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10 Problem-solving strategies to turn challenges on their head

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What is an example of problem-solving?

What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.

Problems come in all shapes and sizes — from workplace conflict to budget cuts.

Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge. 

Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem . 

Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.

Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.

To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high. 

Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one. 

Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions. 

This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.

They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.

The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.

Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving. 

Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.

1. Identify the problem

The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem. 

The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions. 

Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .

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. Generate potential solutions

At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible. 

Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.

Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.

4. Evaluate the possible solutions

Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist. 

There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:

• Will my team be on board with the proposition?
• Does the solution align with organizational goals ?
• Is the solution likely to achieve the desired outcomes?
• Is the solution realistic and possible with current resources and constraints?
• Will the solution solve the problem without causing additional unintended problems?

5. Implement and monitor the solutions

Once you’ve identified your solution and got buy-in from your team, it’s time to implement it. 

But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem. 

Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.

If the solution doesn’t achieve your desired results, start this step-by-step process again.

There are many different ways to approach problem-solving. Each is suitable for different types of problems. 

The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.

Here are 10 effective problem-solving strategies for you to try:

• Use a solution that worked before
• Brainstorming
• Work backward
• Use the Kipling method
• Draw the problem
• Use trial and error
• Sleep on it
• Get advice from your peers
• Use the Pareto principle
• Add successful solutions to your toolkit

Let’s break each of these down.

1. Use a solution that worked before

It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.

2. Brainstorming

The more people you enlist to help solve the problem, the more potential solutions you can come up with.

Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.

3. Work backward

Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.

Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.

4. Use the Kipling method

This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .” 

• What is the problem?
• Why is the problem important?
• When did the problem arise, and when does it need to be solved?
• How did the problem happen?
• Where is the problem occurring?
• Who does the problem affect?

Answering these questions can help you identify possible solutions.

5. Draw the problem

Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.

This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.

6. Use trial-and-error

A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.

7. Sleep on it

Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.

A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level. 

If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.

8. Get advice from your peers

Getting input from a group of people can help you find solutions you may not have thought of on your own. 

For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group. 

For leaders , it might be consulting other members of the leadership team or working with a business coach .

It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone. 

9. Use the Pareto principle

The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.

Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales. 

You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.

10. Add successful solutions to your toolkit

Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit. 

These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.

Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:

• Critical thinking and analytical skills
• Communication skills , including active listening
• Decision-making
• Planning and prioritization
• Emotional intelligence , including empathy and emotional regulation
• Time management
• Data analysis
• Research skills
• Project management

And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.

Ready to work on your problem-solving abilities? Get started with these seven tips.

1. Build your problem-solving skills

One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .

2. Practice

Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life. 

Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.

3. Don’t try to find a solution right away

Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.

Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking. 

4. Ask for feedback

Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve. 

5. Learn new approaches and methodologies

There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject. 

We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman. 

6. Experiment

Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches. 

Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.

7. Analyze the success of your competitors

Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem. 

For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster. 

But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007. 

If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.

Use problem-solving strategies to uplevel your business

When facing a problem, it’s worth taking the time to find the right solution. 

Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.

Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.

If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.

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Elizabeth Perry, ACC

Elizabeth Perry is a Coach Community Manager at BetterUp. She uses strategic engagement strategies to cultivate a learning community across a global network of Coaches through in-person and virtual experiences, technology-enabled platforms, and strategic coaching industry partnerships. With over 3 years of coaching experience and a certification in transformative leadership and life coaching from Sofia University, Elizabeth leverages transpersonal psychology expertise to help coaches and clients gain awareness of their behavioral and thought patterns, discover their purpose and passions, and elevate their potential. She is a lifelong student of psychology, personal growth, and human potential as well as an ICF-certified ACC transpersonal life and leadership Coach.

8 creative solutions to your most challenging problems

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Problem-Solving Strategies and Obstacles

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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

• Discovery of the problem
• Deciding to tackle the issue
• Seeking to understand the problem more fully
• Researching available options or solutions
• Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

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

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

• Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
• Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
• Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
• Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

• Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
• Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
• Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
• Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

• Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
• Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
• Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
• Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
• Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
• Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

5 Effective Problem-Solving Strategies

Got a problem you’re trying to solve? Strategies like trial and error, gut instincts, and “working backward” can help. We look at some examples and how to use them.

We all face problems daily. Some are simple, like deciding what to eat for dinner. Others are more complex, like resolving a conflict with a loved one or figuring out how to overcome barriers to your goals.

No matter what problem you’re facing, these five problem-solving strategies can help you develop an effective solution.

What are problem-solving strategies?

To effectively solve a problem, you need a problem-solving strategy .

If you’ve had to make a hard decision before then you know that simply ruminating on the problem isn’t likely to get you anywhere. You need an effective strategy — or a plan of action — to find a solution.

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 strategies don’t guarantee a solution, but they do help guide you through the process of finding a resolution.

Using problem-solving strategies also has other benefits . For example, having a strategy you can turn to can help you overcome anxiety and distress when you’re first faced with a problem or difficult decision.

The key is to find a problem-solving strategy that works for your specific situation, as well as your personality. One strategy may work well for one type of problem but not another. In addition, some people may prefer certain strategies over others; for example, creative people may prefer to depend on their insights than use algorithms.

It’s important to be equipped with several problem-solving strategies so you use the one that’s most effective for your current situation.

1. Trial and error

One of the most common problem-solving strategies is trial and error. In other words, you try different solutions until you find one that works.

For example, say the problem is that your Wi-Fi isn’t working. You might try different things until it starts working again, like restarting your modem or your devices until you find or resolve the problem. When one solution isn’t successful, you try another until you find what works.

Trial and error can also work for interpersonal problems . For example, if your child always stays up past their bedtime, you might try different solutions — a visual clock to remind them of the time, a reward system, or gentle punishments — to find a solution that works.

2. Heuristics

Sometimes, it’s more effective to solve a problem based on a formula than to try different solutions blindly.

Heuristics are problem-solving strategies or frameworks people use to quickly find an approximate solution. It may not be the optimal solution, but it’s faster than finding the perfect resolution, and it’s “good enough.”

Algorithms or equations are examples of heuristics.

An algorithm is a step-by-step problem-solving strategy based on a formula guaranteed to give you positive results. For example, you might use an algorithm to determine how much food is needed to feed people at a large party.

However, many life problems have no formulaic solution; for example, you may not be able to come up with an algorithm to solve the problem of making amends with your spouse after a fight.

3. Gut instincts (insight problem-solving)

While algorithm-based problem-solving is formulaic, insight problem-solving is the opposite.

When we use insight as a problem-solving strategy we depend on our “gut instincts” or what we know and feel about a situation to come up with a solution. People might describe insight-based solutions to problems as an “aha moment.”

For example, you might face the problem of whether or not to stay in a relationship. The solution to this problem may come as a sudden insight that you need to leave. In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness.

4. Working backward

Working backward is a problem-solving approach often taught to help students solve problems in mathematics. However, it’s useful for real-world problems as well.

Working backward is when you start with the solution and “work backward” to figure out how you got to the solution. For example, if you know you need to be at a party by 8 p.m., you might work backward to problem-solve when you must leave the house, when you need to start getting ready, and so on.

5. Means-end analysis

Means-end analysis is a problem-solving strategy that, to put it simply, helps you get from “point A” to “point B” by examining and coming up with solutions to obstacles.

When using means-end analysis you define the current state or situation (where you are now) and the intended goal. Then, you come up with solutions to get from where you are now to where you need to be.

For example, a student might be faced with the problem of how to successfully get through finals season . They haven’t started studying, but their end goal is to pass all of their finals. Using means-end analysis, the student can examine the obstacles that stand between their current state and their end goal (passing their finals).

They could see, for example, that one obstacle is that they get distracted from studying by their friends. They could devise a solution to this obstacle by putting their phone on “do not disturb” mode while studying.

Let’s recap

Whether they’re simple or complex, we’re faced with problems every day. To successfully solve these problems we need an effective strategy. There are many different problem-solving strategies to choose from.

Although problem-solving strategies don’t guarantee a solution, they can help you feel less anxious about problems and make it more likely that you come up with an answer.

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• Foulds LR. (2017). The heuristic problem-solving approach. https://www.tandfonline.com/doi/abs/10.1057/jors.1983.205
• Gick ML. (1986). Problem-solving strategies. https://www.tandfonline.com/doi/abs/10.1080/00461520.1986.9653026
• Montgomery ME. (2015). Problem solving using means-end analysis. https://sites.psu.edu/psych256sp15/2015/04/19/problem-solving-using-means-end-analysis/
• Posamentier A, et al. (2015). Problem-solving strategies in mathematics. Chapter 3: Working backwards. https://www.worldscientific.com/doi/10.1142/9789814651646_0003
• Sarathy V. (2018). Real world problem-solving. https://www.frontiersin.org/articles/10.3389/fnhum.2018.00261/full
• Woods D. (2000). An evidence-based strategy for problem solving. https://www.researchgate.net/publication/245332888_An_Evidence-Based_Strategy_for_Problem_Solving

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Struggling to overcome challenges in your life? We all face problems, big and small, on a regular basis.

So how do you tackle them effectively? What are some key problem-solving strategies and skills that can guide you?

Effective problem-solving requires breaking issues down logically, generating solutions creatively, weighing choices critically, and adapting plans flexibly based on outcomes. Useful strategies range from leveraging past solutions that have worked to visualizing problems through diagrams. Core skills include analytical abilities, innovative thinking, and collaboration.

Want to improve your problem-solving skills? Keep reading to find out 17 effective problem-solving strategies, key skills, common obstacles to watch for, and tips on improving your overall problem-solving skills.

Key Takeaways:

• Effective problem-solving requires breaking down issues logically, generating multiple solutions creatively, weighing choices critically, and adapting plans based on outcomes.
• Useful problem-solving strategies range from leveraging past solutions to brainstorming with groups to visualizing problems through diagrams and models.
• Core skills include analytical abilities, innovative thinking, decision-making, and team collaboration to solve problems.
• Common obstacles include fear of failure, information gaps, fixed mindsets, confirmation bias, and groupthink.
• Boosting problem-solving skills involves learning from experts, actively practicing, soliciting feedback, and analyzing others’ success.
• Onethread’s project management capabilities align with effective problem-solving tenets – facilitating structured solutions, tracking progress, and capturing lessons learned.

What Is Problem-Solving?

Problem-solving is the process of understanding an issue, situation, or challenge that needs to be addressed and then systematically working through possible solutions to arrive at the best outcome.

It involves critical thinking, analysis, logic, creativity, research, planning, reflection, and patience in order to overcome obstacles and find effective answers to complex questions or problems.

The ultimate goal is to implement the chosen solution successfully.

What Are Problem-Solving Strategies?

Problem-solving strategies are like frameworks or methodologies that help us solve tricky puzzles or problems we face in the workplace, at home, or with friends.

Imagine you have a big jigsaw puzzle. One strategy might be to start with the corner pieces. Another could be looking for pieces with the same colors. 

Just like in puzzles, in real life, we use different plans or steps to find solutions to problems. These strategies help us think clearly, make good choices, and find the best answers without getting too stressed or giving up.

Why Is It Important To Know Different Problem-Solving Strategies?

Knowing different problem-solving strategies is important because different types of problems often require different approaches to solve them effectively. Having a variety of strategies to choose from allows you to select the best method for the specific problem you are trying to solve.

This improves your ability to analyze issues thoroughly, develop solutions creatively, and tackle problems from multiple angles. Knowing multiple strategies also aids in overcoming roadblocks if your initial approach is not working.

Here are some reasons why you need to know different problem-solving strategies:

• Different Problems Require Different Tools: Just like you can’t use a hammer to fix everything, some problems need specific strategies to solve them.
• Improves Creativity: Knowing various strategies helps you think outside the box and come up with creative solutions.
• Saves Time: With the right strategy, you can solve problems faster instead of trying things that don’t work.
• Reduces Stress: When you know how to tackle a problem, it feels less scary and you feel more confident.
• Better Outcomes: Using the right strategy can lead to better solutions, making things work out better in the end.
• Learning and Growth: Each time you solve a problem, you learn something new, which makes you smarter and better at solving future problems.

Knowing different ways to solve problems helps you tackle anything that comes your way, making life a bit easier and more fun!

