research study , you must describe the specific limitations inherent in the subject of analysis. For example, the case of studying how women conceptualize the need for water conservation in a village in Uganda could have limited application in other cultural contexts or in areas where fresh water from rivers or lakes is plentiful and, therefore, conservation is understood differently than preserving access to a scarce resource.

Failure to Extrapolate All Possible Implications Just as you don't want to over-generalize from your case study findings, you also have to be thorough in the consideration of all possible outcomes or recommendations derived from your findings. If you do not, your reader may question the validity of your analysis, particularly if you failed to document an obvious outcome from your case study research. For example, in the case of studying the accident at the railroad crossing to evaluate where and what types of warning signals should be located, you failed to take into consideration speed limit signage as well as warning signals. When designing your case study, be sure you have thoroughly addressed all aspects of the problem and do not leave gaps in your analysis.

Case Studies . Writing@CSU. Colorado State University; Gerring, John. Case Study Research: Principles and Practices . New York: Cambridge University Press, 2007; Merriam, Sharan B. Qualitative Research and Case Study Applications in Education . Rev. ed. San Francisco, CA: Jossey-Bass, 1998; Miller, Lisa L. “The Use of Case Studies in Law and Social Science Research.” Annual Review of Law and Social Science 14 (2018): TBD; Mills, Albert J., Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Putney, LeAnn Grogan. "Case Study." In Encyclopedia of Research Design , Neil J. Salkind, editor. (Thousand Oaks, CA: SAGE Publications, 2010), pp. 116-120; Simons, Helen. Case Study Research in Practice . London: SAGE Publications, 2009;  Kratochwill,  Thomas R. and Joel R. Levin, editors. Single-Case Research Design and Analysis: New Development for Psychology and Education .  Hilldsale, NJ: Lawrence Erlbaum Associates, 1992; Swanborn, Peter G. Case Study Research: What, Why and How? London : SAGE, 2010; Yin, Robert K. Case Study Research: Design and Methods . 6th edition. Los Angeles, CA, SAGE Publications, 2014; Walo, Maree, Adrian Bull, and Helen Breen. “Achieving Economic Benefits at Local Events: A Case Study of a Local Sports Event.” Festival Management and Event Tourism 4 (1996): 95-106.

Writing Tip

At Least Five Misconceptions about Case Study Research

Social science case studies are often perceived as limited in their ability to create new knowledge because they are not randomly selected and findings cannot be generalized to larger populations. Flyvbjerg examines five misunderstandings about case study research and systematically "corrects" each one. To quote, these are:

Misunderstanding 1 :  General, theoretical [context-independent knowledge is more valuable than concrete, practical (context-dependent) knowledge. Misunderstanding 2 :  One cannot generalize on the basis of an individual case; therefore, the case study cannot contribute to scientific development. Misunderstanding 3 :  The case study is most useful for generating hypotheses; that is, in the first stage of a total research process, whereas other methods are more suitable for hypotheses testing and theory building. Misunderstanding 4 :  The case study contains a bias toward verification, that is, a tendency to confirm the researcher’s preconceived notions. Misunderstanding 5 :  It is often difficult to summarize and develop general propositions and theories on the basis of specific case studies [p. 221].

While writing your paper, think introspectively about how you addressed these misconceptions because to do so can help you strengthen the validity and reliability of your research by clarifying issues of case selection, the testing and challenging of existing assumptions, the interpretation of key findings, and the summation of case outcomes. Think of a case study research paper as a complete, in-depth narrative about the specific properties and key characteristics of your subject of analysis applied to the research problem.

Flyvbjerg, Bent. “Five Misunderstandings About Case-Study Research.” Qualitative Inquiry 12 (April 2006): 219-245.

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• URL: https://libguides.pointloma.edu/ResearchPaper

Quality and health impact of groundwater in a coastal region: a case study from west coast of southern India

• Research Article
• Published: 12 September 2024

Cite this article

• Ayushi Agarwal 1 , 2 &
• Ratnakar Dhakate 1 , 2  

Seawater intrusion seriously threatens the quality of coastal groundwater, affecting nearly 40% of the world’s population in coastal areas. A study was conducted in the Kamini watershed situated in the Udupi district of Karnataka to assess the groundwater quality and extent of seawater intrusion. During the pre-monsoon period, 57 groundwater and 3 surface water samples were analyzed to understand the impact of seawater on the groundwater and surface water. The analysis revealed that the groundwater in the study area is slightly alkaline. The weighted overlay analysis map indicated that 11% of the study area is unsuitable for drinking water due to the influence of seawater. The Piper plot analysis revealed that the groundwater is predominantly CaMgCl facies. The hydrogeochemical facies evolution diagram (HFED) showed that 62% of the groundwater is affected by seawater. The HFED and Piper plots also indicate that the surface water is also affected by seawater. These results are also supported by various molar ratios such as Cl − vs. Cl⁻/HCO 3 ⁻, Cl⁻ vs. Na⁺/Cl⁻, Cl − vs. SO 4 2− /Cl − , and Cl⁻/HCO 3 − vs. Mg 2+ /Ca 2+ , suggesting that the majority of the water sample has been affected by seawater. The saturation indices indicated that mineral dissolution has significantly contributed to groundwater salinization. The correlation between sulfate concentration and calcite and dolomite dissolution suggested the influence of seawater intrusion in the coastal aquifer. The process of reverse ion exchange mainly influences the groundwater chemistry according to chloroalkali indices. The total hazard index (THI) values of nitrate and fluoride exceeded limits, posing health risks to adults and children. Studies suggest that with time and space, seawater intrusion is increasing in some pockets of the study area, especially along the west coast.

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Acknowledgements

The authors express their sincere gratitude to the Director, CSIR-NGRI, Hyderabad, for his continuous support of the research activity. The authors express their sincere thanks to the Editor-in-Chief for his encouragement and support. The author also thanks the anonymous reviewers for their constructive and scientific suggestions for improving the manuscript standard. The manuscript Reference No. is NGRI/Lib/2024/Pub-009.

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Ayushi Agarwal: formal analysis, investigation, methodology, software, figure preparation, validation, and manuscript writing.

Ratnakar Dhakate: conceptualization, supervision, data curation, methodology, validation, review and editing.

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Agarwal, A., Dhakate, R. Quality and health impact of groundwater in a coastal region: a case study from west coast of southern India. Environ Sci Pollut Res (2024). https://doi.org/10.1007/s11356-024-34930-2

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Received : 17 January 2024

Accepted : 03 September 2024

Published : 12 September 2024

DOI : https://doi.org/10.1007/s11356-024-34930-2

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• Published: 08 September 2024

Longitudinal analysis of teacher self-efficacy evolution during a STEAM professional development program: a qualitative case study

• Haozhe Jiang   ORCID: orcid.org/0000-0002-7870-0993 1 ,
• Ritesh Chugh   ORCID: orcid.org/0000-0003-0061-7206 2 ,
• Xuesong Zhai   ORCID: orcid.org/0000-0002-4179-7859 1 , 3   nAff7 ,
• Ke Wang 4 &
• Xiaoqin Wang 5 , 6  

Humanities and Social Sciences Communications volume  11 , Article number:  1162 ( 2024 ) Cite this article

Metrics details

Despite the widespread advocacy for the integration of arts and humanities (A&H) into science, technology, engineering, and mathematics (STEM) education on an international scale, teachers face numerous obstacles in practically integrating A&H into STEM teaching (IAT). To tackle the challenges, a comprehensive five-stage framework for teacher professional development programs focussed on IAT has been developed. Through the use of a qualitative case study approach, this study outlines the shifts in a participant teacher’s self-efficacy following their exposure to each stage of the framework. The data obtained from interviews and reflective analyses were analyzed using a seven-stage inductive method. The findings have substantiated the significant impact of a teacher professional development program based on the framework on teacher self-efficacy, evident in both individual performance and student outcomes observed over eighteen months. The evolution of teacher self-efficacy in IAT should be regarded as an open and multi-level system, characterized by interactions with teacher knowledge, skills and other entrenched beliefs. Building on our research findings, an enhanced model of teacher professional learning is proposed. The revised model illustrates that professional learning for STEAM teachers should be conceived as a continuous and sustainable process, characterized by the dynamic interaction among teaching performance, teacher knowledge, and teacher beliefs. The updated model further confirms the inseparable link between teacher learning and student learning within STEAM education. This study contributes to the existing body of literature on teacher self-efficacy, teacher professional learning models and the design of IAT teacher professional development programs.

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Introduction.

