Identify Goal
Define Problem
Define Problem
Gather Data
Define Causes
Identify Options
Clarify Problem
Generate Ideas
Evaluate Options
Generate Ideas
Choose the Best Solution
Implement Solution
Select Solution
Take Action
MacLeod offers her own problem solving procedure, which echoes the above steps:
“1. Recognize the Problem: State what you see. Sometimes the problem is covert. 2. Identify: Get the facts — What exactly happened? What is the issue? 3. and 4. Explore and Connect: Dig deeper and encourage group members to relate their similar experiences. Now you're getting more into the feelings and background [of the situation], not just the facts. 5. Possible Solutions: Consider and brainstorm ideas for resolution. 6. Implement: Choose a solution and try it out — this could be role play and/or a discussion of how the solution would be put in place. 7. Evaluate: Revisit to see if the solution was successful or not.”
Many of these problem solving techniques can be used in concert with one another, or multiple can be appropriate for any given problem. It’s less about facilitating a perfect CPS session, and more about encouraging team members to continually think outside the box and push beyond personal boundaries that inhibit their innovative thinking. So, try out several methods, find those that resonate best with your team, and continue adopting new techniques and adapting your processes along the way.
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Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.
Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.
This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations.
Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies:
Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better.
Strategies can help guide students to the solution when it is difficult ot know when to start.
The ultimate guide to problem solving techniques
Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.
Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem.
Here are 20 strategies to help students develop their problem-solving skills.
Strategies that help students understand the problem before solving it helps ensure they understand:
Following these steps leads students to the correct solution and makes the math word problem easier .
Here are five strategies to help students understand the content of the problem and identify key information.
Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.
When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed. For example, if the word problem asks how many are left, the problem likely requires subtraction. Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.
Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary. Summaries should include only the important information and be in simple terms that help contextualize the problem.
A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer. Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.
Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it. The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer. Encourage students to make a list of each step they need to take to solve the problem before getting started.
1. draw a model or diagram.
Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process. It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.
Similarly, you could draw a model to represent the objects in the problem:
This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives . When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts. The examples below show how 1st-grade students could “act out” an addition and subtraction problem:
The problem | How to act out the problem |
Gia has 6 apples. Jordan has 3 apples. How many apples do they have altogether? | Two students use counters to represent the apples. One student has 6 counters and the other student takes 3. Then, they can combine their “apples” and count the total. |
Michael has 7 pencils. He gives 2 pencils to Sarah. How many pencils does Michael have now? | One student (“Michael”) holds 7 pencils, the other (“Sarah”) holds 2 pencils. The student playing Michael gives 2 pencils to the student playing Sarah. Then the students count how many pencils Michael is left holding. |
Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution. This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.
For example,
To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71. Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.
When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved. It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.
Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve. Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.
Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense.
There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.
Here are five strategies to help students check their solutions.
For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work.
Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable. Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten. For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10. When the estimate is clear the two numbers are close. This means your answer is reasonable.
This method is particularly useful for algebraic equations. Specifically when working with variables. To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.
If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓
Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly. Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills. If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.
A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.
In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems.
Polya’s 4 steps include:
Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall.
Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom.
Here are 5 problem-solving strategies to introduce to students and use in the classroom.
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Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra.
Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.
READ MORE :
There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model • act it out • work backwards • write a number sentence • use a formula
Here are 10 strategies for problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model • Act it out • Work backwards • Write a number sentence • Use a formula
1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back
Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.
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Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.
In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.
Podcast transcript
Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.
Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].
Charles and Hugo, welcome to the podcast. Thank you for being here.
Hugo Sarrazin: Our pleasure.
Charles Conn: It’s terrific to be here.
Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?
Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”
You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”
I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.
I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.
Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.
Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.
Simon London: So this is a concise problem statement.
Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.
Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.
How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.
Hugo Sarrazin: Yeah.
Charles Conn: And in the wrong direction.
Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?
Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.
What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.
Simon London: What’s a good example of a logic tree on a sort of ratable problem?
Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.
If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.
When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.
Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.
Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.
People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.
Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?
Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.
Simon London: Not going to have a lot of depth to it.
Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.
Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.
Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.
Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.
Both: Yeah.
Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.
Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.
Simon London: Right. Right.
Hugo Sarrazin: So it’s the same thing in problem solving.
Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.
Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?
Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.
Simon London: Would you agree with that?
Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.
You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.
Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?
Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.
Simon London: Step six. You’ve done your analysis.
Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”
Simon London: But, again, these final steps are about motivating people to action, right?
Charles Conn: Yeah.
Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.
Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.
Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.
Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.
Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?
Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.
You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.
Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.
Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”
Hugo Sarrazin: Every step of the process.
Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?
Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.
Simon London: Problem definition, but out in the world.
Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.
Simon London: So, Charles, are these complements or are these alternatives?
Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.
Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?
Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.
The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.
Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.
Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.
Hugo Sarrazin: Absolutely.
Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.
Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.
Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.
Charles Conn: It was a pleasure to be here, Simon.
Hugo Sarrazin: It was a pleasure. Thank you.
Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.
Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.
Related articles.
As a leader, how do you approach challenges in your organization? Do you see them as problems to be solved, or puzzles to be pieced together? In today’s rapidly evolving technological landscape, this distinction could be the key to unlocking innovation and thriving in uncertain times.
The shift from problem-solving to puzzle-solving isn’t just a change in terminology – it’s a fundamental shift in mindset that can transform how your team tackles complex issues. Let’s explore why this matters and how you can implement it in your organization.
1. holistic perspective.
Puzzle-solving encourages leaders to step back and consider all possible pieces before jumping to solutions. This holistic view is crucial when dealing with the multifaceted challenges presented to the modern leader.
The Japanese business philosophy kaizen sees problems or challenges as a crucial step in the cycle of improvement. Puzzle-solvers adopt this frame of mind and see difficulty as an opportunity for growth and improvement.
Puzzle-solving thrives on diverse perspectives. By bringing together varied viewpoints, you can uncover pieces of the puzzle you didn’t even know were missing.
Puzzle-solving doesn’t just shift us into an opportunity mindset – it also fosters a culture of continuous learning and adaptation. As you piece together each new puzzle, you and your team grow in knowledge and capability.
Let me share a personal experience that illustrates the power of this approach. During an organizational development event, our team faced the challenge of reducing a contract closure process from several weeks to just two days – a goal that initially seemed impossible.
Instead of being overwhelmed, we reframed the challenge by asking, “What must be true to achieve a two-day turnaround?” This shift in perspective allowed us to rethink the entire process and innovate a solution that met the ambitious target.
By approaching the challenge as a puzzle rather than a problem, we identified aspects of the process we hadn’t previously considered. We brought together team members from different departments, each offering unique insights. This diversity of perspective, combined with a willingness to question our assumptions, led to a breakthrough that transformed our operations.
1. reframe challenges as growth opportunities.
Train your team to see “red” on a scorecard not as a failure, but as an area ripe for improvement and personal growth. This simple reframing can dramatically change how your team approaches challenges.
Before jumping into solution mode, ask, “What information or perspectives might we be overlooking?” This critical thinking approach can reveal crucial insights and areas for development.
Bring together people from different functions, backgrounds, and thinking styles to enrich your problem-solving process and foster mutual growth.
Use generative AI tools to access a wealth of existing knowledge and frameworks. This can provide you with an unprecedented number of lenses through which to examine a challenge and grow your understanding.
Foster an environment where asking questions, seeking out new viewpoints, and continuous learning are encouraged and rewarded.
Growth is the only guarantee that tomorrow will be better. John C. Maxwell
As we navigate the technological complexities of the modern era – including generative AI – the ability to shift from problem-solving to puzzle-solving will be a critical skill for leaders. This approach not only helps us tackle immediate challenges more effectively, but also reinforces our organization’s ability to adapt and innovate in the face of rapid technological change.