17 Effective Problem-Solving Strategies

Effective problem-solving strategies include breaking the problem into smaller parts, brainstorming multiple solutions, evaluating the pros and cons of each, and choosing the most viable option. 

Critical thinking and creativity are essential in developing innovative solutions. Collaboration with others can also provide diverse perspectives and ideas. 

By applying these strategies, you can tackle complex issues more effectively.

Now, consider a challenge you’re dealing with. Which strategy could help you find a solution? Here we will discuss key problem strategies in detail.

1. Use a Past Solution That Worked

This strategy involves looking back at previous similar problems you have faced and the solutions that were effective in solving them.

It is useful when you are facing a problem that is very similar to something you have already solved. The main benefit is that you don’t have to come up with a brand new solution – you already know the method that worked before will likely work again.

However, the limitation is that the current problem may have some unique aspects or differences that mean your old solution is not fully applicable.

The ideal process is to thoroughly analyze the new challenge, identify the key similarities and differences versus the past case, adapt the old solution as needed to align with the current context, and then pilot it carefully before full implementation.

An example is using the same negotiation tactics from purchasing your previous home when putting in an offer on a new house. Key terms would be adjusted but overall it can save significant time versus developing a brand new strategy.

2. Brainstorm Solutions

This involves gathering a group of people together to generate as many potential solutions to a problem as possible.

It is effective when you need creative ideas to solve a complex or challenging issue. By getting input from multiple people with diverse perspectives, you increase the likelihood of finding an innovative solution.

The main limitation is that brainstorming sessions can sometimes turn into unproductive gripe sessions or discussions rather than focusing on productive ideation —so they need to be properly facilitated.

The key to an effective brainstorming session is setting some basic ground rules upfront and having an experienced facilitator guide the discussion. Rules often include encouraging wild ideas, avoiding criticism of ideas during the ideation phase, and building on others’ ideas.

For instance, a struggling startup might hold a session where ideas for turnaround plans are generated and then formalized with financials and metrics.

3. Work Backward from the Solution

This technique involves envisioning that the problem has already been solved and then working step-by-step backward toward the current state.

This strategy is particularly helpful for long-term, multi-step problems. By starting from the imagined solution and identifying all the steps required to reach it, you can systematically determine the actions needed. It lets you tackle a big hairy problem through smaller, reversible steps.

A limitation is that this approach may not be possible if you cannot accurately envision the solution state to start with.

The approach helps drive logical systematic thinking for complex problem-solving, but should still be combined with creative brainstorming of alternative scenarios and solutions.

An example is planning for an event – you would imagine the successful event occurring, then determine the tasks needed the week before, two weeks before, etc. all the way back to the present.

4. Use the Kipling Method

This method, named after author Rudyard Kipling, provides a framework for thoroughly analyzing a problem before jumping into solutions.

It consists of answering six fundamental questions: What, Where, When, How, Who, and Why about the challenge. Clearly defining these core elements of the problem sets the stage for generating targeted solutions.

The Kipling method enables a deep understanding of problem parameters and root causes before solution identification. By jumping to brainstorm solutions too early, critical information can be missed or the problem is loosely defined, reducing solution quality.

Answering the six fundamental questions illuminates all angles of the issue. This takes time but pays dividends in generating optimal solutions later tuned precisely to the true underlying problem.

The limitation is that meticulously working through numerous questions before addressing solutions can slow progress.

The best approach blends structured problem decomposition techniques like the Kipling method with spurring innovative solution ideation from a diverse team. 

An example is using this technique after a technical process failure – the team would systematically detail What failed, Where/When did it fail, How it failed (sequence of events), Who was involved, and Why it likely failed before exploring preventative solutions.

5. Try Different Solutions Until One Works (Trial and Error)

This technique involves attempting various potential solutions sequentially until finding one that successfully solves the problem.

Trial and error works best when facing a concrete, bounded challenge with clear solution criteria and a small number of discrete options to try. By methodically testing solutions, you can determine the faulty component.

A limitation is that it can be time-intensive if the working solution set is large.

The key is limiting the variable set first. For technical problems, this boundary is inherent and each element can be iteratively tested. But for business issues, artificial constraints may be required – setting decision rules upfront to reduce options before testing.

Furthermore, hypothesis-driven experimentation is far superior to blind trial and error – have logic for why Option A may outperform Option B.

Examples include fixing printer jams by testing different paper tray and cable configurations or resolving website errors by tweaking CSS/HTML line-by-line until the code functions properly.

6. Use Proven Formulas or Frameworks (Heuristics)

Heuristics refers to applying existing problem-solving formulas or frameworks rather than addressing issues completely from scratch.

This allows leveraging established best practices rather than reinventing the wheel each time.

It is effective when facing recurrent, common challenges where proven structured approaches exist.

However, heuristics may force-fit solutions to non-standard problems.

For example, a cost-benefit analysis can be used instead of custom weighting schemes to analyze potential process improvements.

Onethread allows teams to define, save, and replicate configurable project templates so proven workflows can be reliably applied across problems with some consistency rather than fully custom one-off approaches each time.

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7. Trust Your Instincts (Insight Problem-Solving)

Insight is a problem-solving technique that involves waiting patiently for an unexpected “aha moment” when the solution pops into your mind.

It works well for personal challenges that require intuitive realizations over calculated logic. The unconscious mind makes connections leading to flashes of insight when relaxing or doing mundane tasks unrelated to the actual problem.

Benefits include out-of-the-box creative solutions. However, the limitations are that insights can’t be forced and may never come at all if too complex. Critical analysis is still required after initial insights.

A real-life example would be a writer struggling with how to end a novel. Despite extensive brainstorming, they feel stuck. Eventually while gardening one day, a perfect unexpected plot twist sparks an ideal conclusion. However, once written they still carefully review if the ending flows logically from the rest of the story.

8. Reverse Engineer the Problem

This approach involves deconstructing a problem in reverse sequential order from the current undesirable outcome back to the initial root causes.

By mapping the chain of events backward, you can identify the origin of where things went wrong and establish the critical junctures for solving it moving ahead. Reverse engineering provides diagnostic clarity on multi-step problems.

However, the limitation is that it focuses heavily on autopsying the past versus innovating improved future solutions.

An example is tracing back from a server outage, through the cascade of infrastructure failures that led to it finally terminating at the initial script error that triggered the crisis. This root cause would then inform the preventative measure.

9. Break Down Obstacles Between Current and Goal State (Means-End Analysis)

This technique defines the current problem state and the desired end goal state, then systematically identifies obstacles in the way of getting from one to the other.

By mapping the barriers or gaps, you can then develop solutions to address each one. This methodically connects the problem to solutions.

A limitation is that some obstacles may be unknown upfront and only emerge later.

For example, you can list down all the steps required for a new product launch – current state through production, marketing, sales, distribution, etc. to full launch (goal state) – to highlight where resource constraints or other blocks exist so they can be addressed.

Onethread allows dividing big-picture projects into discrete, manageable phases, milestones, and tasks to simplify execution just as problems can be decomposed into more achievable components. Features like dependency mapping further reinforce interconnections.

Using Onethread’s issues and subtasks feature, messy problems can be decomposed into manageable chunks.

10. Ask “Why” Five Times to Identify the Root Cause (The 5 Whys)

This technique involves asking “Why did this problem occur?” and then responding with an answer that is again met with asking “Why?” This process repeats five times until the root cause is revealed.

Continually asking why digs deeper from surface symptoms to underlying systemic issues.

It is effective for getting to the source of problems originating from human error or process breakdowns.

However, some complex issues may have multiple tangled root causes not solvable through this approach alone.

An example is a retail store experiencing a sudden decline in customers. Successively asking why five times may trace an initial drop to parking challenges, stemming from a city construction project – the true starting point to address.

11. Evaluate Strengths, Weaknesses, Opportunities, and Threats (SWOT Analysis)

This involves analyzing a problem or proposed solution by categorizing internal and external factors into a 2×2 matrix: Strengths, Weaknesses as the internal rows; Opportunities and Threats as the external columns.

Systematically identifying these elements provides balanced insight to evaluate options and risks. It is impactful when evaluating alternative solutions or developing strategy amid complexity or uncertainty.

The key benefit of SWOT analysis is enabling multi-dimensional thinking when rationally evaluating options. Rather than getting anchored on just the upsides or the existing way of operating, it urges a systematic assessment through four different lenses:

• Internal Strengths: Our core competencies/advantages able to deliver success
• Internal Weaknesses: Gaps/vulnerabilities we need to manage
• External Opportunities: Ways we can differentiate/drive additional value
• External Threats: Risks we must navigate or mitigate

Multiperspective analysis provides the needed holistic view of the balanced risk vs. reward equation for strategic decision making amid uncertainty.

However, SWOT can feel restrictive if not tailored and evolved for different issue types.

Teams should view SWOT analysis as a starting point, augmenting it further for distinct scenarios.

An example is performing a SWOT analysis on whether a small business should expand into a new market – evaluating internal capabilities to execute vs. risks in the external competitive and demand environment to inform the growth decision with eyes wide open.

12. Compare Current vs Expected Performance (Gap Analysis)

This technique involves comparing the current state of performance, output, or results to the desired or expected levels to highlight shortfalls.

By quantifying the gaps, you can identify problem areas and prioritize address solutions.

Gap analysis is based on the simple principle – “you can’t improve what you don’t measure.” It enables facts-driven problem diagnosis by highlighting delta to goals, not just vague dissatisfaction that something seems wrong. And measurement immediately suggests improvement opportunities – address the biggest gaps first.

This data orientation also supports ROI analysis on fixing issues – the return from closing larger gaps outweighs narrowly targeting smaller performance deficiencies.

However, the approach is only effective if robust standards and metrics exist as the benchmark to evaluate against. Organizations should invest upfront in establishing performance frameworks.

Furthermore, while numbers are invaluable, the human context behind problems should not be ignored – quantitative versus qualitative gap assessment is optimally blended.

For example, if usage declines are noted during software gap analysis, this could be used as a signal to improve user experience through design.

13. Observe Processes from the Frontline (Gemba Walk)

A Gemba walk involves going to the actual place where work is done, directly observing the process, engaging with employees, and finding areas for improvement.

By experiencing firsthand rather than solely reviewing abstract reports, practical problems and ideas emerge.

The limitation is Gemba walks provide anecdotes not statistically significant data. It complements but does not replace comprehensive performance measurement.

An example is a factory manager inspecting the production line to spot jam areas based on direct reality rather than relying on throughput dashboards alone back in her office. Frontline insights prove invaluable.

14. Analyze Competitive Forces (Porter’s Five Forces)

This involves assessing the marketplace around a problem or business situation via five key factors: competitors, new entrants, substitute offerings, suppliers, and customer power.

Evaluating these forces illuminates risks and opportunities for strategy development and issue resolution. It is effective for understanding dynamic external threats and opportunities when operating in a contested space.

However, over-indexing on only external factors can overlook the internal capabilities needed to execute solutions.

A startup CEO, for example, may analyze market entry barriers, whitespace opportunities, and disruption risks across these five forces to shape new product rollout strategies and marketing approaches.

15. Think from Different Perspectives (Six Thinking Hats)

The Six Thinking Hats is a technique developed by Edward de Bono that encourages people to think about a problem from six different perspectives, each represented by a colored “thinking hat.”

The key benefit of this strategy is that it pushes team members to move outside their usual thinking style and consider new angles. This brings more diverse ideas and solutions to the table.

It works best for complex problems that require innovative solutions and when a team is stuck in an unproductive debate. The structured framework keeps the conversation flowing in a positive direction.

Limitations are that it requires training on the method itself and may feel unnatural at first. Team dynamics can also influence success – some members may dominate certain “hats” while others remain quiet.

A real-life example is a software company debating whether to build a new feature. The white hat focuses on facts, red on gut feelings, black on potential risks, yellow on benefits, green on new ideas, and blue on process. This exposes more balanced perspectives before deciding.

Onethread centralizes diverse stakeholder communication onto one platform, ensuring all voices are incorporated when evaluating project tradeoffs, just as problem-solving should consider multifaceted solutions.

16. Visualize the Problem (Draw it Out)

Drawing out a problem involves creating visual representations like diagrams, flowcharts, and maps to work through challenging issues.