In the past decade, there has been a surge in the advancement and widespread adoption of Science, Technology, Engineering, and Mathematics (STEM) education on a global scale (Jiang et al. 2021 ; Jiang et al. 2022 ; Jiang et al. 2023 ; Jiang et al. 2024a , b ; Zhan et al. 2023 ; Zhan and Niu 2023 ; Zhong et al. 2022 ; Zhong et al. 2024 ). Concurrently, there has been a growing chorus of advocates urging the integration of Arts and Humanities (A&H) into STEM education (e.g., Alkhabra et al. 2023 ; Land 2020 ; Park and Cho 2022 ; Uştu et al. 2021 ; Vaziri and Bradburn 2021 ). STEM education is frequently characterized by its emphasis on logic and analysis; however, it may be perceived as deficient in emotional and intuitive elements (Ozkan and Umdu Topsakal 2021 ). Through the integration of Arts and Humanities (A&H), the resulting STEAM approach has the potential to become more holistic, incorporating both rationality and emotional intelligence (Ozkan and Umdu Topsakal 2021 ). Many studies have confirmed that A&H can help students increase interest and develop their understanding of the contents in STEM fields, and thus, A&H can attract potential underrepresented STEM learners such as female students and minorities (Land 2020 ; Park and Cho 2022 ; Perignat and Katz-Buonincontro 2019 ). Despite the increasing interest in STEAM, the approaches to integrating A&H, which represent fundamentally different disciplines, into STEM are theoretically and practically ambiguous (Jacques et al. 2020 ; Uştu et al. 2021 ). Moreover, studies have indicated that the implementation of STEAM poses significant challenges, with STEM educators encountering difficulties in integrating A&H into their teaching practices (e.g., Boice et al. 2021 ; Duong et al. 2024 ; Herro et al. 2019 ; Jacques et al. 2020 ; Park and Cho 2022 ; Perignat and Katz-Buonincontro 2019 ). Hence, there is a pressing need to provide STEAM teachers with effective professional training.

Motivated by this gap, this study proposes a novel five-stage framework tailored for teacher professional development programs specifically designed to facilitate the integration of A&H into STEM teaching (IAT). Following the establishment of this framework, a series of teacher professional development programs were implemented. To explain the framework, a qualitative case study is employed, focusing on examining a specific teacher professional development program’s impact on a pre-service teacher’s self-efficacy. The case narratives, with a particular focus on the pre-service teacher’s changes in teacher self-efficacy, are organized chronologically, delineating stages before and after each stage of the teacher professional development program. More specifically, meaningful vignettes of the pre-service teacher’s learning and teaching experiences during the teacher professional development program are offered to help understand the five-stage framework. This study contributes to understanding teacher self-efficacy, teacher professional learning model and the design of IAT teacher professional development programs.

Theoretical background

The conceptualization of steam education.

STEM education can be interpreted through various lenses (e.g., Jiang et al. 2021 ; English 2016 ). As Li et al. (2020) claimed, on the one hand, STEM education can be defined as individual STEM disciplinary-based education (i.e., science education, technology education, engineering education and mathematics education). On the other hand, STEM education can also be defined as interdisciplinary or cross-disciplinary education where individual STEM disciplines are integrated (Jiang et al. 2021 ; English 2016 ). In this study, we view it as individual disciplinary-based education separately in science, technology, engineering and mathematics (English 2016 ).

STEAM education emerged as a new pedagogy during the Americans for the Arts-National Policy Roundtable discussion in 2007 (Perignat and Katz-Buonincontro 2019 ). This pedagogy was born out of the necessity to enhance students’ engagement, foster creativity, stimulate innovation, improve problem-solving abilities, and cultivate employability skills such as teamwork, communication and adaptability (Perignat and Katz-Buonincontro 2019 ). In particular, within the framework of STEAM education, the ‘A’ should be viewed as a broad concept that represents arts and humanities (A&H) (Herro and Quigley 2016 ; de la Garza 2021 , Park and Cho 2022 ). This conceptualization emphasizes the need to include humanities subjects alongside arts (Herro and Quigley 2016 ; de la Garza 2021 ; Park and Cho 2022 ). Sanz-Camarero et al. ( 2023 ) listed some important fields of A&H, including physical arts, fine arts, manual arts, sociology, politics, philosophy, history, psychology and so on.

In general, STEM education does not necessarily entail the inclusion of all STEM disciplines collectively (Ozkan and Umdu Topsakal 2021 ), and this principle also applies to STEAM education (Gates 2017 ; Perignat and Katz-Buonincontro 2019 ; Quigley et al. 2017 ; Smith and Paré 2016 ). As an illustration, Smith and Paré ( 2016 ) described a STEAM activity in which pottery (representing A&H) and mathematics were integrated, while other STEAM elements such as science, technology and engineering were not included. In our study, STEAM education is conceptualized as an interdisciplinary approach that involves the integration of one or more components of A&H into one or more STEM school subjects within educational activities (Ozkan and Umdu Topsakal 2021 ; Vaziri and Bradburn 2021 ). Notably, interdisciplinary collaboration entails integrating one or more elements from arts and humanities (A&H) with one or more STEM school subjects, cohesively united by a shared theme while maintaining their distinct identities (Perignat and Katz-Buonincontro 2019 ).

In our teacher professional development programs, we help mathematics, technology, and science pre-service teachers integrate one component of A&H into their disciplinary-based teaching practices. For instance, we help mathematics teachers integrate history (a component of A&H) into mathematics teaching. In other words, in our study, integrating A&H into STEM teaching (IAT) can be defined as integrating one component of A&H into the teaching of one of the STEM school subjects. The components of A&H and the STEM school subject are brought together under a common theme, but each of them remains discrete. Engineering is not taught as an individual subject in the K-12 curriculum in mainland China. Therefore, A&H is not integrated into engineering teaching in our teacher professional development programs.

Self-efficacy and teacher self-efficacy

Self-efficacy was initially introduced by Bandura ( 1977 ) as a key concept within his social cognitive theory. Bandura ( 1997 ) defined self-efficacy as “people’s beliefs about their capabilities to produce designated levels of performance that exercise influence over events that affect their lives” (p. 71). Based on Bandura’s ( 1977 ) theory, Tschannen-Moran et al. ( 1998 ) defined the concept of teacher self-efficacy Footnote 1 as “a teacher’s belief in her or his ability to organize and execute the courses of action required to successfully accomplish a specific teaching task in a particular context” (p. 233). Blonder et al. ( 2014 ) pointed out that this definition implicitly included teachers’ judgment of their ability to bring about desired outcomes in terms of students’ engagement and learning. Moreover, OECD ( 2018 ) defined teacher self-efficacy as “the beliefs that teachers have of their ability to enact certain teaching behavior that influences students’ educational outcomes, such as achievement, interest, and motivation” (p. 51). This definition explicitly included two dimensions: teachers’ judgment of the ability related to their teaching performance (i.e., enacting certain teaching behavior) and their influence on student outcomes.

It is argued that teacher self-efficacy should not be regarded as a general or overarching construct (Zee et al. 2017 ; Zee and Koomen 2016 ). Particularly, in the performance-driven context of China, teachers always connect their beliefs in their professional capabilities with the educational outcomes of their students (Liu et al. 2018 ). Therefore, we operationally conceptualize teacher self-efficacy as having two dimensions: self-efficacy in individual performance and student outcomes (see Table 1 ).

Most importantly, given its consistent association with actual teaching performance and student outcomes (Bray-Clark and Bates 2003 ; Kelley et al. 2020 ), teacher self-efficacy is widely regarded as a pivotal indicator of teacher success (Kelley et al. 2020 ). Moreover, the enhancement of teaching self-efficacy reflects the effectiveness of teacher professional development programs (Bray-Clark and Bates 2003 ; Kelley et al. 2020 ; Wong et al. 2022 ; Zhou et al. 2023 ). For instance, Zhou et al. ( 2023 ) claimed that in STEM teacher education, effective teacher professional development programs should bolster teachers’ self-efficacy “in teaching the content in the STEM discipline” (p. 2).

It has been documented that teachers frequently experience diminished confidence and comfort when teaching subject areas beyond their expertise (Kelley et al. 2020 ; Stohlmann et al. 2012 ). This diminished confidence extends to their self-efficacy in implementing interdisciplinary teaching approaches, such as integrated STEM teaching and IAT (Kelley et al. 2020 ). For instance, Geng et al. ( 2019 ) found that STEM teachers in Hong Kong exhibited low levels of self-efficacy, with only 5.53% of teachers rating their overall self-efficacy in implementing STEM education as higher than a score of 4 out of 5. Additionally, Hunter-Doniger and Sydow ( 2016 ) found that teachers may experience apprehension and lack confidence when incorporating A&H elements into the classroom context, particularly within the framework of IAT. Considering the critical importance of teacher self-efficacy in STEM and STEAM education (Kelley et al. 2020 ; Zakariya, 2020 ; Zhou et al. 2023 ), it is necessary to explore effective measures, frameworks and teacher professional development programs to help teachers improve their self-efficacy regarding interdisciplinary teaching (e.g., IAT).

Teacher professional learning models

The relationship between teachers’ professional learning and students’ outcomes (such as achievements, skills and attitudes) has been a subject of extensive discussion and research for many years (Clarke and Hollingsworth 2002 ). For instance, Clarke and Hollingsworth ( 2002 ) proposed and validated the Interconnected Model of Professional Growth, which illustrates that teacher professional development is influenced by the interaction among four interconnected domains: the personal domain (teacher knowledge, beliefs and attitudes), the domain of practice (professional experimentation), the domain of consequence (salient outcomes), and the external domain (sources of information, stimulus or support). Sancar et al. ( 2021 ) emphasized that teachers’ professional learning or development never occurs independently. In practice, this process is inherently intertwined with many variables, including student outcomes, in various ways (Sancar et al. 2021 ). However, many current teacher professional development programs exclude real in-class teaching and fail to establish a comprehensive link between teachers’ professional learning and student outcomes (Cai et al. 2020 ; Sancar et al. 2021 ). Sancar et al. ( 2021 ) claimed that exploring the complex relationships between teachers’ professional learning and student outcomes should be grounded in monitoring and evaluating real in-class teaching, rather than relying on teachers’ self-assessment. It is essential to understand these relationships from a holistic perspective within the context of real classroom teaching (Sancar et al. 2021 ). However, as Sancar et al. ( 2021 ) pointed out, such efforts in teacher education are often considered inadequate. Furthermore, in the field of STEAM education, such efforts are further exacerbated.