Remember, the goal isn’t just to solve the problem at hand, but to build a culture and mindset that thrives on complexity and change. By viewing challenges as puzzles and embracing diverse perspectives – both human and AI-generated – you’ll be better equipped to lead your team through the ever-changing landscape of modern business.
What challenge are you currently facing that could benefit from a puzzle-solving approach? How might reframing this challenge and seeking out diverse perspectives lead to innovative solutions?
Take some time this week to practice puzzle-solving with your team. Start by reframing a current challenge as an opportunity, then brainstorm what pieces might be missing from your current understanding. You might be surprised at the innovative solutions that emerge.
Gain practical insights and discover real-world examples of how tools like AI can support your leadership development journey. Subscribe to the Maxwell Leadership blog for more content from AI researcher Daniel Englebretson and other professionals championing transformation in today’s marketplace.
Daniel Englebretson is an AI researcher, innovator, and entrepreneur. He is also the founder and CEO of Elynox, the co-founder and managing partner of ShiftHX, and an adjunct professor of artificial intelligence and communications at Wake Forest University and Elon University. Daniel is committed to empowering and enabling others with the skills and mindset shifts required to create opportunities to collaborate more effectively with AI.
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Social eye tracking: gaze recall with online crowds.
Eye tracking is a compelling tool for revealing people's spatial-temporal distribution of visual attention. But quality eye tracking hardware is expensive and can only be used with one person at a time. Further, webcam eye tracking systems have ...
Continuous awareness of learners' progress is one of the central tasks of any educational technology system. On the level of second-to-second behavior, eye-tracking has frequently been used as a technique to understand the interplay between higher level ...
This paper presents an approach of using FIR Median Hybrid Filters for analysis of eye tracking movements. The proposed filter can remove the eye blink artifact from the eye movement signal. The background of the project is described first. The whole ...
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Is training the answer how to find the right solution to a business problem.
Training and development is an imperative key to any business strategy. Continuous training ensures that employees have the skills and capabilities needed to achieve business objectives. Across organizations, learning and development (L&D) leaders are responsible for identifying training opportunities and skills gaps, and then using that information to deliver content that solves business problems. This makes L&D professionals vital to a company’s success.
The significance of L&D is well-recognized, yet — what if training isn’t always the answer?
In this article, we’ll share tips by L&D experts on how to determine if a business problem is really a training issue, and if it is not, the steps to addressing this challenge with senior leaders.
If learning leaders do not evaluate the business challenge before implementing a solution, they risk wasting time, costs and efforts. With a targeted approach to determining if training is the solution, L&D leaders can position themselves as strategic business partners.
Let’s consider some examples of when training isn’t the answer:
To ensure that training effectively addresses business problems, it’s crucial to connect the issue to specific employee performance metrics. Thomas Harrell, CPTM, instructional designer at Great HealthWorks, shares some insight on this. “The key indicator that training is the correct answer to a business problem is when we can link the problem to employee performance. Anything less than that is fuzzy conjecture at worst and an educated guess at best.” Harrell notes that revealing this link can be challenging and time-consuming, but it is worth it when the business need is critical enough to isolate and resolve.
Evaluating the need for new training programs involves determining whether current practices are effective or need changes. Jenessa Jacobs, CPTM, vice president of development and growth strategy at Aspen Sales, Inc., shares that, “There’s no sense in changing something that isn’t broken. For example, your organization may want leadership training… However, if your organization is not in a spot where they’re regularly doing one-on-ones or performance reviews, putting training in place may not make a difference.”
Instead of developing more leadership training content, the organization might need to foster a more human-centered culture by encouraging leaders to have one-on-ones and other personal touchpoints with their employees. L&D should focus on communicating new changes and ideas rather than creating additional training.
When employees lack the tools and resources needed for their jobs, it can reflect as poor performance. This misconception often leads managers to assume that training is the answer. However, there’s a hiccup somewhere — and as an L&D professional, it’s your job to identify it.