This strategy is helpful when dealing with complex situations with lots of interconnected components. The visuals simplify the complexity so you can thoroughly understand the problem and all its nuances.

Key benefits are that it allows more stakeholders to get on the same page regarding root causes and it sparks new creative solutions as connections are made visually.

However, simple problems with few variables don’t require extensive diagrams. Additionally, some challenges are so multidimensional that fully capturing every aspect is difficult.

A real-life example would be mapping out all the possible causes leading to decreased client satisfaction at a law firm. An intricate fishbone diagram with branches for issues like service delivery, technology, facilities, culture, and vendor partnerships allows the team to trace problems back to their origins and brainstorm targeted fixes.

17. Follow a Step-by-Step Procedure (Algorithms)

An algorithm is a predefined step-by-step process that is guaranteed to produce the correct solution if implemented properly.

Using algorithms is effective when facing problems that have clear, binary right and wrong answers. Algorithms work for mathematical calculations, computer code, manufacturing assembly lines, and scientific experiments.

Key benefits are consistency, accuracy, and efficiency. However, they require extensive upfront development and only apply to scenarios with strict parameters. Additionally, human error can lead to mistakes.

For example, crew members of fast food chains like McDonald’s follow specific algorithms for food prep – from grill times to ingredient amounts in sandwiches, to order fulfillment procedures. This ensures uniform quality and service across all locations. However, if a step is missed, errors occur.

The Problem-Solving Process

The problem-solving process typically includes defining the issue, analyzing details, creating solutions, weighing choices, acting, and reviewing results.

In the above, we have discussed several problem-solving strategies. For every problem-solving strategy, you have to follow these processes. Here’s a detailed step-by-step process of effective problem-solving:

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.

Identifying the problem is crucial. It means figuring out exactly what needs fixing. This involves looking at the situation closely, understanding what’s wrong, and knowing how it affects things. It’s about asking the right questions to get a clear picture of the issue. 

This step is important because it guides the rest of the problem-solving process. Without a clear understanding of the problem, finding a solution is much harder. It’s like diagnosing an illness before treating it. Once the problem is identified accurately, you can move on to exploring possible solutions and deciding on the best course of action.

Step 2: Break Down the Problem

Breaking down the problem is a key step in the problem-solving process. It involves dividing the main issue into smaller, more manageable parts. This makes it easier to understand and tackle each component one by one.

After identifying the problem, the next step is to break it down. This means splitting the big issue into smaller pieces. It’s like solving a puzzle by handling one piece at a time. 

By doing this, you can focus on each part without feeling overwhelmed. It also helps in identifying the root causes of the problem. Breaking down the problem allows for a clearer analysis and makes finding solutions more straightforward. 

Each smaller problem can be addressed individually, leading to an effective resolution of the overall issue. This approach not only simplifies complex problems but also aids in developing a systematic plan to solve them.

Step 3: Come up with potential solutions

Coming up with potential solutions is the third step in the problem-solving process. It involves brainstorming various options to address the problem, considering creativity and feasibility to find the best approach.

After breaking down the problem, it’s time to think of ways to solve it. This stage is about brainstorming different solutions. You look at the smaller issues you’ve identified and start thinking of ways to fix them. This is where creativity comes in. 

You want to come up with as many ideas as possible, no matter how out-of-the-box they seem. It’s important to consider all options and evaluate their pros and cons. This process allows you to gather a range of possible solutions. 

Later, you can narrow these down to the most practical and effective ones. This step is crucial because it sets the stage for deciding on the best solution to implement. It’s about being open-minded and innovative to tackle the problem effectively.

Step 4: Analyze the possible solutions

Analyzing the possible solutions is the fourth step in the problem-solving process. It involves evaluating each proposed solution’s advantages and disadvantages to determine the most effective and feasible option.

After coming up with potential solutions, the next step is to analyze them. This means looking closely at each idea to see how well it solves the problem. You weigh the pros and cons of every solution.

Consider factors like cost, time, resources, and potential outcomes. This analysis helps in understanding the implications of each option. It’s about being critical and objective, ensuring that the chosen solution is not only effective but also practical.

This step is vital because it guides you towards making an informed decision. It involves comparing the solutions against each other and selecting the one that best addresses the problem.

By thoroughly analyzing the options, you can move forward with confidence, knowing you’ve chosen the best path to solve the issue.

Step 5: Implement and Monitor the Solutions

Implementing and monitoring the solutions is the final step in the problem-solving process. It involves putting the chosen solution into action and observing its effectiveness, making adjustments as necessary.

Once you’ve selected the best solution, it’s time to put it into practice. This step is about action. You implement the chosen solution and then keep an eye on how it works. Monitoring is crucial because it tells you if the solution is solving the problem as expected. 

If things don’t go as planned, you may need to make some changes. This could mean tweaking the current solution or trying a different one. The goal is to ensure the problem is fully resolved. 

This step is critical because it involves real-world application. It’s not just about planning; it’s about doing and adjusting based on results. By effectively implementing and monitoring the solutions, you can achieve the desired outcome and solve the problem successfully.

Why This Process is Important

Following a defined process to solve problems is important because it provides a systematic, structured approach instead of a haphazard one. Having clear steps guides logical thinking, analysis, and decision-making to increase effectiveness. Key reasons it helps are:

• Clear Direction: This process gives you a clear path to follow, which can make solving problems less overwhelming.
• Better Solutions: Thoughtful analysis of root causes, iterative testing of solutions, and learning orientation lead to addressing the heart of issues rather than just symptoms.
• Saves Time and Energy: Instead of guessing or trying random things, this process helps you find a solution more efficiently.
• Improves Skills: The more you use this process, the better you get at solving problems. It’s like practicing a sport. The more you practice, the better you play.
• Maximizes collaboration: Involving various stakeholders in the process enables broader inputs. Their communication and coordination are streamlined through organized brainstorming and evaluation.
• Provides consistency: Standard methodology across problems enables building institutional problem-solving capabilities over time. Patterns emerge on effective techniques to apply to different situations.

The problem-solving process is a powerful tool that can help us tackle any challenge we face. By following these steps, we can find solutions that work and learn important skills along the way.

Key Skills for Efficient Problem Solving

Efficient problem-solving requires breaking down issues logically, evaluating options, and implementing practical solutions.

Key skills include critical thinking to understand root causes, creativity to brainstorm innovative ideas, communication abilities to collaborate with others, and decision-making to select the best way forward. Staying adaptable, reflecting on outcomes, and applying lessons learned are also essential.

With practice, these capacities will lead to increased personal and team effectiveness in systematically addressing any problem.

 Let’s explore the powers you need to become a problem-solving hero!

Critical Thinking and Analytical Skills

Critical thinking and analytical skills are vital for efficient problem-solving as they enable individuals to objectively evaluate information, identify key issues, and generate effective solutions. 

These skills facilitate a deeper understanding of problems, leading to logical, well-reasoned decisions. By systematically breaking down complex issues and considering various perspectives, individuals can develop more innovative and practical solutions, enhancing their problem-solving effectiveness.

Communication Skills

Effective communication skills are essential for efficient problem-solving as they facilitate clear sharing of information, ensuring all team members understand the problem and proposed solutions. 

These skills enable individuals to articulate issues, listen actively, and collaborate effectively, fostering a productive environment where diverse ideas can be exchanged and refined. By enhancing mutual understanding, communication skills contribute significantly to identifying and implementing the most viable solutions.

Decision-Making

Strong decision-making skills are crucial for efficient problem-solving, as they enable individuals to choose the best course of action from multiple alternatives. 

These skills involve evaluating the potential outcomes of different solutions, considering the risks and benefits, and making informed choices. Effective decision-making leads to the implementation of solutions that are likely to resolve problems effectively, ensuring resources are used efficiently and goals are achieved.

Planning and Prioritization

Planning and prioritization are key for efficient problem-solving, ensuring resources are allocated effectively to address the most critical issues first. This approach helps in organizing tasks according to their urgency and impact, streamlining efforts towards achieving the desired outcome efficiently.

Emotional Intelligence

Emotional intelligence enhances problem-solving by allowing individuals to manage emotions, understand others, and navigate social complexities. It fosters a positive, collaborative environment, essential for generating creative solutions and making informed, empathetic decisions.

Leadership skills drive efficient problem-solving by inspiring and guiding teams toward common goals. Effective leaders motivate their teams, foster innovation, and navigate challenges, ensuring collective efforts are focused and productive in addressing problems.

Time Management

Time management is crucial in problem-solving, enabling individuals to allocate appropriate time to each task. By efficiently managing time, one can ensure that critical problems are addressed promptly without neglecting other responsibilities.

Data Analysis

Data analysis skills are essential for problem-solving, as they enable individuals to sift through data, identify trends, and extract actionable insights. This analytical approach supports evidence-based decision-making, leading to more accurate and effective solutions.

Research Skills

Research skills are vital for efficient problem-solving, allowing individuals to gather relevant information, explore various solutions, and understand the problem’s context. This thorough exploration aids in developing well-informed, innovative solutions.

Becoming a great problem solver takes practice, but with these skills, you’re on your way to becoming a problem-solving hero. 

How to Improve Your Problem-Solving Skills?

Improving your problem-solving skills can make you a master at overcoming challenges. Learn from experts, practice regularly, welcome feedback, try new methods, experiment, and study others’ success to become better.

Learning from Experts

Improving problem-solving skills by learning from experts involves seeking mentorship, attending workshops, and studying case studies. Experts provide insights and techniques that refine your approach, enhancing your ability to tackle complex problems effectively.

To enhance your problem-solving skills, learning from experts can be incredibly beneficial. Engaging with mentors, participating in specialized workshops, and analyzing case studies from seasoned professionals can offer valuable perspectives and strategies. 

Experts share their experiences, mistakes, and successes, providing practical knowledge that can be applied to your own problem-solving process. This exposure not only broadens your understanding but also introduces you to diverse methods and approaches, enabling you to tackle challenges more efficiently and creatively.

Improving problem-solving skills through practice involves tackling a variety of challenges regularly. This hands-on approach helps in refining techniques and strategies, making you more adept at identifying and solving problems efficiently.

One of the most effective ways to enhance your problem-solving skills is through consistent practice. By engaging with different types of problems on a regular basis, you develop a deeper understanding of various strategies and how they can be applied. 

This hands-on experience allows you to experiment with different approaches, learn from mistakes, and build confidence in your ability to tackle challenges.

Regular practice not only sharpens your analytical and critical thinking skills but also encourages adaptability and innovation, key components of effective problem-solving.

Openness to Feedback

Being open to feedback is like unlocking a secret level in a game. It helps you boost your problem-solving skills. Improving problem-solving skills through openness to feedback involves actively seeking and constructively responding to critiques. 

This receptivity enables you to refine your strategies and approaches based on insights from others, leading to more effective solutions. 

Learning New Approaches and Methodologies

Learning new approaches and methodologies is like adding new tools to your toolbox. It makes you a smarter problem-solver. Enhancing problem-solving skills by learning new approaches and methodologies involves staying updated with the latest trends and techniques in your field. 

This continuous learning expands your toolkit, enabling innovative solutions and a fresh perspective on challenges.

Experimentation

Experimentation is like being a scientist of your own problems. It’s a powerful way to improve your problem-solving skills. Boosting problem-solving skills through experimentation means trying out different solutions to see what works best. This trial-and-error approach fosters creativity and can lead to unique solutions that wouldn’t have been considered otherwise.

Analyzing Competitors’ Success

Analyzing competitors’ success is like being a detective. It’s a smart way to boost your problem-solving skills. Improving problem-solving skills by analyzing competitors’ success involves studying their strategies and outcomes. Understanding what worked for them can provide valuable insights and inspire effective solutions for your own challenges. 

Challenges in Problem-Solving

Facing obstacles when solving problems is common. Recognizing these barriers, like fear of failure or lack of information, helps us find ways around them for better solutions.

Fear of Failure

Fear of failure is like a big, scary monster that stops us from solving problems. It’s a challenge many face. Because being afraid of making mistakes can make us too scared to try new solutions. 

How can we overcome this? First, understand that it’s okay to fail. Failure is not the opposite of success; it’s part of learning. Every time we fail, we discover one more way not to solve a problem, getting us closer to the right solution. Treat each attempt like an experiment. It’s not about failing; it’s about testing and learning.