Cai et al. ( 2020 ) proposed a teacher professional learning model where student outcomes are emphasized. This model was developed based on Cai ( 2017 ), Philipp ( 2007 ) and Thompson ( 1992 ). It has also been used and justified in a series of teacher professional development programs (e.g., Calabrese et al. 2024 ; Hwang et al. 2024 ; Marco and Palatnik 2024 ; Örnek and Soylu 2021 ). The model posits that teachers typically increase their knowledge and modify their beliefs through professional teacher learning, subsequently improving their classroom instruction, enhancing teaching performance, and ultimately fostering improved student learning outcomes (Cai et al. 2020 ). Notably, this model can be updated in several aspects. Firstly, prior studies have exhibited the interplay between teacher knowledge and beliefs (e.g., Basckin et al. 2021 ; Taimalu and Luik 2019 ). This indicates that the increase in teacher knowledge and the change in teacher belief may not be parallel. The two processes can be intertwined. Secondly, the Interconnected Model of Professional Growth highlights that the personal domain and the domain of practice are interconnected (Clarke and Hollingsworth 2002 ). Liu et al. ( 2022 ) also confirmed that improvements in classroom instruction may, in turn, influence teacher beliefs. This necessitates a reconsideration of the relationships between classroom instruction, teacher knowledge and teacher beliefs in Cai et al.’s ( 2020 ) model. Thirdly, the Interconnected Model of Professional Growth also exhibits the connections between the domain of consequence and the personal domain (Clarke and Hollingsworth 2002 ). Hence, the improvement of learning outcomes may signify the end of teacher learning. For instance, students’ learning feedback may be a vital source of teacher self-efficacy (Bandura 1977 ). Therefore, the improvement of student outcomes may, in turn, affect teacher beliefs. The aforementioned arguments highlight the need for an updated model that integrates Cai et al.’s ( 2020 ) teacher professional learning model with Clarke and Hollingsworth’s ( 2002 ) Interconnected Model of Professional Growth. This integration may provide a holistic view of the teacher’s professional learning process, especially within the complex contexts of STEAM teacher education.

The framework for teacher professional development programs of integrating arts and humanities into STEM teaching

In this section, we present a framework for IAT teacher professional development programs, aiming to address the practical challenges associated with STEAM teaching implementation. Our framework incorporates the five features of effective teacher professional development programs outlined by Archibald et al. ( 2011 ), Cai et al. ( 2020 ), Darling-Hammond et al. ( 2017 ), Desimone and Garet ( 2015 ) and Roth et al. ( 2017 ). These features include: (a) alignment with shared goals (e.g., school, district, and national policies and practice), (b) emphasis on core content and modeling of teaching strategies for the content, (c) collaboration among teachers within a community, (d) adequate opportunities for active learning of new teaching strategies, and (e) embedded follow-up and continuous feedback. It is worth noting that two concepts, namely community of practice and lesson study, have been incorporated into our framework. Below, we delineate how these features are reflected in our framework.

(a) The Chinese government has issued a series of policies to facilitate STEAM education in K-12 schools (Jiang et al. 2021 ; Li and Chiang 2019 ; Lyu et al. 2024 ; Ro et al. 2022 ). The new curriculum standards released in 2022 mandate that all K-12 teachers implement interdisciplinary teaching, including STEAM education. Our framework for teacher professional development programs, which aims to help teachers integrate A&H into STEM teaching, closely aligns with these national policies and practices supporting STEAM education in K-12 schools.

(b) The core content of the framework is IAT. Specifically, as A&H is a broad concept, we divide it into several subcomponents, such as history, culture, and visual and performing arts (e.g., drama). We are implementing a series of teacher professional development programs to help mathematics, technology and science pre-service teachers integrate these subcomponents of A&H into their teaching Footnote 2 . Notably, pre-service teachers often lack teaching experience, making it challenging to master and implement new teaching strategies. Therefore, our framework provides five step-by-step stages designed to help them effectively model the teaching strategies of IAT.

(c) Our framework advocates for collaboration among teachers within a community of practice. Specifically, a community of practice is “a group of people who share an interest in a domain of human endeavor and engage in a process of collective learning that creates bonds between them” (Wenger et al. 2002 , p. 1). A teacher community of practice can be considered a group of teachers “sharing and critically observing their practices in growth-promoting ways” (Näykki et al. 2021 , p. 497). Long et al. ( 2021 ) claimed that in a teacher community of practice, members collaboratively share their teaching experiences and work together to address teaching problems. Our community of practice includes three types of members. (1) Mentors: These are professors and experts with rich experience in helping pre-service teachers practice IAT. (2) Pre-service teachers: Few have teaching experience before the teacher professional development programs. (3) In-service teachers: All in-service teachers are senior teachers with rich teaching experience. All the members work closely together to share and improve their IAT practice. Moreover, our community includes not only mentors and in-service teachers but also pre-service teachers. We encourage pre-service teachers to collaborate with experienced in-service teachers in various ways, such as developing IAT lesson plans, writing IAT case reports and so on. In-service teachers can provide cognitive and emotional support and share their practical knowledge and experience, which may significantly benefit the professional growth of pre-service teachers (Alwafi et al. 2020 ).

(d) Our framework offers pre-service teachers various opportunities to engage in lesson study, allowing them to actively design and implement IAT lessons. Based on the key points of effective lesson study outlined by Akiba et al. ( 2019 ), Ding et al. ( 2024 ), and Takahashi and McDougal ( 2016 ), our lesson study incorporates the following seven features. (1) Study of IAT materials: Pre-service teachers are required to study relevant IAT materials under the guidance of mentors. (2) Collaboration on lesson proposals: Pre-service teachers should collaborate with in-service teachers to develop comprehensive lesson proposals. (3) Observation and data collection: During the lesson, pre-service teachers are required to carefully observe and collect data on student learning and development. (4) Reflection and analysis: Pre-service teachers use the collected data to reflect on the lesson and their teaching effects. (5) Lesson revision and reteaching: If needed, pre-service teachers revise and reteach the lesson based on their reflections and data analysis. (6) Mentor and experienced in-service teacher involvement: Mentors and experienced in-service teachers, as knowledgeable others, are involved throughout the lesson study process. (7) Collaboration on reporting: Pre-service teachers collaborate with in-service teachers to draft reports and disseminate the results of the lesson study. Specifically, recognizing that pre-service teachers often lack teaching experience, we do not require them to complete all the steps of lesson study independently at once. Instead, we guide them through the lesson study process in a step-by-step manner, allowing them to gradually build their IAT skills and confidence. For instance, in Stage 1, pre-service teachers primarily focus on studying IAT materials. In Stage 2, they develop lesson proposals, observe and collect data, and draft reports. However, the implementation of IAT lessons is carried out by in-service teachers. This approach prevents pre-service teachers from experiencing failures due to their lack of teaching experience. In Stage 3, pre-service teachers implement, revise, and reteach IAT lessons, experiencing the lesson study process within a simulated environment. In Stage 4, pre-service teachers engage in lesson study in an actual classroom environment. However, their focus is limited to one micro-course during each lesson study session. It is not until the fifth stage that they experience a complete lesson study in an actual classroom environment.

(e) Our teacher professional development programs incorporate assessments specifically designed to evaluate pre-service teachers’ IAT practices. We use formative assessments to measure their understanding and application of IAT strategies. Pre-service teachers receive ongoing and timely feedback from peers, mentors, in-service teachers, and students, which helps them continuously refine their IAT practices throughout the program. Recognizing that pre-service teachers often have limited contact with real students and may not fully understand students’ learning needs, processes and outcomes, our framework requires them to actively collect and analyze student feedback. By doing so, they can make informed improvements to their instructional practice based on student feedback.

After undergoing three rounds of theoretical and practical testing and revision over the past five years, we have successfully finalized the optimization of the framework design (Zhou 2021 ). Throughout each cycle, we collected feedback from both participants and researchers on at least three occasions. Subsequently, we analyzed this feedback and iteratively refined the framework. For example, we enlisted the participation of in-service teachers to enhance the implementation of STEAM teaching, extended practice time through micro-teaching sessions, and introduced a stage of micro-course development within the framework to provide more opportunities for pre-service teachers to engage with real teaching situations. In this process, we continuously improved the coherence between each stage of the framework, ensuring that they mutually complement one another. The five-stage framework is described as follows.