Sarah Parlett, CPTM, vice president of human resources (HR) at Cooperative Teacher Credit, points out that, rather than needing training, an employee might need clearer instructions for specific tasks or a better understanding of their job role. For example, if an employee is unsure about their authority to make decisions like reversing a fee, it can slow down the transaction. What might seem like poor sales is actually a result of unclear communication.
Don’t assume training is the solution — first, evaluate whether the issue lies elsewhere.
According to Jacobs, cultural issues and communication breakdowns are often misdiagnosed and addressed with training. “Are you setting up the right infrastructure for your team? Do you have the right people in place, and are you providing the necessary products, tools, and resources they need to succeed?” If these elements are not in place, training alone will not be effective.
Harrell suggests analyzing the problem through focus group discussions. “The learning and performance development team can meet with a handful of employees who are okay with the business process and software, and those who are not. During the discussion, the L&D team can ascertain where the disconnect is and if a training intervention is needed.”
To ensure employees have what they need to work effectively, Parlett suggests creating a structured checklist. “We shouldn’t expect people to memorize how to perform all the functions of their job and every task.” Implementing a decision-making process matrix or chart can help employees understand their decision-making authority and when to escalate issues to a supervisor.
Training isn’t always the answer. Some business problems stem from a lack of communication, clarity and resources. By addressing these underlying issues, learning leaders can drive meaningful change and help achieve business goals.
Danielle Johnson
Danielle Johnson is an editor at Training Industry, Inc. with 5+ years’ experience in writing/editing and the talent to curate compelling, creative content for a target audience. At Training Industry, Danielle connects with thought leaders to publish articles with actionable solutions
Leveraging ai for better learning: navigating innovation and accessibility, why didn’t my learning strategy work a critical examination for business leaders, upskilling: the catalyst to supporting equitable career growth.
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COMMENTS
In general, effective problem-solving strategies include the following steps: Define the problem. Come up with alternative solutions. Decide on a solution. Implement the solution. Problem-solving ...
2. Break the problem down. Identifying the problem allows you to see which steps need to be taken to solve it. First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage. 3.
Several mental processes are at work during problem-solving. Among them are: Perceptually recognizing the problem. Representing the problem in memory. Considering relevant information that applies to the problem. Identifying different aspects of the problem. Labeling and describing the problem.
Step 1: Identify the Problem. The problem-solving process starts with identifying the problem. This step involves understanding the issue's nature, its scope, and its impact. Once the problem is clearly defined, it sets the foundation for finding effective solutions.
A problem-solving strategy is a plan used to find a solution or overcome a challenge. Each problem-solving strategy includes multiple steps to provide you with helpful guidelines on how to resolve a business problem or industry challenge. Effective problem-solving requires you to identify the problem, select the right process to approach it and ...
7. Solution evaluation. 1. Problem identification. The first stage of any problem solving process is to identify the problem (s) you need to solve. This often looks like using group discussions and activities to help a group surface and effectively articulate the challenges they're facing and wish to resolve.
4 steps to better problem solving. While it might be tempting to dive into a problem head first, take the time to move step by step. Here's how you can effectively break down the problem-solving process with your team: 1. Identify the problem that needs to be solved. One of the easiest ways to identify a problem is to ask questions.
Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything ...
Problem-solving is a strategy-driven approach that uses logical thinking, creativity, and collaboration to analyze obstacles and build actionable solutions to overcome them. Life rarely goes exactly to plan, and problem-solving skills remove barriers that stop your team from reaching objectives when things go awry. ...
The McKinsey guide to problem solving. Become a better problem solver with insights and advice from leaders around the world on topics including developing a problem-solving mindset, solving problems in uncertain times, problem solving with AI, and much more.
The problem-solving process typically includes the following steps: Identify the issue: Recognize the problem that needs to be solved. Analyze the situation: Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present. Generate potential solutions: Brainstorm a list of possible ...