Lack of Information

Lack of information is like trying to solve a puzzle with missing pieces. It’s a big challenge in problem-solving. Because without all the necessary details, finding a solution is much harder. 

How can we fix this? Start by gathering as much information as you can. Ask questions, do research, or talk to experts. Think of yourself as a detective looking for clues. The more information you collect, the clearer the picture becomes. Then, use what you’ve learned to think of solutions. 

Fixed Mindset

A fixed mindset is like being stuck in quicksand; it makes solving problems harder. It means thinking you can’t improve or learn new ways to solve issues. 

How can we change this? First, believe that you can grow and learn from challenges. Think of your brain as a muscle that gets stronger every time you use it. When you face a problem, instead of saying “I can’t do this,” try thinking, “I can’t do this yet.” Look for lessons in every challenge and celebrate small wins. 

Everyone starts somewhere, and mistakes are just steps on the path to getting better. By shifting to a growth mindset, you’ll see problems as opportunities to grow. Keep trying, keep learning, and your problem-solving skills will soar!

Jumping to Conclusions

Jumping to conclusions is like trying to finish a race before it starts. It’s a challenge in problem-solving. That means making a decision too quickly without looking at all the facts. 

How can we avoid this? First, take a deep breath and slow down. Think about the problem like a puzzle. You need to see all the pieces before you know where they go. Ask questions, gather information, and consider different possibilities. Don’t choose the first solution that comes to mind. Instead, compare a few options. 

Feeling Overwhelmed

Feeling overwhelmed is like being buried under a mountain of puzzles. It’s a big challenge in problem-solving. When we’re overwhelmed, everything seems too hard to handle. 

How can we deal with this? Start by taking a step back. Breathe deeply and focus on one thing at a time. Break the big problem into smaller pieces, like sorting puzzle pieces by color. Tackle each small piece one by one. It’s also okay to ask for help. Sometimes, talking to someone else can give you a new perspective. 

Confirmation Bias

Confirmation bias is like wearing glasses that only let you see what you want to see. It’s a challenge in problem-solving. Because it makes us focus only on information that agrees with what we already believe, ignoring anything that doesn’t. 

How can we overcome this? First, be aware that you might be doing it. It’s like checking if your glasses are on right. Then, purposely look for information that challenges your views. It’s like trying on a different pair of glasses to see a new perspective. Ask questions and listen to answers, even if they don’t fit what you thought before.

Groupthink is like everyone in a group deciding to wear the same outfit without asking why. It’s a challenge in problem-solving. It means making decisions just because everyone else agrees, without really thinking it through. 

How can we avoid this? First, encourage everyone in the group to share their ideas, even if they’re different. It’s like inviting everyone to show their unique style of clothes. 

Listen to all opinions and discuss them. It’s okay to disagree; it helps us think of better solutions. Also, sometimes, ask someone outside the group for their thoughts. They might see something everyone in the group missed.

Overcoming obstacles in problem-solving requires patience, openness, and a willingness to learn from mistakes. By recognizing these barriers, we can develop strategies to navigate around them, leading to more effective and creative solutions.

What are the most common problem-solving techniques?

The most common techniques include brainstorming, the 5 Whys, mind mapping, SWOT analysis, and using algorithms or heuristics. Each approach has its strengths, suitable for different types of problems.

What’s the best problem-solving strategy for every situation?

There’s no one-size-fits-all strategy. The best approach depends on the problem’s complexity, available resources, and time constraints. Combining multiple techniques often yields the best results.

How can I improve my problem-solving skills?

Improve your problem-solving skills by practicing regularly, learning from experts, staying open to feedback, and continuously updating your knowledge on new approaches and methodologies.

Are there any tools or resources to help with problem-solving?

Yes, tools like mind mapping software, online courses on critical thinking, and books on problem-solving techniques can be very helpful. Joining forums or groups focused on problem-solving can also provide support and insights.

What are some common mistakes people make when solving problems?

Common mistakes include jumping to conclusions without fully understanding the problem, ignoring valuable feedback, sticking to familiar solutions without considering alternatives, and not breaking down complex problems into manageable parts.

Final Words

Mastering problem-solving strategies equips us with the tools to tackle challenges across all areas of life. By understanding and applying these techniques, embracing a growth mindset, and learning from both successes and obstacles, we can transform problems into opportunities for growth. Continuously improving these skills ensures we’re prepared to face and solve future challenges more effectively.

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A guide to problem-solving techniques, steps, and skills

You might associate problem-solving with the math exercises that a seven-year-old would do at school. But problem-solving isn’t just about math — it’s a crucial skill that helps everyone make better decisions in everyday life or work.

Problem-solving involves finding effective solutions to address complex challenges, in any context they may arise.

Unfortunately, structured and systematic problem-solving methods aren’t commonly taught. Instead, when solving a problem, PMs tend to rely heavily on intuition. While for simple issues this might work well, solving a complex problem with a straightforward solution is often ineffective and can even create more problems.

In this article, you’ll learn a framework for approaching problem-solving, alongside how you can improve your problem-solving skills.

The 7 steps to problem-solving

When it comes to problem-solving there are seven key steps that you should follow: define the problem, disaggregate, prioritize problem branches, create an analysis plan, conduct analysis, synthesis, and communication.

1. Define the problem

Problem-solving begins with a clear understanding of the issue at hand. Without a well-defined problem statement, confusion and misunderstandings can hinder progress. It’s crucial to ensure that the problem statement is outcome-focused, specific, measurable whenever possible, and time-bound.

Additionally, aligning the problem definition with relevant stakeholders and decision-makers is essential to ensure efforts are directed towards addressing the actual problem rather than side issues.

2. Disaggregate

Complex issues often require deeper analysis. Instead of tackling the entire problem at once, the next step is to break it down into smaller, more manageable components.

Various types of logic trees (also known as issue trees or decision trees) can be used to break down the problem. At each stage where new branches are created, it’s important for them to be “MECE” – mutually exclusive and collectively exhaustive. This process of breaking down continues until manageable components are identified, allowing for individual examination.

The decomposition of the problem demands looking at the problem from various perspectives. That is why collaboration within a team often yields more valuable results, as diverse viewpoints lead to a richer pool of ideas and solutions.

3. Prioritize problem branches

The next step involves prioritization. Not all branches of the problem tree have the same impact, so it’s important to understand the significance of each and focus attention on the most impactful areas. Prioritizing helps streamline efforts and minimize the time required to solve the problem.

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4. Create an analysis plan

For prioritized components, you may need to conduct in-depth analysis. Before proceeding, a work plan is created for data gathering and analysis. If work is conducted within a team, having a plan provides guidance on what needs to be achieved, who is responsible for which tasks, and the timelines involved.

5. Conduct analysis

Data gathering and analysis are central to the problem-solving process. It’s a good practice to set time limits for this phase to prevent excessive time spent on perfecting details. You can employ heuristics and rule-of-thumb reasoning to improve efficiency and direct efforts towards the most impactful work.

6. Synthesis

After each individual branch component has been researched, the problem isn’t solved yet. The next step is synthesizing the data logically to address the initial question. The synthesis process and the logical relationship between the individual branch results depend on the logic tree used.

7. Communication

The last step is communicating the story and the solution of the problem to the stakeholders and decision-makers. Clear effective communication is necessary to build trust in the solution and facilitates understanding among all parties involved. It ensures that stakeholders grasp the intricacies of the problem and the proposed solution, leading to informed decision-making.

Exploring problem-solving in various contexts

While problem-solving has traditionally been associated with fields like engineering and science, today it has become a fundamental skill for individuals across all professions. In fact, problem-solving consistently ranks as one of the top skills required by employers.

Problem-solving techniques can be applied in diverse contexts:

• Individuals — What career path should I choose? Where should I live? These are examples of simple and common personal challenges that require effective problem-solving skills
• Organizations — Businesses also face many decisions that are not trivial to answer. Should we expand into new markets this year? How can we enhance the quality of our product development? Will our office accommodate the upcoming year’s growth in terms of capacity?
• Societal issues — The biggest world challenges are also complex problems that can be addressed with the same technique. How can we minimize the impact of climate change? How do we fight cancer?

Despite the variation in domains and contexts, the fundamental approach to solving these questions remains the same. It starts with gaining a clear understanding of the problem, followed by decomposition, conducting analysis of the decomposed branches, and synthesizing it into a result that answers the initial problem.

Real-world examples of problem-solving

Let’s now explore some examples where we can apply the problem solving framework.

Problem: In the production of electronic devices, you observe an increasing number of defects. How can you reduce the error rate and improve the quality?

Before delving into analysis, you can deprioritize branches that you already have information for or ones you deem less important. For instance, while transportation delays may occur, the resulting material degradation is likely negligible. For other branches, additional research and data gathering may be necessary.

Once results are obtained, synthesis is crucial to address the core question: How can you decrease the defect rate?

While all factors listed may play a role, their significance varies. Your task is to prioritize effectively. Through data analysis, you may discover that altering the equipment would bring the most substantial positive outcome. However, executing a solution isn’t always straightforward. In prioritizing, you should consider both the potential impact and the level of effort needed for implementation.

By evaluating impact and effort, you can systematically prioritize areas for improvement, focusing on those with high impact and requiring minimal effort to address. This approach ensures efficient allocation of resources towards improvements that offer the greatest return on investment.

Problem : What should be my next job role?

When breaking down this problem, you need to consider various factors that are important for your future happiness in the role. This includes aspects like the company culture, our interest in the work itself, and the lifestyle that you can afford with the role.

However, not all factors carry the same weight for us. To make sense of the results, we can assign a weight factor to each branch. For instance, passion for the job role may have a weight factor of 1, while interest in the industry may have a weight factor of 0.5, because that is less important for you.

By applying these weights to a specific role and summing the values, you can have an estimate of how suitable that role is for you. Moreover, you can compare two roles and make an informed decision based on these weighted indicators.

Key problem-solving skills

This framework provides the foundation and guidance needed to effectively solve problems. However, successfully applying this framework requires the following:

• Creativity — During the decomposition phase, it’s essential to approach the problem from various perspectives and think outside the box to generate innovative ideas for breaking down the problem tree
• Decision-making — Throughout the process, decisions must be made, even when full confidence is lacking. Employing rules of thumb to simplify analysis or selecting one tree cut over another requires decisiveness and comfort with choices made
• Analytical skills — Analytical and research skills are necessary for the phase following decomposition, involving data gathering and analysis on selected tree branches
• Teamwork — Collaboration and teamwork are crucial when working within a team setting. Solving problems effectively often requires collective effort and shared responsibility
• Communication — Clear and structured communication is essential to convey the problem solution to stakeholders and decision-makers and build trust

How to enhance your problem-solving skills

Problem-solving requires practice and a certain mindset. The more you practice, the easier it becomes. Here are some strategies to enhance your skills:

• Practice structured thinking in your daily life — Break down problems or questions into manageable parts. You don’t need to go through the entire problem-solving process and conduct detailed analysis. When conveying a message, simplify the conversation by breaking the message into smaller, more understandable segments
• Regularly challenging yourself with games and puzzles — Solving puzzles, riddles, or strategy games can boost your problem-solving skills and cognitive agility.
• Engage with individuals from diverse backgrounds and viewpoints — Conversing with people who offer different perspectives provides fresh insights and alternative solutions to problems. This boosts creativity and helps in approaching challenges from new angles

Final thoughts

Problem-solving extends far beyond mathematics or scientific fields; it’s a critical skill for making informed decisions in every area of life and work. The seven-step framework presented here provides a systematic approach to problem-solving, relevant across various domains.

Now, consider this: What’s one question currently on your mind? Grab a piece of paper and try to apply the problem-solving framework. You might uncover fresh insights you hadn’t considered before.

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How to Solve Coding Problems with a Simple Four Step Method

By Madison Kanna

I had fifteen minutes left, and I knew I was going to fail.

I had spent two months studying for my first technical interview.

I thought I was prepared, but as the interview came to a close, it hit me: I had no idea how to solve coding problems.

Of all the tutorials I had taken when I was learning to code, not one of them had included an approach to solving coding problems.

I had to find a method for problem-solving—my career as a developer depended on it.