Stage 1 Literature study

Pre-service teachers are provided with a series of reading materials from A&H. On a weekly basis, two pre-service teachers are assigned to present their readings and reflections to the entire group, followed by critical discussions thereafter. Mentors and all pre-service teachers discuss and explore strategies for translating the original A&H materials into viable instructional resources suitable for classroom use. Subsequently, pre-service teachers select topics of personal interest for further study under mentor guidance.

Stage 2 Case learning

Given that pre-service teachers have no teaching experience, collaborative efforts between in-service teachers and pre-service teachers are undertaken to design IAT lesson plans. Subsequently, the in-service teachers implement these plans. Throughout this process, pre-service teachers are afforded opportunities to engage in lesson plan implementation. Figure 1 illustrates the role of pre-service teachers in case learning. In the first step, pre-service teachers read about materials related to A&H, select suitable materials, and report their ideas on IAT lesson design to mentors, in-service teachers, and fellow pre-service teachers.

Note: A&H refers to arts and humanities.

In the second step, they liaise with the in-service teachers responsible for implementing the lesson plan, discussing the integration of A&H into teaching practices. Pre-service teachers then analyze student learning objectives aligned with curriculum standards, collaboratively designing the IAT lesson plan with in-service teachers. Subsequently, pre-service teachers present lesson plans for feedback from mentors and other in-service teachers.

In the third step, pre-service teachers observe the lesson plan’s implementation, gathering and analyzing feedback from students and in-service teachers using an inductive approach (Merriam 1998 ). Feedback includes opinions on the roles and values of A&H, perceptions of the teaching effect, and recommendations for lesson plan implementation and modification. The second and third steps may iterate multiple times to refine the IAT lesson plan. In the fourth step, pre-service teachers consolidate all data, including various versions of teaching instructions, classroom videos, feedback, and discussion notes, composing reflection notes. Finally, pre-service teachers collaborate with in-service teachers to compile the IAT case report and submit it for publication.

Stage 3 Micro-teaching

Figure 2 illustrates the role of pre-service teachers in micro-teaching. Before entering the micro-classrooms Footnote 3 , all the discussions and communications occur within the pre-service teacher group, excluding mentors and in-service teachers. After designing the IAT lesson plan, pre-service teachers take turns implementing 40-min lesson plans in a simulated micro-classroom setting. Within this simulated environment, one pre-service teacher acts as the teacher, while others, including mentors, in-service teachers, and other fellow pre-service teachers, assume the role of students Footnote 4 . Following the simulated teaching, the implementer reviews the video of their session and self-assesses their performance. Subsequently, the implementer receives feedback from other pre-service teachers, mentors, and in-service teachers. Based on this feedback, the implementer revisits steps 2 and 3, revising the lesson plan and conducting the simulated teaching again. This iterative process typically repeats at least three times until the mentors, in-service teachers, and other pre-service teachers are satisfied with the implementation of the revised lesson plan. Finally, pre-service teachers complete reflection notes and submit a summary of their reflections on the micro-teaching experience. Each pre-service teacher is required to choose at least three topics and undergo at least nine simulated teaching sessions.

Stage 4 Micro-course development

While pre-service teachers may not have the opportunity to execute the whole lesson plans in real classrooms, they can design and create five-minute micro-courses Footnote 5 before class, subsequently presenting these videos to actual students. The process of developing micro-courses closely mirrors that of developing IAT cases in the case learning stage (see Fig. 1 ). However, in Step 3, pre-service teachers assume dual roles, not only as observers of IAT lesson implementation but also as implementers of a five-minute IAT micro-course.

Stage 5 Classroom teaching

Pre-service teachers undertake the implementation of IAT lesson plans independently, a process resembling micro-teaching (see Fig. 2 ). However, pre-service teachers engage with real school students in partner schools Footnote 6 instead of simulated classrooms. Furthermore, they collect feedback not only from the mentors, in-service teachers, and fellow pre-service teachers but also from real students.

To provide our readers with a better understanding of the framework, we provide meaningful vignettes of a pre-service teacher’s learning and teaching experiences in one of the teacher professional development programs based on the framework. In addition, we choose teacher self-efficacy as an indicator to assess the framework’s effectiveness, detailing the pre-service teacher’s changes in teacher self-efficacy.

Research design

Research method.

Teacher self-efficacy can be measured both quantitatively and qualitatively (Bandura 1986 , 1997 ; Lee and Bobko 1994 ; Soprano and Yang 2013 ; Unfried et al. 2022 ). However, researchers and theorists in the area of teacher self-efficacy have called for more qualitative and longitudinal studies (Klassen et al. 2011 ). As some critiques stated, most studies were based on correlational and cross-sectional data obtained from self-report surveys, and qualitative studies of teacher efficacy were overwhelmingly neglected (Henson 2002 ; Klassen et al. 2011 ; Tschannen-Moran et al. 1998 ; Xenofontos and Andrews 2020 ). There is an urgent need for more longitudinal studies to shed light on the development of teacher efficacy (Klassen et al. 2011 ; Xenofontos and Andrews 2020 ).

This study utilized a longitudinal qualitative case study methodology to delve deeply into the context (Jiang et al. 2021 ; Corden and Millar 2007 ; Dicks et al. 2023 ; Henderson et al. 2012 ; Matusovich et al. 2010 ; Shirani and Henwood 2011 ), presenting details grounded in real-life situations and analyzing the inner relationships rather than generalize findings about the change of a large group of pre-service teachers’ self-efficacy.

Participant

This study forms a component of a broader multi-case research initiative examining teachers’ professional learning in the STEAM teacher professional development programs in China (Jiang et al. 2021 ; Wang et al. 2018 ; Wang et al. 2024 ). Within this context, one participant, Shuitao (pseudonym), is selected and reported in this current study. Shuitao was a first-year graduate student at a first-tier Normal university in Shanghai, China. Normal universities specialize in teacher education. Her graduate major was mathematics curriculum and instruction. Teaching practice courses are offered to students in this major exclusively during their third year of study. The selection of Shuitao was driven by three primary factors. Firstly, Shuitao attended the entire teacher professional development program and actively engaged in nearly all associated activities. Table 2 illustrates the timeline of the five stages in which Shuitao was involved. Secondly, her undergraduate major was applied mathematics, which was not related to mathematics teaching Footnote 7 . She possessed no prior teaching experience and had not undergone any systematic study of IAT before her involvement in the teacher professional development program. Thirdly, her other master’s courses during her first two years of study focused on mathematics education theory and did not include IAT Footnote 8 . Additionally, she scarcely participated in any other teaching practice outside of the teacher professional development program. As a pre-service teacher, Shuitao harbored a keen interest in IAT. Furthermore, she discovered that she possessed fewer teaching skills compared to her peers who had majored in education during their undergraduate studies. Hence, she had a strong desire to enhance her teaching skills. Consequently, Shuitao decided to participate in our teacher professional development program.

Shuitao was grouped with three other first-year graduate students during the teacher professional development program. She actively collaborated with them at every stage of the program. For instance, they advised each other on their IAT lesson designs, observed each other’s IAT practice and offered constructive suggestions for improvement.

Research question

Shuitao was a mathematics pre-service teacher who participated in one of our teacher professional development programs, focusing on integrating history into mathematics teaching (IHT) Footnote 9 . Notably, this teacher professional development program was designed based on our five-stage framework for teacher professional development programs of IAT. To examine the impact of this teacher professional development program on Shuitao’s self-efficacy related to IHT, this case study addresses the following research question:

What changes in Shuitao’s self-efficacy in individual performance regarding integrating history into mathematics teaching (SE-IHT-IP) may occur through participation in the teacher professional development program?

What changes in Shuitao’s self-efficacy in student outcomes regarding integrating history into mathematics teaching (SE-IHT-SO) may occur through participation in the teacher professional development program?

Data collection and analysis

Before Shuitao joined the teacher professional development program, a one-hour preliminary interview was conducted to guide her in self-narrating her psychological and cognitive state of IHT.

During the teacher professional development program, follow-up unstructured interviews were conducted once a month with Shuitao. All discussions in the development of IHT cases were recorded, Shuitao’s teaching and micro-teaching were videotaped, and the reflection notes, journals, and summary reports written by Shuitao were collected.

After completing the teacher professional development program, Shuitao participated in a semi-structured three-hour interview. The objectives of this interview were twofold: to reassess her self-efficacy and to explore the relationship between her self-efficacy changes and each stage of the teacher professional development program.

Interview data, discussions, reflection notes, journals, summary reports and videos, and analysis records were archived and transcribed before, during, and after the teacher professional development program.

In this study, we primarily utilized data from seven interviews: one conducted before the teacher professional development program, five conducted after each stage of the program, and one conducted upon completion of the program. Additionally, we reviewed Shuitao’s five reflective notes, which were written after each stage, as well as her final summary report that encompassed the entire teacher professional development program.