1. Define the problem. Diagnose the situation so that your focus is on the problem, not just its symptoms. Helpful problem-solving techniques include using flowcharts to identify the expected steps of a process and cause-and-effect diagrams to define and analyze root causes.. The sections below help explain key problem-solving steps.
Problem solving strategies. Problem solving strategies are methods of approaching and facilitating the process of problem-solving with a set of techniques, actions, and processes.Different strategies are more effective if you are trying to solve broad problems such as achieving higher growth versus more focused problems like, how do we improve our customer onboarding process?
Get the app: https://www.alux.com/app00:00 - Intr000:31 - Define the Problem Clearly01:28 - Gather Information02:15 - Analyze from Different Perspectives03:0...
Learning problem-solving techniques is a must for working professionals in any field. No matter your title or job description, the ability to find the root cause of a difficult problem and formulate viable solutions is a skill that employers value. Learning the soft skills and critical thinking techniques that good problem solvers use can help ...
Creativity. Critical thinking. Leadership. Communication. Time management. Emotional intelligence. Solving a problem is complex and requires the ability to recognize the issue, collect and analyze relevant data, and make decisions about the best course of action.
Problem-solving is the process of breaking down challenges to find solutions. Typically it is a four-stage process of 1) identifying an issue, 2) establishing a plan, 3) executing the plan, and 4) finding a resolution. However, problem-solving can begin before a problem even occurs. For example, crisis management includes pre-planning for ...
7 strategies for solving problems There are several different ways of approaching and handling a problem, depending on the nature of the challenge and the resources available to you. Choosing the most suitable strategy is crucial for devising a workable solution. Below is a list of seven strategies, methods and tips for problem-solving: Take ...
How to Solve Problems. To bring the best ideas forward, teams must build psychological safety. by Laura Amico. Teams today aren't just asked to execute tasks: They're called upon to solve ...
Defer or suspend judgement. Focus on "Yes, and…" rather than "No, but…". According to Carella, "Creative problem solving is the mental process used for generating innovative and imaginative ideas as a solution to a problem or a challenge. Creative problem solving techniques can be pursued by individuals or groups.".
Here are five strategies to help students check their solutions. 1. Use the Inverse Operation. For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7.
In this episode of the McKinsey Podcast, Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.. Podcast transcript. Simon London: Hello, and welcome to this episode of the McKinsey Podcast, with me, Simon London.
Discover 5 strategies for solving problems in the modern era. In a world that changes rapidly, constant growth keeps you effective. Discover 5 strategies for solving problems in the modern era. ... The shift from problem-solving to puzzle-solving isn't just a change in terminology - it's a fundamental shift in mindset that can transform ...
Problem-Solving Strategy. Read the problem. Make sure all the words and ideas are understood. Identify what we are looking for. Name what we are looking for. Choose a variable to represent that quantity. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the ...
Part 1—Knowing Key Terms (3 points): Fill in the blanks from the crossword puzzle above using key terms from the textbook and/or lecture notes. Across 4. the process of solving problems by combining ideas or behavior in new ways.- Creativity 5. aspects of language involving the practical aspects of communicating with others, or the social "niceties" of language.
Through an analysis of eye movements, participants were categorized into three distinct groups based on their problem-solving strategies. This categorization facilitated an exploration of the correlation between the chosen strategy and the success rate in solving geometry problems without computational aids. The findings underscore the ...
Training and development is an imperative key to any business strategy. Continuous training ensures that employees have the skills and capabilities needed to achieve business objectives. ... In this article, we'll share tips by L&D experts on how to determine if a business problem is really a training issue, and if it is not, the steps to ...
Collaborative cooperation (CC) and division of labor cooperation (DLC) are two prevalent forms of cooperative problem-solving approaches in daily life. Despite extensive research on the neural mechanisms underlying cooperative problem-solving approaches, a notable gap exists between the neural processes that support CC and DLC. The present study utilized a functional near-infrared spectroscopy ...