I immediately began researching methods. And I found one. In fact, what I uncovered was an invaluable strategy. It was a time-tested four-step method that was somehow under the radar in the developer ecosystem.

In this article, I’ll go over this four-step problem-solving method that you can use to start confidently solving coding problems.

Solving coding problems is not only part of the developer job interview process—it’s what a developer does all day. After all, writing code is problem-solving.

A method for solving problems

This method is from the book How to Solve It by George Pólya. It originally came out in 1945 and has sold over one million copies.

His problem-solving method has been used and taught by many programmers, from computer science professors (see Udacity’s Intro to CS course taught by professor David Evans) to modern web development teachers like Colt Steele.

Let’s walk through solving a simple coding problem using the four-step problem-solving method. This allows us to see the method in action as we learn it. We'll use JavaScript as our language of choice. Here’s the problem:

Create a function that adds together two numbers and returns that value.

There are four steps to the problem-solving method:

• Understand the problem.
• Devise a plan.
• Carry out the plan.

Let’s get started with step one.

Step 1: Understand the problem.

When given a coding problem in an interview, it’s tempting to rush into coding. This is hard to avoid, especially if you have a time limit.

However, try to resist this urge. Make sure you actually understand the problem before you get started with solving it.

Read through the problem. If you’re in an interview, you could read through the problem out loud if that helps you slow down.

As you read through the problem, clarify any part of it you do not understand. If you’re in an interview, you can do this by asking your interviewer questions about the problem description. If you’re on your own, think through and/or Google parts of the question you might not understand.

This first step is vital as we often don’t take the time to fully understand the problem. When you don’t fully understand the problem, you’ll have a much harder time solving it.

To help you better understand the problem, ask yourself:

What are the inputs?

What kinds of inputs will go into this problem? In this example, the inputs are the arguments that our function will take.

Just from reading the problem description so far, we know that the inputs will be numbers. But to be more specific about what the inputs will be, we can ask:

Will the inputs always be just two numbers? What should happen if our function receives as input three numbers?

Here we could ask the interviewer for clarification, or look at the problem description further.

The coding problem might have a note saying, “You should only ever expect two inputs into the function.” If so, you know how to proceed. You can get more specific, as you’ll likely realize that you need to ask more questions on what kinds of inputs you might be receiving.

Will the inputs always be numbers? What should our function do if we receive the inputs “a” and “b”? Clarify whether or not our function will always take in numbers.

Optionally, you could write down possible inputs in a code comment to get a sense of what they’ll look like:

//inputs: 2, 4

What are the outputs?

What will this function return? In this case, the output will be one number that is the result of the two number inputs. Make sure you understand what your outputs will be.

Create some examples.

Once you have a grasp of the problem and know the possible inputs and outputs, you can start working on some concrete examples.

Examples can also be used as sanity checks to test your eventual problem. Most code challenge editors that you’ll work in (whether it’s in an interview or just using a site like Codewars or HackerRank) have examples or test cases already written for you. Even so, writing out your own examples can help you cement your understanding of the problem.

Start with a simple example or two of possible inputs and outputs. Let's return to our addition function.

Let’s call our function “add.”

What’s an example input? Example input might be:

// add(2, 3)

What is the output to this? To write the example output, we can write:

// add(2, 3) ---> 5

This indicates that our function will take in an input of 2 and 3 and return 5 as its output.

Create complex examples.

By walking through more complex examples, you can take the time to look for edge cases you might need to account for.

For example, what should we do if our inputs are strings instead of numbers? What if we have as input two strings, for example, add('a', 'b')?

Your interviewer might possibly tell you to return an error message if there are any inputs that are not numbers. If so, you can add a code comment to handle this case if it helps you remember you need to do this.

Your interviewer might also tell you to assume that your inputs will always be numbers, in which case you don’t need to write any extra code to handle this particular input edge case.

If you don’t have an interviewer and you’re just solving this problem, the problem might say what happens when you enter invalid inputs.

For example, some problems will say, “If there are zero inputs, return undefined.” For cases like this, you can optionally write a comment.

// check if there are no inputs.

// If no inputs, return undefined.

For our purposes, we’ll assume that our inputs will always be numbers. But generally, it’s good to think about edge cases.

Computer science professor Evans says to write what developers call defensive code. Think about what could go wrong and how your code could defend against possible errors.

Before we move on to step 2, let’s summarize step 1, understand the problem:

-Read through the problem.

-What are the inputs?

-What are the outputs?

Create simple examples, then create more complex ones.

2. Devise a plan for solving the problem.

Next, devise a plan for how you’ll solve the problem. As you devise a plan, write it out in pseudocode.

Pseudocode is a plain language description of the steps in an algorithm. In other words, your pseudocode is your step-by-step plan for how to solve the problem.

Write out the steps you need to take to solve the problem. For a more complicated problem, you’d have more steps. For this problem, you could write:

// Create a sum variable.

Add the first input to the second input using the addition operator .

// Store value of both inputs into sum variable.

// Return as output the sum variable.

Now you have your step-by-step plan to solve the problem.

For more complex problems, professor Evans notes, “Consider systematically how a human solves the problem.” That is, forget about how your code might solve the problem for a moment, and think about how you would solve it as a human. This can help you see the steps more clearly.

3. Carry out the plan (Solve the problem!)

The next step in the problem-solving strategy is to solve the problem. Using your pseudocode as your guide, write out your actual code.

Professor Evans suggests focusing on a simple, mechanical solution. The easier and simpler your solution is, the more likely you can program it correctly.

Taking our pseudocode, we could now write this:

Professor Evans adds, remember not to prematurely optimize. That is, you might be tempted to start saying, “Wait, I’m doing this and it’s going to be inefficient code!”

First, just get out your simple, mechanical solution.

What if you can’t solve the entire problem? What if there's a part of it you still don't know how to solve?

Colt Steele gives great advice here: If you can’t solve part of the problem, ignore that hard part that’s tripping you up. Instead, focus on everything else that you can start writing.

Temporarily ignore that difficult part of the problem you don’t quite understand and write out the other parts. Once this is done, come back to the harder part.

This allows you to get at least some of the problem finished. And often, you’ll realize how to tackle that harder part of the problem once you come back to it.

Step 4: Look back over what you've done.

Once your solution is working, take the time to reflect on it and figure out how to make improvements. This might be the time you refactor your solution into a more efficient one.

As you look at your work, here are some questions Colt Steele suggests you ask yourself to figure out how you can improve your solution:

• Can you derive the result differently? What other approaches are there that are viable?
• Can you understand it at a glance? Does it make sense?
• Can you use the result or method for some other problem?
• Can you improve the performance of your solution?
• Can you think of other ways to refactor?
• How have other people solved this problem?

One way we might refactor our problem to make our code more concise: removing our variable and using an implicit return:

With step 4, your problem might never feel finished. Even great developers still write code that they later look at and want to change. These are guiding questions that can help you.

If you still have time in an interview, you can go through this step and make your solution better. If you are coding on your own, take the time to go over these steps.

When I’m practicing coding on my own, I almost always look at the solutions out there that are more elegant or effective than what I’ve come up with.

Wrapping Up

In this post, we’ve gone over the four-step problem-solving strategy for solving coding problems.

Let's review them here:

• Step 1: understand the problem.
• Step 2: create a step-by-step plan for how you’ll solve it .
• Step 3: carry out the plan and write the actual code.
• Step 4: look back and possibly refactor your solution if it could be better.

Practicing this problem-solving method has immensely helped me in my technical interviews and in my job as a developer.

If you don't feel confident when it comes to solving coding problems, just remember that problem-solving is a skill that anyone can get better at with time and practice.

If you enjoyed this post, join my coding club , where we tackle coding challenges together every Sunday and support each other as we learn new technologies.

If you have feedback or questions on this post, feel free to tweet me @madisonkanna ..

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My experience with Solve, McKinsey’s assessment game.

August 21, 2020 Ana, a former architect and current fellow in Rio de Janeiro , and Carl, a former engineer and current digital associate in Brussels , joined McKinsey earlier this year. We sat down with them virtually to learn about their experiences with Solve .

How did you hear about Solve?

Ana - I heard about the game at a recruiting event. The recruiters and the consultants I met explained the game would give us a chance to show our problem-solving skills. I was curious about the experience, so I watched the video and browsed the interviewing  page. It was my first time hearing of such a test for recruiting, so I was intrigued and nervous as I don’t play videogames.

Carl - I first heard about it when I received the interview instructions. I was quite surprised and excited about this unusual approach. Like Ana, I had a look at the guide on the McKinsey website  which put me at ease.

What was your experience with Solve?

Ana - I was nervous at first. I got so in my head that the instructions didn’t sink in. Then I tried to relax, understand what I had to do, and go with the flow of the game. It was super intuitive, so my anxiety was immediately eased. I really enjoyed learning what I had to do and what strategies to change. As the phases went on, I understood more of what I had to do and found better ways to accomplish my main task.

Carl - After the first five minutes of playing the game, I felt completely drawn into the story and virtual world. In a way, I forgot I was doing an assessment. It was quite fun to play.

Did anything surprise you?

Ana - I was really surprised at how fast I learned how to play the game and evolved my strategy with each new phase. It was easy for me to test out what I thought was the right approach, and shift my strategy when I saw that it was needed.

Carl - By playing the game and trying to find an optimal solution, I realized why McKinsey uses it as part of the assessment process. The game is about understanding a complex situation, determining influencing factors and dynamics, testing a few hypotheses and eventually developing an approach to solve for the game objective. This is precisely what we do every day at McKinsey with our clients.

How did you prepare?

Ana - As there is no preparation required, I made sure I had a good night’s rest prior to playing. During the game I was given guidance for how to manage time and could track my progress.

Carl - I didn’t prepare beforehand as there isn’t a way or need to study or practice. This alleviated some of the normal stress of interviewing for a new role. Once I was in the game, I created some generic steps to structure my approach and set time limits on each step. Of course, these were mainly self-imposed guidelines as I didn’t really know what to expect, but it ended up working well.

What advice would you give someone who is going to play McKinsey’s assessment game?

Ana - You don’t need to prepare or be familiar with video games to do well. When I was told this by a McKinsey recruiter, I didn’t believe them, but now I can reassure people first hand. There is no need to stress – just go into it with an open mind and willingness to try.

Also, take your time. Understand what is in front of you and list what is asked of you – not what you think you should be doing. The format will allow you to showcase how you approach problems, so just try your best.

Carl -Take your time to understand and reflect on the objective. For instance, should you go for quick wins or for long-term solutions and what are the influencing factors. Only then can you prioritize your actions and test the hypotheses to quickly reach a good solution.

Want more interviewing tips and tricks? Read more stories from our colleagues.

Learn more about interviewing at McKinsey

More about Ana

Ana graduated with a bachelor’s degree in architecture and urbanism from the Pontifícia Universidade Católica do Rio de Janeiro, Brazil. After graduating, she worked at a small architecture firm for a year before joining the City Hall of Niterói, as an architect in the Department of Environment, Water Resources and Sustainability.

As a fellow at McKinsey, Ana has been working with retail banking clients.

More about Carl

Carl earned a bachelor’s degree in engineering (mechanics) from KULeuven. He went on to earn a Master’s degree in Engineering (robotics & mechatronics) from KULeuven and TUMunchen. He started his career as a product engineer at Audi. Prior to joining McKinsey, Carl was a consultant focused on digital operations at PwC.

As a digital associate at McKinsey, Carl works on digital transformations in a variety of industries.

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McKinsey Solve (2024)

• Fundamentals
• How it works
• Skills tested
• How to prepare
• A guide to the McKinsey Problem Solving Game

MCC is here to help

McKinsey’s Solve assessment has been making candidates sweat ever since it was initially trialled at the firm’s London office back in 2017 - and things have gotten even more difficult since a new version launched in Spring 2023, adding the Redrock case study and trialling the Ocean Cleanup in 2024.

In Summer 2023, we have seen a new iteration of that Redrock case, as we continue to interview test takers to keep you updated. This replaces the case study about optimising wolf pack populations across Redrock Island with one about boosting the overall plant biodiversity on the same island.

Since its initial roll-out, the Solve assessment has definitely been the most idiosyncratic, but also the most advanced, of the screening tests used by the MBB firms.