Merriam’s ( 1998 ) approach to coding data and inductive approach to retrieving possible concepts and themes were employed using a seven-stage method. Considering theoretical underpinnings in qualitative research is common when interpreting data (Strauss and Corbin 1990 ). First, a list based on our conceptual framework of teacher self-efficacy (see Table 1 ) was developed. The list included two codes (i.e., SE-IHT-IP and SE-IHT-SO). Second, all data were sorted chronologically, read and reread to be better understood. Third, texts were coded into multi-colored highlighting and comment balloons. Fourth, the data for groups of meanings, themes, and behaviors were examined. How these groups were connected within the conceptual framework of teacher self-efficacy was confirmed. Fifth, after comparing, confirming, and modifying, the selective codes were extracted and mapped onto the two categories according to the conceptual framework of teacher self-efficacy. Accordingly, changes in SE-IHT-IP and SE-IHT-SO at the five stages of the teacher professional development program were identified, respectively, and then the preliminary findings came (Strauss and Corbin 1990 ). In reality, in Shuitao’s narratives, SE-IHT-IP and SE-IHT-SO were frequently intertwined. Through our coding process, we differentiated between SE-IHT-IP and SE-IHT-SO, enabling us to obtain a more distinct understanding of how these two aspects of teacher self-efficacy evolved over time. This helped us address the two research questions effectively.

Reliability and validity

Two researchers independently analyzed the data to establish inter-rater reliability. The inter-rater reliability was established as kappa = 0.959. Stake ( 1995 ) suggested that the most critical assertions in a study require the greatest effort toward confirmation. In this study, three methods served this purpose and helped ensure the validity of the findings. The first way to substantiate the statement about the changes in self-efficacy was by revisiting each transcript to confirm whether the participant explicitly acknowledged the changes (Yin 2003 ). Such a check was repeated in the analysis of this study. The second way to confirm patterns in the data was by examining whether Shuitao’s statements were replicated in separate interviews (Morris and Usher 2011 ). The third approach involved presenting the preliminary conclusions to Shuitao and affording her the opportunity to provide feedback on the data and conclusions. This step aimed to ascertain whether we accurately grasped the true intentions of her statements and whether our subjective interpretations inadvertently influenced our analysis of her statements. Additionally, data from diverse sources underwent analysis by at least two researchers, with all researchers reaching consensus on each finding.

As each stage of our teacher professional development programs spanned a minimum of three months, numerous documented statements regarding the enhancement of Shuitao’s self-efficacy regarding IHT were recorded. Notably, what we present here offers only a concise overview of findings derived from our qualitative analysis. The changes in Shuitao’s SE-IHT-IP and SE-IHT-SO are organized chronologically, delineating the period before and during the teacher professional development program.

Before the teacher professional development program: “I have no confidence in IHT”

Before the teacher professional development program, Shuitao frequently expressed her lack of confidence in IHT. On the one hand, Shuitao expressed considerable apprehension about her individual performance in IHT. “How can I design and implement IHT lesson plans? I do not know anything [about it]…” With a sense of doubt, confusion and anxiety, Shuitao voiced her lack of confidence in her ability to design and implement an IHT case that would meet the requirements of the curriculum standards. Regarding the reasons for her lack of confidence, Shuitao attributed it to her insufficient theoretical knowledge and practical experience in IHT:

I do not know the basic approaches to IHT that I could follow… it is very difficult for me to find suitable historical materials… I am very confused about how to organize [historical] materials logically around the teaching goals and contents… [Furthermore,] I am [a] novice, [and] I have no IHT experience.

On the other hand, Shuitao articulated very low confidence in the efficacy of her IHT on student outcomes:

I think my IHT will have a limited impact on student outcomes… I do not know any specific effects [of history] other than making students interested in mathematics… In fact, I always think it is difficult for [my] students to understand the history… If students cannot understand [the history], will they feel bored?

This statement suggests that Shuitao did not fully grasp the significance of IHT. In fact, she knew little about the educational significance of history for students, and she harbored no belief that her IHT approach could positively impact students. In sum, her SE-IHT-SO was very low.

After stage 1: “I can do well in the first step of IHT”

After Stage 1, Shuitao indicated a slight improvement in her confidence in IHT. She attributed this improvement to her acquisition of theoretical knowledge in IHT, the approaches for selecting history-related materials, and an understanding of the educational value of history.

One of Shuitao’s primary concerns about implementing IHT before the teacher professional development program was the challenge of sourcing suitable history-related materials. However, after Stage 1, Shuitao explicitly affirmed her capability in this aspect. She shared her experience of organizing history-related materials related to logarithms as an example.

Recognizing the significance of suitable history-related materials in effective IHT implementation, Shuitao acknowledged that conducting literature studies significantly contributed to enhancing her confidence in undertaking this initial step. Furthermore, she expressed increased confidence in designing IHT lesson plans by utilizing history-related materials aligned with teaching objectives derived from the curriculum standards. In other words, her SE-IHT-IP was enhanced. She said:

After experiencing multiple discussions, I gradually know more about what kinds of materials are essential and should be emphasized, what kinds of materials should be adapted, and what kinds of materials should be omitted in the classroom instructions… I have a little confidence to implement IHT that could meet the requirements [of the curriculum standards] since now I can complete the critical first step [of IHT] well…

However, despite the improvement in her confidence in IHT following Stage 1, Shuitao also expressed some concerns. She articulated uncertainty regarding her performance in the subsequent stages of the teacher professional development program. Consequently, her confidence in IHT experienced only a modest increase.

After stage 2: “I participate in the development of IHT cases, and my confidence is increased a little bit more”

Following Stage 2, Shuitao reported further increased confidence in IHT. She attributed this growth to two main factors. Firstly, she successfully developed several instructional designs for IHT through collaboration with in-service teachers. These collaborative experiences enabled her to gain a deeper understanding of IHT approaches and enhance her pedagogical content knowledge in this area, consequently bolstering her confidence in her ability to perform effectively. Secondly, Shuitao observed the tangible impact of IHT cases on students in real classroom settings, which reinforced her belief in the efficacy of IHT. These experiences instilled in her a greater sense of confidence in her capacity to positively influence her students through her implementation of IHT. Shuitao remarked that she gradually understood how to integrate suitable history-related materials into her instructional designs (e.g., employ a genetic approach Footnote 10 ), considering it as the second important step of IHT. She shared her experience of developing IHT instructional design on the concept of logarithms. After creating several iterations of IHT instructional designs, Shuitao emphasized that her confidence in SE-IHT-IP has strengthened. She expressed belief in her ability to apply these approaches to IHT, as well as the pedagogical content knowledge of IHT, acquired through practical experience, in her future teaching endeavors. The following is an excerpt from the interview:

I learned some effective knowledge, skills, techniques and approaches [to IHT]… By employing these approaches, I thought I could [and] I had the confidence to integrate the history into instructional designs very well… For instance, [inspired] by the genetic approach, we designed a series of questions and tasks based on the history of logarithms. The introduction of the new concept of logarithms became very natural, and it perfectly met the requirements of our curriculum standards, [which] asked students to understand the necessity of learning the concept of logarithms…

Shuitao actively observed the classroom teaching conducted by her cooperating in-service teacher. She helped her cooperating in-service teacher in collecting and analyzing students’ feedback. Subsequently, discussions ensued on how to improve the instructional designs based on this feedback. The refined IHT instructional designs were subsequently re-implemented by the in-service teacher. After three rounds of developing IHT cases, Shuitao became increasingly convinced of the significance and efficacy of integrating history into teaching practices, as evidenced by the following excerpt:

The impacts of IHT on students are visible… For instance, more than 93% of the students mentioned in the open-ended questionnaires that they became more interested in mathematics because of the [historical] story of Napier… For another example, according to the results of our surveys, more than 75% of the students stated that they knew log a ( M  +  N ) = log a M  × log a N was wrong because of history… I have a little bit more confidence in the effects of my IHT on students.

This excerpt highlights that Shuitao’s SE-IHT-SO was enhanced. She attributed this enhancement to her realization of the compelling nature of history and her belief in her ability to effectively leverage its power to positively influence her students’ cognitive and emotional development. This also underscores the importance of reinforcing pre-service teachers’ awareness of the significance of history. Nonetheless, Shuiato elucidated that she still retained concerns regarding the effectiveness of her IHT implementation. Her following statement shed light on why her self-efficacy only experienced a marginal increase in this stage:

Knowing how to do it successfully and doing it successfully in practice are two totally different things… I can develop IHT instructional designs well, but I have no idea whether I can implement them well and whether I can introduce the history professionally in practice… My cooperation in-service teacher has a long history of teaching mathematics and gains rich experience in educational practices… If I cannot acquire some required teaching skills and capabilities, I still cannot influence my students powerfully.

After stage 3: “Practice makes perfect, and my SE-IHT-IP is steadily enhanced after a hit”

After successfully developing IHT instructional designs, the next critical step was the implementation of these designs. Drawing from her observations of her cooperating in-service teachers’ IHT implementations and discussions with other pre-service teachers, Shuitao developed her own IHT lesson plans. In Stage 3, she conducted simulated teaching sessions and evaluated her teaching performance ten times Footnote 11 . Shuitao claimed that her SE-IHT-IP steadily improved over the course of these sessions. According to Shuitao, two main processes in Stage 3 facilitated this steady enhancement of SE-IHT-IP.

On the one hand, through the repeated implementation of simulated teaching sessions, Shuitao’s teaching proficiency and fluency markedly improved. Shuitao first described the importance of teaching proficiency and fluency:

Since the detailed history is not included in our curriculum standards and textbooks, if I use my historical materials in class, I have to teach more contents than traditional teachers. Therefore, I have to teach proficiently so that teaching pace becomes a little faster than usual… I have to teach fluently so as to use each minute efficiently in my class. Otherwise, I cannot complete the teaching tasks required [by curriculum standards].