It can be hard to understand how an ecology-themed video game can tell McKinsey whether you’ll make a good management consultant, let alone know how to prepare yourself to do well in that game. When you consider that McKinsey are potentially cutting 70%+ of the applicant pool based on this single test, you can hardly blame applicants for being worried.

Matters are definitely not helped by the dearth of reliable, up-to-date information about what could very well be - with a top-tier consulting job on the line - the most important test you will take over your entire career. This was already true with the version of Solve that had been around for a few years, let alone the new iterations.

What information is available online is then often contradictory. For a long time, there was huge disagreement as to whether it is actually possible to meaningfully prepare for the Solve assessment - before you’ve even considered how to go about that preparation. There is also a lot of confusion and inaccuracy around the new Redrock case - largely as it is such a recent addition, and individual test takers tend to misremember details.

Luckily, we at MCC have been interviewing test takers both before and after the Redrock case rollout and have been following up to see which strategies and approaches actually work to push individuals through to interview.

Here, we’ll explain that it is indeed possible to prepare effectively for both versions of Solve and give you some ideas for how you can get started. Understanding how the Solve assessment works, what it tests you for and how is critical for all but the most hurried preparations.

This article makes for a great introduction to the Solve assessment. However, if you are going to be facing this aptitude test yourself and want full information and advice for preparation, then you should ideally get our full PDF guide:

Master the Solve Assessment

What is the mckinsey solve assessment.

In simple terms, the McKinsey Solve assessment is a set of ecology-themed video games. In these games, you must do things like build food chains, protect endangered species, manage predator and prey populations, boost biodiversity and potentially diagnose diseases within animal populations or identify natural disasters.

Usually, you will be given around 70 minutes to complete two separate games, spending about the same amount of time on each.

Until recently, these games had uniformly been Ecosystem Building and Plant Defence. However, since Spring 2023, McKinsey has been rolling out a new version across certain geographies. This replaces the Plant Defence game with the new Redrock case study. Some other games have also been run as tests.

We’ll run through a little more on all these games below to give you an idea of what you’ll be up against for both versions and possible new iterations.

An important aspect that we'll cover in more detail here is that the Solve games don't only score you on your answers (your "product score"), but also on the method you use to arrive at them (your "process score") - considerably impacting optimal strategy.

In the past, candidates had to show up to a McKinsey office and take what was then the Digital Assessment or PSG on a company computer. However, candidates are now able to take the re-branded Solve assessment at home on their own computers.

Test takers are allowed to leverage any assistance they like (you aren’t spied on through your webcam as you would be with some other online tests), and it is common to have a calculator or even another computer there to make use of.

Certainly, we strongly advise every candidate to have at least a pen, paper and calculator on their desk when they take the Solve assessment.

Common Question: Is the Solve assessment the same thing as the PSG?

In short, yes - “Solve” is just the newer name for the McKinsey Problem Solving Game.

We want to clear up any potential confusion right at the beginning. You will hear this same screening test called a few different things in different places. The Solve moniker itself is a relatively recent re-branding by McKinsey. Previously, the same test was known as either the Problem Solving Game (usually abbreviated to PSG) or the Digital Assessment. You will also often see that same test referred to as the Imbellus test or game, after the firm that created the first version.

You will still see all these names used across various sites and forums - and even within some older articles and blog posts here on MyConsultingCoach. McKinsey has also been a little inconsistent on what they call their own assessment internally. Candidates can often become confused when trying to do their research, but you can rest assured that all these names refer to the same screening test - though, of course, folk might be referring to either the legacy or Redrock versions.

How and why does McKinsey use the Solve assessment?

It’s useful to understand where the Solve assessment fits into McKinsey’s overall selection process and why they have felt the need to include it.

Let’s dive right in…

How is the Solve Assessment used by McKinsey?

McKinsey's own account of how the Solve assessment is used in selection can be seen in the following video:

Whilst some offices initially stuck with the old PST, the legacy Solve assessment was soon rolled out globally and given universally to candidates for roles at pretty well every level of the hierarchy. Certainly, if you are a recent grad from a Bachelor’s, MBA, PhD or similar, or a standard experienced hired, you can expect to be asked to complete the Solve assessment.

Likewise, the new Redrock case study versions seem to be in the process of being rolled out globally - though at this point it seems you might be given either (especially as McKinsey has been having significant technical problems with this new online case study) and so should be ready for both.

At present, it seems that only those applying for very senior positions, or perhaps those with particularly strong referrals and/or connections, are allowed to skip the test. Even this will be office-dependent.

As noted above, one of the advantages of the Solve assessment is that it can be given to all of McKinsey’s hires. Thus, you can expect to be run into the same games whether you are applying as a generalist consultant or to a specialist consulting role - with McKinsey Digital , for example.

The takeaway here is that, if you are applying to McKinsey for any kind of consulting role, you should be fully prepared to sit the Solve Assessment!

Where does the Solve assessment fit into the recruitment process?

You can expect to receive an invitation to take the Solve assessment shortly after submitting your resume.

It seems that an initial screen of resumes is made, but that most individuals who apply are invited to take the Solve assessment.

Any initial screen is not used to make a significant cut of the candidate pool, but likely serves mostly to weed out fraudulent applications from fake individuals (such as those wishing to access the Solve assessment more than once so they can practice...) and perhaps to eliminate a few individuals who are clearly far from having the required academic or professional background, or have made a total mess of their resumes.

Your email invitation will generally give you either one or two weeks to complete the test, though our clients have seen some variation here - with one individual being given as little as three days.

Certainly, you should plan to be ready to sit the Solve assessment within one week of submitting your resume!

Once you have completed the test, McKinsey explain on their site that they look at both your test scores and resume (in more detail this time) to determine who will be invited to live case interviews. This will only be around 30% of the candidates who applied - possibly even fewer.

One thing to note here is that you shouldn’t expect a good resume to make up for bad test scores and vice versa. We have spoken to excellent candidates whose academic and professional achievements were not enough to make up for poor Solve performance. Similarly, we don’t know of anyone invited to interview who hadn’t put together an excellent resume.

Blunty, you need great Solve scores and a great resume to be advanced to interview.

Your first port of call to craft the best possible resume and land your invitation to interview is our excellent free consulting resume guide .

Why does this test exist?

As with Bain, BCG and other major management consulting firms, McKinsey receives far far more applications for each position than they can ever hope to interview. Compounding this issue is that case interviews are expensive and inconvenient for firms like McKinsey to conduct. Having a consultant spend a day interviewing just a few candidates means disrupting a whole engagement and potentially having to fly that consultant back to their home office from wherever their current project was located. This problem is even worse for second-round interviews given by partners.

Thus, McKinsey need to cut down their applicant pool as far as possible, so as to shrink the number of case interviews they need to give without losing the candidates they actually want to hire. Of course, they want to accomplish this as cheaply and conveniently as possible.

The Problem Solving Test (invariably shortened to PST) had been used by McKinsey for many years. However, it had a number of problems that were becoming more pronounced over time, and it was fundamentally in need of replacement. Some of these were deficiencies with the test itself, though many were more concerned with how the test fitted with the changing nature of the consulting industry.

The Solve assessment was originally developed and iterated by the specialist firm Imbellus ( now owned by gaming giant Roblox ) to replace the long-standing PST in this screening role and offers solutions to those problems with its predecessor.

We could easily write a whole article on what McKinsey aimed to gain from the change, but the following few points cover most of the main ideas:

• New Challenges: Previously, candidates were largely coming out of MBAs or similar business-focussed backgrounds and the PST’s quickfire business questions were thus perfectly sufficient to select for non-technical generalist consulting roles. However, as consulting projects increasingly call for a greater diversity and depth of expertise, McKinsey cannot assume the most useful talent – especially for technical roles – is going to come with pre-existing business expertise. A non-business aptitude test was therefore required.
• Fairness and the Modern Context: The covid pandemic necessitated at-home aptitude testing. However, even aside from this, online testing dramatically reduces the amount of travel required of candidates. This allows McKinsey to cast a wider net, providing more opportunities to those living away from hub cities, whilst also hugely reducing the carbon footprint associated with the McKinsey selection process.
• Gaming the System: More pragmatically, the Solve assessment is a much harder test to “game” than was the PST, where highly effective prep resources were available and readily allowed a bad candidate with good preparation to do better than a good candidate. The fact that game parameters change for every individual test taker further cuts down the risk of candidates benefitting from shared information. The recent move towards the Redrock version then also helps McKinsey stay ahead of those developing prep resources for the legacy Solve assessment.
• Cost Cutting: A major advantage of scrapping the old pen-and-paper PST is that the formidable task of thinning down McKinsey’s applicant pool can be largely automated. No test rooms and invigilation staff need to be organised and no human effort is required to devise, transport, catalogue and mark papers.

Impress your interviewer

There has been a bit of variation in the games included in the Solve assessment/PSG over the years and what specific form those games take. Imbellus and McKinsey had experimented with whole new configurations as well as making smaller, iterative tweaks over time. That being said, the 2023 Redrock case studies (seemingly added by McKinsey themselves without Imbellus) are by far the largest change to Solve since that assessment's genesis back in 2017.

Given that innovation seems to continue (especially with the lengthy feedback forms some candidates are being asked to fill in after sitting the newest iteration), there is always the chance you might be the first to receive something new.

However, our surveys of, and interviews with, those taking the Solve assessment - both before and after recent changes - mean we can give you a good idea of what to expect if you are presented with either the legacy or one of the Redrock versions of Solve.

We provide much more detailed explanation of each of the games in our Solve Assessment PDF Guide - including guidance on optimal scenarios to maximise your performance. Here, though, we can give a quick overview of each scenario:

Ecosystem Building

Scenario and objectives.

In this scenario, you’re tasked with creating a self-sustaining ecosystem in either an aquatic, alpine, or jungle environment. Additional environments may be introduced without altering the core mechanics . We will use an aquatic (ocean) environment as an example for this article but the same advice is applicable to all other environments in the exact same way.

The enviroment will be chacterised by a number of characteristics. For the ocean, for instance, we will have:

• Water current
• Temperature
• Salt Content

You’ll be given 39 species (both plants and animals) to choose from, each suited to specific environmental conditions, like depth and salinity in an ocean. For a mountain ridge, it could be altitude or sun exposure.

Each species has two main sets of data points:

• Environmental Suitability : Conditions like depth or temperature where they can survive.
• Nutritional Needs : The number of calories they need, which they obtain by consuming other species. Some species are producers (providing calories and consuming none) while others are animals (requiring and providing calories). For example, in an ocean setting, algae are producers and fish are animals.

The picture above shows different fishes together with their characteristics. Each card has the following information:

• Environmental Suitability
• Depth: range they can live within
• Water current: range they can live within
• Temperature: range they can live within
• Salt Content: range they can live within
• Nutritional Needs
• Calories needed: calories they need when eating
• Calories provided: calories they provide when eaten
• Can eat: species they can eat
• Is eaten: species they can be eaten by. This can be inferred from other cards but we will see that it is a useful data point.

The game requires you to select a location for your ecosystem. Several different options are given, all with different prevailing conditions. You then have to select a number of different plant and animal species to populate a functioning food chain within that location.

In previous versions of the game, you would have had to fit as many different species as possible into a functioning food chain. However, newer iterations of the Solve assessment require a fixed number of eight or, possibly, seven species to be selected. The strategy for the seven species is the same as the one with eight.

Let's look at the game objectives in more details

• Species Selection : Identify a set of eight (or seven) species that are in equilibrium, meaning all their caloric needs are met within the ecosystem. This means that each animal will need to have their calorie need satisfied while no animal needs to be depleted. Check the eating rules below to learn more.
• Location Selection : Choose a suitable location for your ecosystem from several options, each with distinct environmental conditions.

The former is the actual challenge while the latter is somewhat trivial. Before delving into the strategy, let's outline the eating rules in more details as these are key to successfully tackle the game.

• Species eat only once.
• If a species does not obtain the required calories or their calories are depleted, it dies.
• The species with the highest calories provided feeds first.
• A species eats the prey that provides the highest calories among available options.
• Calories consumed from prey are equal to the calories needed by the predator.
• If multiple prey provide the same amount of calories, the predator consumes an equal proportion from each.
• This process is repeated for the species with the next highest calories provided.

How to approach the game

At its core, this game isn’t really a game but more of a logical puzzle administered through a more advanced User Interface (UI). The limited interactions make it a straightforward problem once you understand that the UI is not required and only add complexity. All the essential information could be presented in a table , as shown below, and you could easily solve the puzzle on paper.

Nerdy aside - Skip if not interested

To take abstraction a level further, the problem is in fact a constraint optimisation one. For those of you who are interested (possibly 2 or 3), you can actually model it and solve it analytically. While it does not help in solving the game, I will show the formulation so you can see how this is more of an analytical problem than a game. Entities are

• Producers (P): 9 producers, each with a specific depth range and caloric output.
• Animals (A): 30 animals, each with a specific depth range, caloric need, and allowed prey.

Variables are

• x ij : Binary decision variable indicating if animal i eats species j .
• C i : Caloric need of animal i .
• E j : Caloric output provided by species j .
• D i min , D i max : Constraint range limits for species i (D is a vector) .
• A ij : Binary interaction matrix indicating whether animal i can eat species j .

Enough theory, let’s dive into how to solve the game. You’ll be given 39 species, grouped into three sets of 13, each sharing the same environmental constraints like depth and salinity. Each group includes three producers and ten animals.

Your first task is to pick the group most likely to produce a balanced ecosystem. To do this, quickly estimate the total calorie output for all species, check how many animals can consume the producers, and evaluate how many animals are limited to eating other animals. Use your judgment here , as these factors are equally important. Be aware that some combinations won’t lead to a solution.

Once you’ve selected your group, start building the food chain. Ideally, include all three producers (with at least one animal consuming them) as they provide calories without needing any. Then, choose animals that can:

• Eat one or more producers without depleting them
• Provide the highest calories
• Be consumed by as many other animals as possible - this is where the eaten by info becomes useful

To do this, look at the list of animals that can consume producers without depleting them (there will be one or two), then pick those with the highest calories and that can be eaten by multiple animals. You’ll find this information on the animal card.

Continue adding animals iteratively , checking your solution at every step.

If you don't manage to find a combination, move onto the next group. In order to practice and understand which groups can lead to solutions, you can use our solver.

Once you've established a balanced ecosystem, select a location where the environmental conditions meet the needs of all species. You’re likely to find such a spot. The game provides more conditions than necessary; focus only on the relevant factors mentioned in the species cards. For example, in an ocean scenario, depth and salinity might be crucial, while factors like water speed can be disregarded. This is done to simulate a consulting scenario where you have more data than needed.

Once you have decided on your food chain, you simply submit it and you are moved on to the next game. In the past, test takers were apparently shown whether their solution was correct or not, but this is no longer the case.

Test takers generally report that this game is the easier of the two, whether it is paired with the Plant Defence game in the legacy Solve or the Redrock case study in the new version. Candidates will not usually struggle to assemble a functioning ecosystem and do not find themselves under enormous time pressure. Thus, we can assume that process scores will be the main differentiator between individuals for this component of the Solve assessment.

So far, this sounds pretty easy. However, the complexity arises from the strict rules around the manner and order in which the different species eat one another. We run through these in detail in our guide, with tips for getting your food chain right. However, the upshot is that you are going to have to spend some significant time checking your initial food chain - and then likely iterating it and replacing one or more species when it turns out that the food chain does not adhere to the eating rules.

For ideas on how to optimise your process score for this game, you can see our PDF Solve guide .

We have also developed the Solve simulator to help you practice effectively. It features a purposedly simple UI, allowing you to focus on mastering the game mechanics. It generates an arbitrary number of scenarios for you to practice on. After a scenario is generated, you can download the data or work directly from the table to select the 13 species most likely to create a balanced ecosystem. You can then submit your solution in a CSV file to check its sustainability. More interestingly, you can explore all possible combinations by uploading a CSV of your selected species to see what works best. The simulator is part of the guide package.

Plant Defence

As mentioned, this game has been replaced with the Redrock case study in the new newer version of the Solve assessment, rolled out from Spring 2023 and further iterated in Summer 2023. However, you might still be asked to sit the legacy version, with this game, when applying to certain offices - so you should be ready for it!

This scenario tasks you with protecting an endangered plant species from invasive species trying to destroy it.

The game set-up is much like a traditional board game, with play taking place over a square area of terrain divided into a grid of the order of 10x10 squares.

Your plant is located in a square near the middle of the grid and groups of invaders - shown as rats, foxes or similar - enter from the edges of the grid before making a beeline towards your plant.

Your job then is to eliminate the invaders before they get to your plant. You do this by placing defences along their path. These can be terrain features, such as mountains or forests, that either force the invaders to slow down their advance or change their path to move around an obstacle. To actually destroy the invaders though, you use animal defenders, like snakes or eagles, that are able to deplete the groups of invaders as they pass by their area of influence.

Complication here comes from a few features of the game. In particular:

• You are restricted in terms of both the numbers of different kinds of defenders you can use and where you are allowed to place them. Thus, you might only have a couple of mountains to place and only be allowed to place these in squares adjacent to existing mountains.
• The main complication is the fact that gameplay is not dynamic but rather proceeds in quite a restricted turnwise manner. By this, we mean that you cannot place or move around your defences continuously as the invaders advance inwards. Rather, turns alternate between you and invaders and you are expected to plan your use of defences in blocks of five turns at once, with only minimal allowance for you to make changes on the fly as the game develops.

The plant defence game is split into three mini-games. Each mini-game is further split into three blocks of five turns. On the final turn, the game does not stop, but continues to run, with the invaders in effect taking more and more turns whilst you are not able to place any more defences or change anything about your set-up.

More and more groups of invaders pour in, and your plant will eventually be destroyed. The test with this “endgame” is simply how many turns your defences can stand up to the surge of invaders before they are overwhelmed.

As opposed to the Ecosystem Building scenario, there are stark differences in immediate candidate performance - and thus product score - in this game. Some test takers’ defences will barely make it to the end of the standard 15 turns, whilst others will survive 50+ turns of endgame before they are overwhelmed.

In this context, as opposed to the Ecosystem Building game typically preceding it, it seems likely that product score will be the primary differentiator between candidates.

We have a full discussion of strategies to optimise your defence placement - and thus boost your product score - in our Solve guide .

Redrock Case Study

This is the replacement for the Plant Defence game in the newest iteration of Solve.

One important point to note is that, where the Solve assessment contains this case study, you have a strict, separate time limit of 35 minutes for each half of the assessment. You cannot finish one game early and use the extra time in the other, as you could in the legacy Solve assessment.

McKinsey has had significant issues with this case study, with test takers noting several major problems. In particular:

• Glitches/crashes - Whilst the newest, Summer 2023 version seems to have done a lot to address this issue, many test takers have had the Redrock case crash on them. Usually, this is just momentary and the assessment returns to where it was in a second or two. If this happens to you, try to just keep calm and carry on. However, there are reports online of some candidates having the whole Solve assessment crash and being locked out as a result. If this happens, contact HR.
• Poor interface - Even where there are no explicit glitches, users note that several aspects of the interface are difficult to use and/or finicky, and that they generally seem poorly designed compared to the older Ecosystem Building game preceding it. For example, test takers have noted that navigation is difficult or unclear and the drag and drop feature for data points is temperamental - all of this costing precious time.
• Confusing language - Related to the above is that the English used is often rather convoluted and sometimes poorly phrased. This can be challenging even for native English speakers but is even worse for those sitting Solve in their second language. It can make the initial instructions difficult to understand - compounding the previous interface problem. It can also make questions difficult, requiring a few readings to comprehend.
• Insufficient time - Clearly, McKinsey intended for Redrock to be time pressured. Whilst the newest, Summer 2023 iteration of the Redrock case seems slightly more forgiving in this regard, time is still so scarce that many candidates don't get through all the questions. This is plainly sub-optimal for McKinsey - as well as being stressful and disheartening for candidates. We would expect further changes to be made to address this issue in future.

McKinsey are clearly aware of these issues, as even those sitting the new version of Redrock have been asked to complete substantial feedback surveys. Do note, then, that this raises the likelihood of further changes to the Redrock case study in the near term - meaning you should always be ready to tackle something new.

For the time being, though, we can take you through the fundamentals of the current version of the Redrock case study. For more detail, see our freshly updated PDF Guide .

The interface

The image above shows a very simple wireframe of the UI used. You will find the main sections on the left, main body at the center and the research journal to the right. In the first section you will need to drag key information and data points from charts to the research journal. In the analysis section you will find the calculator while in the last section you will find charts to choose from.

The Scenario

Whilst changes to the details are likely in future, the current Redrock case study is set on the Island of Redrock. This island is a nature reserve with populations of various species, including wolves, elk and several varieties of plant.

In the original Redrock case, it is explained that the island's wolves are split into four packs, associated with four geographical locales. These packs predate the elk and depend upon them for food, such that there is a dynamic relationship between the population numbers of both species. Your job is to ensure ecological balance by optimising the numbers of wolves in the four packs, such that both wolves and elk can sustainably coexist.

In the newer iteration of the case, first observed in Summer 2023, you are asked to assess which, if any, of three possible strategies can successfully boost the island's plant biodiversity by a certain specified percentage. Plants here are segmented into grasses, trees and shrubs.

The Questions

The Redrock case study's questions were initially split into three sections, but a fourth was added later. These sections break down as follows:

Here, you have access to the full description of the case, with all the data on the various animal populations. Your task is to efficiently extract all the most salient data points and drag-and-drop them to your "Research Journal" workspace area. This is important, as you subsequently lose access to all the information you don't save at this stage.

To solve the case, focus on the key data points highlighted in boxes on the screen, which you can move around for easier analysis. These include case objectives, calculation instructions, and numerical data. While background information and instructions provide context, they aren’t crucial for your calculations. Only about 10-15% of the numerical data is essential for solving the case, so prioritize collecting and using those figures in your analysis. Ideally, you should read instructions carefully, understanding case objectives, figuring out which formulae you need and then collect the necessary data.

In the Redrock test, you can drag important data points into the Journal for collection, where they appear as labeled cards. These cards can be used in calculations or answering questions. You can edit labels for clarity and highlight key data with an "I" button for easier analysis. Organize collected data within the Journal, as McKinsey might evaluate your organization method. This organization process is subject to updates, so stay tuned for the latest recommendations.

You must answer three numerical questions using information you saved in the Investigation section. This can include you dragging and dropping values to and from an in-game calculator.

According to recent reports, it is better to use the in game calculator to perform calculations as McKinsey will use the log to calculate your score. You will only need to perform basic operations, such as fundamental arithmentics, ratios and percentages. The only tricker operation to perform will be compound growth rates so make sure you are comfortable with these. Make sure to collect your data into the journal.

Formerly the final section, you must complete a pre-written report on the wolf populations or plant biodiversity levels, including calculating numerical values to fill in gaps and using an in-game interface to make a chart to illustrate your findings. You will leverage information saved in the Investigation section, as well as answers calculated in the Analysis section.

You will also have to choose a chart to display your results. The choice will be among simple ones, such as bar, line, and pie. Some guidelines:

• Bar Chart: Use for comparing quantities across different categories (e.g., sales by region, number of products sold).
• Line Chart: Ideal for showing trends over time (e.g., monthly revenue growth, temperature changes throughout the year).
• Pie Chart: Best for displaying parts of a whole, usually as percentages (e.g., market share distribution, budget allocation).

Visit our Our consulting math page for more details.

This section adds a further ten individual case questions. These can be wolf-themed, so are thematically similar to the original Redrock case, but are slightly incongruous with the newer, plant-themed version of Redrock. In both instances, though, these questions are entirely separable from the main case preceding them, not relying on any information from the previous sections. The ten questions are highly quantitative and extremely time pressured. Few test takers finish them before being timed out.

• Critical reasoning : understanding and elaboring information
• Understanding charts : getting information out of charts and graphs
• Math problems : these are simple math questions that can be formulated as word problems or formulae problems, where the output answer is a formula.

Approach this game with a structured, top-down strategy to demonstrate your problem-solving skills. Always label your data clearly to showcase your ability to work with metadata, a crucial skill for consultants. Additionally, minimize back-and-forth actions in the game; although it’s possible in the interface, doing so suggests ineffective data collection and planning.