As Shuitao said, at the beginning of Stage 3, her self-efficacy even decreased because she lacked teaching proficiency and fluency and was unable to complete the required teaching tasks:

In the first few times of simulated teaching, I always needed to think for a second about what I should say next when I finish one sentence. I also felt very nervous when I stood in the front of the classrooms. This made my narration of the historical story between Briggs and Napier not fluent at all. I paused many times to look for some hints on my notes… All these made me unable to complete the required teaching tasks… My [teaching] confidence took a hit.

Shuitao quoted the proverb, “practice makes perfect”, and she emphasized that it was repeated practice that improved her teaching proficiency and fluency:

I thought I had no other choice but to practice IHT repeatedly… [At the end of Stage 3,] I could naturally remember most words that I should say when teaching the topics that I selected… My teaching proficiency and fluency was improved through my repeated review of my instructional designs and implementation of IHT in the micro-classrooms… With the improvement [of my teaching proficiency and fluency], I could complete the teaching tasks, and my confidence was increased as well.

In addition, Shuitao also mentioned that through this kind of self-exploration in simulated teaching practice, her teaching skills and capabilities (e.g., blackboard writing, abilities of language organization abilities, etc.) improved. This process was of great help to her enhancement of SE-IHT-IP.

On the other hand, Shuitao’s simulated teaching underwent assessment by herself, with mentors, in-service teachers and fellow pre-service teachers. This comprehensive evaluation process played a pivotal role in enhancing her individual performance and self-efficacy. Reflecting on this aspect, Shuitao articulated the following sentiments in one of her reflection reports:

By watching the videos, conducting self-assessment, and collecting feedback from others, I can understand what I should improve or emphasize in my teaching. [Then,] I think my IHT can better meet the requirements [of curriculum standards]… I think my teaching performance is getting better and better.

After stage 4: “My micro-courses influenced students positively, and my SE-IHT-SO is steadily enhanced”

In Stage 4, Shuitao commenced by creating 5-min micro-course videos. Subsequently, she played these videos in her cooperating in-service teachers’ authentic classroom settings and collected student feedback. This micro-course was played at the end of her cooperating in-service teachers’ lesson Footnote 12 . Shuitao wrote in her reflections that this micro-course of logarithms helped students better understand the nature of mathematics:

According to the results of our surveys, many students stated that they knew the development and evolution of the concept of logarithms is a long process and many mathematicians from different countries have contributed to the development of the concept of logarithms… This indicated that my micro-course helped students better understand the nature of mathematics… My micro-course about the history informed students that mathematics is an evolving and human subject and helped them understand the dynamic development of the [mathematics] concept…

Meanwhile, Shuitao’s micro-course positively influenced some students’ beliefs towards mathematics. As evident from the quote below, integrating historical context into mathematics teaching transformed students’ perception of the subject, boosting Shuitao’s confidence too.

Some students’ responses were very exciting… [O]ne [typical] response stated, he always regarded mathematics as abstract, boring, and dreadful subject; but after seeing the photos of mathematicians and great men and learning the development of the concept of logarithms through the micro-course, he found mathematics could be interesting. He wanted to learn more the interesting history… Students’ such changes made me confident.

Furthermore, during post-class interviews, several students expressed their recognition of the significance of the logarithms concept to Shuitao, attributing this realization to the insights provided by prominent figures in the micro-courses. They also conveyed their intention to exert greater effort in mastering the subject matter. This feedback made Shuitao believe that her IHT had the potential to positively influence students’ attitudes towards learning mathematics.

In summary, Stage 4 marked Shuitao’s first opportunity to directly impact students through her IHT in authentic classroom settings. Despite implementing only brief 5-min micro-courses integrating history during each session, the effectiveness of her short IHT implementation was validated by student feedback. Shuitao unequivocally expressed that students actively engaged with her micro-courses and that these sessions positively influenced them, including attitudes and motivation toward mathematics learning, understanding of mathematics concepts, and beliefs regarding mathematics. These collective factors contributed to a steady enhancement of her confidence in SE-IHT-SO.

After stage 5: “My overall self-efficacy is greatly enhanced”

Following Stage 5, Shuitao reported a significant increase in her overall confidence in IHT, attributing it to gaining mastery through successful implementations of IHT in real classroom settings. On the one hand, Shuitao successfully designed and executed her IHT lesson plans, consistently achieving the teaching objectives mandated by curriculum standards. This significantly enhanced her SE-IHT-IP. On the other hand, as Shuitao’s IHT implementation directly influenced her students, her confidence in SE-IHT-SO experienced considerable improvement.

According to Bandura ( 1997 ), mastery experience is the most powerful source of self-efficacy. Shuitao’s statements confirmed this. As she claimed, her enhanced SE-IHT-IP in Stage 5 mainly came from the experience of successful implementations of IHT in real classrooms:

[Before the teacher professional development program,] I had no idea about implementing IHT… Now, I successfully implemented IHT in senior high school [classrooms] many times… I can complete the teaching tasks and even better completed the teaching objectives required [by the curriculum standards]… The successful experience greatly enhances my confidence to perform well in my future implementation of IHT… Yeah, I think the successful teaching practice experience is the strongest booster of my confidence.

At the end of stage 5, Shuitao’s mentors and in-service teachers gave her a high evaluation. For instance, after Shuitao’s IHT implementation of the concept of logarithms, all mentors and in-service teachers consistently provided feedback that her IHT teaching illustrated the necessity of learning the concept of logarithms and met the requirements of the curriculum standards very well. This kind of verbal persuasion (Bandura 1997 ) enhanced her SE-IHT-IP.

Similarly, Shuitao’s successful experience of influencing students positively through IHT, as one kind of mastery experience, powerfully enhanced her SE-IHT-SO. She described her changes in SE-IHT-SO as follows:

I could not imagine my IHT could be so influential [before]… But now, my IHT implementation directly influenced students in so many aspects… When I witnessed students’ real changes in various cognitive and affective aspects, my confidence was greatly improved.

Shuitao described the influence of her IHT implementation of the concept of logarithms on her students. The depiction is grounded in the outcomes of surveys conducted by Shuitao following her implementation. Shuitao asserted that these results filled her with excitement and confidence regarding her future implementation of IHT.

In summary, following Stage 5 of the teacher professional development program, Shuitao experienced a notable enhancement in her overall self-efficacy, primarily attributed to her successful practical experience in authentic classroom settings during this stage.

A primary objective of our teacher professional development programs is to equip pre-service teachers with the skills and confidence needed to effectively implement IAT. Our findings show that one teacher professional development program, significantly augmented a participant’s TSE-IHT across two dimensions: individual performance and student outcomes. Considering the pressing need to provide STEAM teachers with effective professional training (e.g., Boice et al. 2021 ; Duong et al. 2024 ; Herro et al. 2019 ; Jacques et al. 2020 ; Park and Cho 2022 ; Perignat and Katz-Buonincontro 2019 ), the proposed five-stage framework holds significant promise in both theoretical and practical realms. Furthermore, this study offers a viable solution to address the prevalent issue of low levels of teacher self-efficacy in interdisciplinary teaching, including IAT, which is critical in STEAM education (Zhou et al. 2023 ). This study holds the potential to make unique contributions to the existing body of literature on teacher self-efficacy, teacher professional learning models and the design of teacher professional development programs of IAT.

Firstly, this study enhances our understanding of the development of teacher self-efficacy. Our findings further confirm the complexity of the development of teacher self-efficacy. On the one hand, the observed enhancement of the participant’s teacher self-efficacy did not occur swiftly but unfolded gradually through a protracted, incremental process. Moreover, it is noteworthy that the participant’s self-efficacy exhibited fluctuations, underscoring that the augmentation of teacher self-efficacy is neither straightforward nor linear. On the other hand, the study elucidated that the augmentation of teacher self-efficacy constitutes an intricate, multi-level system that interacts with teacher knowledge, skills, and other beliefs. This finding resonates with prior research on teacher self-efficacy (Morris et al. 2017 ; Xenofontos and Andrews 2020 ). For example, our study revealed that Shuitao’s enhancement of SE-IHT-SO may always be interwoven with her continuous comprehension of the significance of the A&H in classroom settings. Similarly, the participant progressively acknowledged the educational value of A&H in classroom contexts in tandem with the stepwise enhancement of SE-IHT-SO. Factors such as the participant’s pedagogical content knowledge of IHT, instructional design, and teaching skills were also identified as pivotal components of SE-IHT-IP. This finding corroborates Morris and Usher ( 2011 ) assertion that sustained improvements in self-efficacy stem from developing teachers’ skills and knowledge. With the bolstering of SE-IHT-IP, the participant’s related teaching skills and content knowledge also exhibited improvement.

Methodologically, many researchers advocate for qualitative investigations into self-efficacy (e.g., Philippou and Pantziara 2015; Klassen et al. 2011 ; Wyatt 2015 ; Xenofontos and Andrews 2020 ). While acknowledging limitations in sample scope and the generalizability of the findings, this study offers a longitudinal perspective on the stage-by-stage development of teacher self-efficacy and its interactions with different factors (i.e., teacher knowledge, skills, and beliefs), often ignored by quantitative studies. Considering that studies of self-efficacy have been predominantly quantitative, typically drawing on survey techniques and pre-determined scales (Xenofontos and Andrews, 2020 ; Zhou et al. 2023 ), this study highlights the need for greater attention to qualitative studies so that more cultural, situational and contextual factors in the development of self-efficacy can be captured.

Our study provides valuable practical implications for enhancing pre-service teachers’ self-efficacy. We conceptualize teacher self-efficacy in two primary dimensions: individual performance and student outcomes. On the one hand, pre-service teachers can enhance their teaching qualities, boosting their self-efficacy in individual performance. The adage “practice makes perfect” underscores the necessity of ample teaching practice opportunities for pre-service teachers who lack prior teaching experience. Engaging in consistent and reflective practice helps them develop confidence in their teaching qualities. On the other hand, pre-service teachers should focus on positive feedback from their students, reinforcing their self-efficacy in individual performance. Positive student feedback serves as an affirmation of their teaching effectiveness and encourages continuous improvement. Furthermore, our findings highlight the significance of mentors’ and peers’ positive feedback as critical sources of teacher self-efficacy. Mentors and peers play a pivotal role in the professional growth of pre-service teachers by actively encouraging them and recognizing their teaching achievements. Constructive feedback from experienced mentors and supportive peers fosters a collaborative learning environment and bolsters the self-confidence of pre-service teachers. Additionally, our research indicates that pre-service teachers’ self-efficacy may fluctuate. Therefore, mentors should be prepared to help pre-service teachers manage teaching challenges and setbacks, and alleviate any teaching-related anxiety. Mentors can help pre-service teachers build resilience and maintain a positive outlook on their teaching journey through emotional support and guidance. Moreover, a strong correlation exists between teacher self-efficacy and teacher knowledge and skills. Enhancing pre-service teachers’ knowledge base and instructional skills is crucial for bolstering their overall self-efficacy.

Secondly, this study also responds to the appeal to understand teachers’ professional learning from a holistic perspective and interrelate teachers’ professional learning process with student outcome variables (Sancar et al. 2021 ), and thus contributes to the understanding of the complexity of STEAM teachers’ professional learning. On the one hand, we have confirmed Cai et al.’s ( 2020 ) teacher professional learning model in a new context, namely STEAM teacher education. Throughout the teacher professional development program, the pre-service teacher, Shuitao, demonstrated an augmentation in her knowledge, encompassing both content knowledge and pedagogical understanding concerning IHT. Moreover, her beliefs regarding IHT transformed as a result of her engagement in teacher learning across the five stages. This facilitated her in executing effective IHT teaching and improving her students’ outcomes. On the other hand, notably, in our studies (including this current study and some follow-up studies), student feedback is a pivotal tool to assist teachers in discerning the impact they are effectuating. This enables pre-service teachers to grasp the actual efficacy of their teaching efforts and subsequently contributes significantly to the augmentation of their self-efficacy. Such steps have seldom been conducted in prior studies (e.g., Cai et al. 2020 ), where student outcomes are often perceived solely as the results of teachers’ instruction rather than sources informing teacher beliefs. Additionally, this study has validated both the interaction between teaching performance and teacher beliefs and between teacher knowledge and teacher beliefs. These aspects were overlooked in Cai et al.’s ( 2020 ) model. More importantly, while Clarke and Hollingsworth’s ( 2002 ) Interconnected Model of Professional Growth illustrates the connections between the domain of consequence and the personal domain, as well as between the personal domain and the domain of practice, it does not adequately clarify the complex relationships among the factors within the personal domain (e.g., the interaction between teacher knowledge and teacher beliefs). Therefore, our study also supplements Clarke and Hollingsworth’s ( 2002 ) model by addressing these intricacies. Based on our findings, an updated model of teacher professional learning has been proposed, as shown in Fig. 3 . This expanded model indicates that teacher learning should be an ongoing and sustainable process, with the enhancement of student learning not marking the conclusion of teacher learning, but rather serving as the catalyst for a new phase of learning. In this sense, we advocate for further research to investigate the tangible impacts of teacher professional development programs on students and how those impacts stimulate subsequent cycles of teacher learning.

Note: Paths in blue were proposed by Cai et al. ( 2020 ), and paths in yellow are proposed and verified in this study.

Thirdly, in light of the updated model of teacher professional learning (see Fig. 3 ), this study provides insights into the design of teacher professional development programs of IAT. According to Huang et al. ( 2022 ), to date, very few studies have set goals to “develop a comprehensive understanding of effective designs” for STEM (or STEAM) teacher professional development programs (p. 15). To fill this gap, this study proposes a novel and effective five-stage framework for teacher professional development programs of IAT. This framework provides a possible and feasible solution to the challenges of STEAM teacher professional development programs’ design and planning, and teachers’ IAT practice (Boice et al. 2021 ; Herro et al. 2019 ; Jacques et al. 2020 ; Park and Cho 2022 ; Perignat and Katz-Buonincontro 2019 ).

Specifically, our five-stage framework incorporates at least six important features. Firstly, teacher professional development programs should focus on specific STEAM content. Given the expansive nature of STEAM, teacher professional development programs cannot feasibly encompass all facets of its contents. Consistent with recommendations by Cai et al. ( 2020 ), Desimone et al. ( 2002 ) and Garet et al. ( 2001 ), an effective teacher professional development program should prioritize content focus. Our five-stage framework is centered on IAT. Throughout an 18-month duration, each pre-service teacher is limited to selecting one subcomponent of A&H, such as history, for integration into their subject teaching (i.e., mathematics teaching, technology teaching or science teaching) within one teacher professional development program. Secondly, in response to the appeals that teacher professional development programs should shift from emphasizing teaching and instruction to emphasizing student learning (Cai et al. 2020 ; Calabrese et al. 2024 ; Hwang et al. 2024 ; Marco and Palatnik 2024 ; Örnek and Soylu 2021 ), our framework requires pre-service teachers to pay close attention to the effects of IAT on student learning outcomes, and use students’ feedback as the basis of improving their instruction. Thirdly, prior studies found that teacher education with a preference for theory led to pre-service teachers’ dissatisfaction with the quality of teacher professional development program and hindered the development of pre-service teachers’ teaching skills and teaching beliefs, which also widened the gap between theory and practice (Hennissen et al. 2017 ; Ord and Nuttall 2016 ). In this regard, our five-stage framework connects theory and teaching practice closely. In particular, pre-service teachers can experience the values of IAT not only through theoretical learning but also through diverse teaching practices. Fourthly, we build a teacher community of practice tailored for pre-service teachers. Additionally, we aim to encourage greater participation of in-service teachers in such teacher professional development programs designed for pre-service educators in STEAM teacher education. By engaging in such programs, in-service teachers can offer valuable teaching opportunities for pre-service educators and contribute their insights and experiences from teaching practice. Importantly, pre-service teachers stand to gain from the in-service teachers’ familiarity with textbooks, subject matter expertise, and better understanding of student dynamics. Fifthly, our five-stage framework lasts for an extended period, spanning 18 months. This duration ensures that pre-service teachers engage in a sustained and comprehensive learning journey. Lastly, our framework facilitates a practical understanding of “integration” by offering detailed, sequential instructions for blending two disciplines in teaching. For example, our teacher professional development programs prioritize systematic learning of pedagogical theories and simulated teaching experiences before pre-service teachers embark on real STEAM teaching endeavors. This approach is designed to mitigate the risk of unsuccessful experiences during initial teaching efforts, thereby safeguarding pre-service teachers’ teacher self-efficacy. Considering the complexity of “integration” in interdisciplinary teaching practices, including IAT (Han et al. 2022 ; Ryu et al. 2019 ), we believe detailed stage-by-stage and step-by-step instructions are crucial components of relevant pre-service teacher professional development programs. Notably, this aspect, emphasizing structural instructional guidance, has not been explicitly addressed in prior research (e.g., Cai et al. 2020 ). Figure 4 illustrates the six important features outlined in this study, encompassing both established elements and the novel addition proposed herein, describing an effective teacher professional development program.

Note: STEAM refers to science, technology, engineering, arts and humanities, and mathematics.

The successful implementation of this framework is also related to the Chinese teacher education system and cultural background. For instance, the Chinese government has promoted many university-school collaboration initiatives, encouraging in-service teachers to provide guidance and practical opportunities for pre-service teachers (Lu et al. 2019 ). Influenced by Confucian values emphasizing altruism, many experienced in-service teachers in China are eager to assist pre-service teachers, helping them better realize their teaching career aspirations. It is reported that experienced in-service teachers in China show significantly higher motivation than their international peers when mentoring pre-service teachers (Lu et al. 2019 ). Therefore, for the successful implementation of this framework in other countries, it is crucial for universities to forge close collaborative relationships with K-12 schools and actively involve K-12 teachers in pre-service teacher education.

Notably, approximately 5% of our participants dropped out midway as they found that the IAT practice was too challenging or felt overwhelmed by the number of required tasks in the program. Consequently, we are exploring options to potentially simplify this framework in future iterations.

Without minimizing the limitations of this study, it is important to recognize that a qualitative longitudinal case study can be a useful means of shedding light on the development of a pre-service STEAM teacher’s self-efficacy. However, this methodology did not allow for a pre-post or a quasi-experimental design, and the effectiveness of our five-stage framework could not be confirmed quantitatively. In the future, conducting more experimental or design-based studies could further validate the effectiveness of our framework and broaden our findings. Furthermore, future studies should incorporate triangulation methods and utilize multiple data sources to enhance the reliability and validity of the findings. Meanwhile, owing to space limitations, we could only report the changes in Shuitao’s SE-IHT-IP and SE-IHT-SO here, and we could not describe the teacher self-efficacy of other participants regarding IAT. While nearly all of the pre-service teachers experienced an improvement in their teacher self-efficacy concerning IAT upon participating in our teacher professional development programs, the processes of their change were not entirely uniform. We will need to report the specific findings of these variations in the future. Further studies are also needed to explore the factors contributing to these variations. Moreover, following this study, we are implementing more teacher professional development programs of IAT. Future studies can explore the impact of this framework on additional aspects of pre-service STEAM teachers’ professional development. This will help gain a more comprehensive understanding of its effectiveness and potential areas for further improvement. Additionally, our five-stage framework was initially developed and implemented within the Chinese teacher education system. Future research should investigate how this framework can be adapted in other educational systems and cultural contexts.

The impetus behind this study stems from the burgeoning discourse advocating for the integration of A&H disciplines into STEM education on a global scale (e.g., Land 2020 ; Park and Cho 2022 ; Uştu et al. 2021 ; Vaziri and Bradburn 2021 ). Concurrently, there exists a pervasive concern regarding the challenges teachers face in implementing STEAM approaches, particularly in the context of IAT practices (e.g., Boice et al. 2021 ; Herro et al. 2019 ; Jacques et al. 2020 ; Park and Cho 2022 ; Perignat and Katz-Buonincontro 2019 ). To tackle this challenge, we first proposed a five-stage framework designed for teacher professional development programs of IAT. Then, utilizing this innovative framework, we implemented a series of teacher professional development programs. Drawing from the recommendations of Bray-Clark and Bates ( 2003 ), Kelley et al. ( 2020 ) and Zhou et al. ( 2023 ), we have selected teacher self-efficacy as a key metric to examine the effectiveness of the five-stage framework. Through a qualitative longitudinal case study, we scrutinized the influence of a specific teacher professional development program on the self-efficacy of a single pre-service teacher over an 18-month period. Our findings revealed a notable enhancement in teacher self-efficacy across both individual performance and student outcomes. The observed enhancement of the participant’s teacher self-efficacy did not occur swiftly but unfolded gradually through a prolonged, incremental process. Building on our findings, an updated model of teacher learning has been proposed. The updated model illustrates that teacher learning should be viewed as a continuous and sustainable process, wherein teaching performance, teacher beliefs, and teacher knowledge dynamically interact with one another. The updated model also confirms that teacher learning is inherently intertwined with student learning in STEAM education. Furthermore, this study also summarizes effective design features of STEAM teacher professional development programs.

Data availability

The datasets generated and/or analyzed during this study are not publicly available due to general data protection regulations, but are available from the corresponding author on reasonable request.

In their review article, Morris et al. ( 2017 ) equated “teaching self-efficacy” and “teacher self-efficacy” as synonymous concepts. This perspective is also adopted in this study.

An effective teacher professional development program should have specific, focused, and clear content instead of broad and scattered ones. Therefore, each pre-service teacher can only choose to integrate one subcomponent of A&H into their teaching in one teacher professional development program. For instance, Shuitao, a mathematics pre-service teacher, participated in one teacher professional development program focused on integrating history into mathematics teaching. However, she did not explore the integration of other subcomponents of A&H into her teaching during her graduate studies.

In the micro-classrooms, multi-angle, and multi-point high-definition video recorders are set up to record the teaching process.

In micro-teaching, mentors, in-service teachers, and other fellow pre-service teachers take on the roles of students.

In China, teachers can video record one section of a lesson and play them in formal classes. This is a practice known as a micro-course. For instance, in one teacher professional development program of integrating history into mathematics teaching, micro-courses encompass various mathematics concepts, methods, ideas, history-related material and related topics. Typically, teachers use these micro-courses to broaden students’ views, foster inquiry-based learning, and cultivate critical thinking skills. Such initiatives play an important role in improving teaching quality.

Many university-school collaboration initiatives in China focus on pre-service teachers’ practicum experiences (Lu et al. 2019 ). Our teacher professional development program is also supported by many K-12 schools in Shanghai. Personal information in videos is strictly protected.

In China, students are not required to pursue a graduate major that matches their undergraduate major. Most participants in our teacher professional development programs did not pursue undergraduate degrees in education-related fields.

Shuitao’s university reserves Wednesday afternoons for students to engage in various programs or clubs, as classes are not scheduled during this time. Similarly, our teacher professional development program activities are planned for Wednesday afternoons to avoid overlapping with participants’ other coursework commitments.

History is one of the most important components of A&H (Park and Cho 2022 ).

To learn more about genetic approach (i.e., genetic principle), see Jankvist ( 2009 ).

For the assessment process, see Fig. 2 .

Shuitao’s cooperating in-service teacher taught the concept of logarithms in Stage 2. In Stage 4, the teaching objective of her cooperating in-service teacher’s review lesson was to help students review the concept of logarithms to prepare students for the final exam.

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Acknowledgements

This research is funded by 2021 National Natural Science Foundation of China (Grant No.62177042), 2024 Zhejiang Provincial Natural Science Foundation of China (Grant No. Y24F020039), and 2024 Zhejiang Educational Science Planning Project (Grant No. 2024SCG247).

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Xuesong Zhai

Present address: School of Education, City University of Macau, Macau, China

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College of Education, Zhejiang University, Hangzhou, China

Haozhe Jiang & Xuesong Zhai

School of Engineering and Technology, CML‑NET & CREATE Research Centres, Central Queensland University, North Rockhampton, QLD, Australia

Ritesh Chugh

Hangzhou International Urbanology Research Center & Zhejiang Urban Governance Studies Center, Hangzhou, China

Department of Teacher Education, Nicholls State University, Thibodaux, LA, USA

School of Mathematical Sciences, East China Normal University, Shanghai, China

Xiaoqin Wang

College of Teacher Education, Faculty of Education, East China Normal University, Shanghai, China

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Conceptualization - Haozhe Jiang; methodology - Haozhe Jiang; software - Xuesong Zhai; formal analysis - Haozhe Jiang & Ke Wang; investigation - Haozhe Jiang; resources - Haozhe Jiang, Xuesong Zhai & Xiaoqin Wang; data curation - Haozhe Jiang & Ke Wang; writing—original draft preparation - Haozhe Jiang & Ritesh Chugh; writing—review and editing - Ritesh Chugh & Ke Wang; visualization - Haozhe Jiang, Ke Wang & Xiaoqin Wang; supervision - Xuesong Zhai & Xiaoqin Wang; project administration - Xuesong Zhai & Xiaoqin Wang; and funding acquisition - Xuesong Zhai & Xiaoqin Wang. All authors have read and agreed to the published version of the manuscript.

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Jiang, H., Chugh, R., Zhai, X. et al. Longitudinal analysis of teacher self-efficacy evolution during a STEAM professional development program: a qualitative case study. Humanit Soc Sci Commun 11 , 1162 (2024). https://doi.org/10.1057/s41599-024-03655-5

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Entrepreneurship and corporate esg performance—a case study of china’s a-share listed companies.

1. Introduction

2. literature review and theoretical analysis, 2.1. entrepreneurship, 2.3. literature summary, 2.4. theoretical and hypothetical analysis, 3. data and method, 4. empirical analysis, 4.1. benchmark effects regression, 4.2. robustness check, 4.2.1. replace the explained variable, 4.2.2. endogenous test, 4.2.3. change core explanatory variable, 4.2.4. controlling for industry fixed effects, 4.2.5. incorporating additional control variables, 4.2.6. abnormal year exclusion, 4.2.7. replace the estimation model, 4.3. mechanism analysis, 4.4. analysis of moderating effect, 4.4.1. environmental uncertainty, 4.4.2. market concentration, 4.4.3. marketization level, 4.4.4. artificial intelligence, 4.5. further analysis, 5. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Share and Cite

Xie, H.; Qin, Z.; Li, J. Entrepreneurship and Corporate ESG Performance—A Case Study of China’s A-Share Listed Companies. Sustainability 2024 , 16 , 7964. https://doi.org/10.3390/su16187964

Xie H, Qin Z, Li J. Entrepreneurship and Corporate ESG Performance—A Case Study of China’s A-Share Listed Companies. Sustainability . 2024; 16(18):7964. https://doi.org/10.3390/su16187964

Xie, Hanjin, Zilong Qin, and Jun Li. 2024. "Entrepreneurship and Corporate ESG Performance—A Case Study of China’s A-Share Listed Companies" Sustainability 16, no. 18: 7964. https://doi.org/10.3390/su16187964

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