This is a very brief summary - more detail is available in our PDF Guide . You will also find 100+ Redrock specific exercises for you to practice.

Ocean Cleanup (2024)

The Ocean Cleanup is a new game that McKinsey began rolling out in the spring of 2024. This game is played after the Solve and Redrock assessments. Although it's not part of the official assessment yet, McKinsey is currently testing it as a potential addition to their suite of evaluation tools. You will still have to sit through the assessment. It does not count towards your final score.

The objective of the Ocean Cleanup game is to identify microbes that can survive in a specific ocean area. While it shares some similarities with the Solve game, particularly in its focus on selecting viable species, it has a different logic.

Game mechanics and strategy

The first step in the Ocean Cleanup game involves defining attributes (continuous variables) and traits (binary variables) to characterize each ocean area. Attributes might include factors like rigidity or size, while traits could be binary qualities such as being water-repellent or not. These distinctions help in precisely characterizing the environment and determining which microbes are best suited for survival. This process should be relatively straightforward.

Once you selected your variables, you will be given a value for each parameter each ranging from 1 to 10 for 2 sites. You'll be given specific goals, such as 2 for the parameter one, 3 for two, and 8 for the three. You then select up to 4 microbes to match the characteristics of your sites as closely as possible. In each of the 4 rounds, you'll choose 1 microbe from a group of three, aiming to find the best fit for the site's conditions. The system will automatically fill the remaining slots automatically filled to create a total set of 10. This process allows you to strategically build a group of microbes that best meets the objectives.

After selecting your 10 microbes, you’ll narrow it down to 3 that, when averaged, best match your target values. For instance, if your goal is to achieve specific values like 2, 3, and 8, you’d choose microbes where the first parameter is consistently close to 2. For the second parameter, you might opt for values which would average to your target of 3. This strategy ensures that the selected microbes closely align with your desired outcomes. There will be an element of iteration involved since microbes with an average close to parameter 1 may have an average which is off for parameter 3. You will have to repeat this for both sites

Note that the game is still being rolled out so details may change - we will try to keep this page as updated as possible.

• Selecting the initial parameters and 4 microbes is straightforward , but aim to match the parameters closely to the target to simplify choosing the final 3 microbes .
• When selecting the 3 microbes, focus on the most extreme values first , as they are the hardest to adjust. For example, if a target value is 1, you’ll only have options for higher numbers.
• After addressing the extreme values, fine-tune the remaining variables by adjusting the averages .
• Keep pen, paper, and a calculator handy . Excel is an option, but the calculations are simple enough that it might not provide a significant advantage.
• Avoid using Excel Solvers or advanced techniques . The test isn’t scored, so just focus on doing your best.

Other Games - Disease and Disaster Identification

There have been accounts of some test takers being given a third game as part of their Solve assessment. At time of writing, these third games have always been clearly introduced as non-scored beta tests for Imbellus to try out potential new additions to the assessment. However, the fact that these have been tested means that there is presumably a good chance we’ll see them as scored additions in future.

Notably, these alternative scenarios are generally variations on a fairly consistent theme and tend to share a good deal of the character of the Ecosystem Building game. Usually, candidates will be given a whole slew of information on how an animal population has changed over time. They will then have to wade through that information to figure out either which kind of natural disaster or which disease has been damaging that population - the commonality with the Ecosystem Building game being in the challenge of dealing with large volumes of information and figuring out which small fraction of it is actually relevant.

Join thousands of other candidates cracking cases like pros

What does the solve assessment test for.

Whilst information on the Solve assessment can be hard to come by, Imbellus and McKinsey have at least been explicit on what traits the test was designed to look for. These are:

• Critical Thinking : making judgements based on the objective analysis of information
• Decision Making : choosing the best course of action, especially under time pressure or with incomplete information
• Metacognition : deploying appropriate strategies to tackle problems efficiently
• Situational Awareness : the ability to interpret and subsequently predict an environment
• Systems Thinking : understanding the complex causal relationships between the elements of a system

Equally important to understanding the raw facts of the particular skillset being sought out, though, is understanding the very idiosyncratic ways in which the Solve assessment tests for these traits.

Let's dive deeper:

Process Scores

Perhaps the key difference between the Solve assessment and any other test you’ve taken before is Imbellus’s innovation around “process scores”.

To explain, when you work through each of the games, the software examines the solutions you generate to the various problems you are faced with. How well you do here is measured by your “product score”.

However, scoring does not end there. Rather, Solve's software also constantly monitors and assesses the method you used to arrive at that solution. The quality of the method you used is then captured in your “process score”.

To make things more concrete here, if you are playing the Ecosystem Building game, you will not only be judged on whether the ecosystem you put together is self-sustaining. You will also be judged on the way you have worked in figuring out that ecosystem - presumably, on how efficient and organised you were. The program tracks all your mouse clicks and other actions and will thus be able to capture things like how you navigate around the various groups of species, how you place the different options you select, whether you change your mind before you submit the solution and so on.

You can find more detail on these advanced aspects of the Solve assessment and the innovative work behind it in the presentation by Imbellus founder Rebecca Kantar in the first section of the following video:

Compared to other tests, this is far more like the level of assessment you face from an essay-based exam, where the full progression of your argument towards a conclusion is marked - or a maths exam, where you are scored on your working as well as the final answer (with, of course, the major advantage that there is no highly qualified person required to mark papers).

Clearly, the upshot of all this is that you will want to be very careful how you approach the Solve assessment. You should generally try to think before you act and to show yourself in a very rational, rigorous, ordered light.

We have some advice to help look after your process scores in our PDF Guide to the McKinsey Solve Assessment .

A Different Test for Every Candidate

Another remarkable and seriously innovative aspect of the Solve assessment is that no two candidates receive exactly the same test.

Imbellus automatically varies the parameters of their games to be different for each individual test taker, so that each will be given a meaningfully different game to everyone else’s.

Within a game, this might mean a different terrain setting, having a different number of species or different types of species to work with or more or fewer restrictions on which species will eat which others.

Consequently, even if your buddy takes the assessment for the same level role at the same office just the day before you do, whatever specific strategy they used in their games might very well not work for you.

This is an intentional feature designed to prevent test takers from sharing information with one another and thus advantaging some over others. At the extreme, this feature would also be a robust obstacle to any kind of serious cheating.

To manage to give every candidate a different test and still be able to generate a reliable ranking of those candidates across a fundamental skillset, without that test being very lengthy, is a considerable achievement from Imbellus. At high level, this would seem to be approximately equivalent to reliably extracting a faint signal from a very noisy background on the first attempt almost every time.

(Note that we are yet to confirm to what extent and how this also happens with the new Redrock case studies, but it seems to be set up to allow for easy changes to be made to the numerical values describing the case, so we assume there will be similar, widespread of variation.)

Preparation for the McKinsey Solve assessment

Understanding what the Solve assessment tests for immediately begs the question as to whether it is possible to usefully prepare and, if so, what that preparation should look like.

Is it Really Possible to Prepare for the McKinsey Solve Assessment?

In short, yes you can - and you should!

As noted previously, there has been a lot of disagreement over whether it is really possible to prep for the Solve assessment in a way that actually makes a difference.

Especially for the legacy version, there has been a widespread idea that the Solve assessment functions as something like an IQ test, so that preparation beyond very basic familiarisation to ensure you don’t panic on test day will not do anything to reliably boost your scores (nobody is going to build up to scoring an IQ of 200 just by doing practice tests, for example).

This rationale says that the best you can do is familiarise yourself with what you are up against to calm your nerves and avoid misunderstanding instructions on test day. However, this school of thought says there will be minimal benefit from practice and/or skill building.

The utility of preparation has become a clearer with the addition of the Redrock case study to the new version of Solve. Its heavily quantitative nature, strong time pressure and structure closely resembling a traditional business case make for a clearer route to improvement.

However, as we explain in more detail in our PDF guide to the Solve assessment, the idea that any aspect of either version of Solve can't be prepared for has been based on some fundamental misunderstandings about what kind of cognitive traits are being tested. Briefly put, the five key skills the Solve assessment explicitly examines are what are known as higher-order thinking skills.

Crucially, these are abilities that can be meaningfully built over time.

McKinsey and Imbellus have generally advised that you shouldn’t prepare. However, this is not the same as saying that there is no benefit in doing so. McKinsey benefits from ensuring as even a playing field as possible. To have the Solve test rank candidates based purely on their pre-existing ability, they would ideally wish for a completely unprepared population.

How to prep

We discuss how to prep for the Solve assessment in full detail in our PDF guide . Here, though, we can give you a few initial pointers to get you started. In particular, there are some great ways to simulate different games as well as build up the skills the Solve assessment tests for.

Playing video games is great prep for the legacy Solve assessment in particular, but remains highly relevant to the new Redrock version.

Contrary to what McKinsey and Imbellus have said - and pretty unfortunately for those of us with other hobbies - test takers have consistently said that they reckoned the Problem Solving Game, and now the Solve assessment, favours those with strong video gaming experience.

If you listened when your parents told you video games were a waste of time and really don’t have any experience, then putting in some hours on pretty much anything will be useful. However, the closer the games you play are to the Solve scenarios, the better. We give some great recommendations on specific games and what to look for more generally in our Solve guide - including one free-to-play game that our clients have found hugely useful as prep for the plant defence game!

PST-Style Questions

The inclusion of the Redrock case studies in the new version of Solve really represents a return to something like a modernised PST. Along with the similar new BCG Casey assessment, this seems to be the direction of travel for consulting recruitment in general.

Luckily, this means that you can leverage the wealth of existing PST-style resources to your advantage in preparation.

Our PST article - which links to some free PST questions and our full PST prep resources - is a great place to start. We also include PST questions in our McKinsey Solve preparation bundle so that you can practice for the Redrock case as well.

Quick Mathematics With a Calculator and/or Excel

Again, specifically for the Redrock assessment, you will be expected to solve math problems very quickly. The conceptual level of mathematics required is not particularly high, but you need to know what you are doing and get through it fast using a calculator nand/or Excel, if you are already comfortable with that program.

Our article on consulting math is a great place to start to understand what is expected of you throughout the recruiting process, with our consulting math package (a subset of our Case Academy course) providing more in-depth lessons and practice material.

Learn to Solve Case Studies

With the Redrock case studies clearly being ecology-themed analogues to standard business case studies, it's pretty obvious that getting good at case studies will be useful.

However, the Solve assessment as a whole is developed and calibrated to be predictive of case interview performance, so you can expect that improving your case solving ability will indirectly bring up your performance across the board.

Of course, this overlaps with your prep for McKinsey's case interviews. For more on how to get started there, see the final section of this article.

Learning About Optimal Strategies for the Games

The first thing to do is to familiarise yourself with the common game scenarios from the Solve assessment and how you can best approach them to help boost your chances of success.

Now, one thing to understand is that, since the parameters for the games change for each test taker, there might not be a single definitive optimal strategy for every single possible iteration of a particular game. As such, you shouldn’t rely on just memorising one approach and hoping it matches up to what you get on test day.

Instead, it is far better to understand why a strategy is sensible in some circumstances and when it might be better to do something else instead if the version of the game you personally receive necessitates a different approach.

In this article, we have given you a useful overview of the games currently included in the Solve assessment. However, a full discussion with suggested strategies is provided in our comprehensive Solve guide .

With the limited space available here, this is only a very brief sketch of a subset of the ways you can prep.

As noted, what will help with all of these and more is reading the extensive prep guidance in our full PDF guide to the Solve assessment...

The MCC Solve Assessment Bundle

Preparing for the Solve assessment doesn’t have to be a matter of stumbling around on your own. This article is a good introduction. From here, though our new, McKinsey Solve Assessment bundle is your first stop to optimise your Solve preparation.

• Access to our McKinsey Solve simulator , where you can practice by playing the game and building your ecosystem. The simulator not only provides scenarios but also calculates all possible combinations with a detailed consumption log for each scenario you encounter, allowing you to fully understand the problem and strategy. This approach is more beneficial than simply playing the game, as it gives you a comprehensive view rather than just confirming whether you're right or wrong. The guide inclues the password and link for the simulator.
• A comprehensive PDF guide covering everything you need to know about the test .
• A set of targeted exercises for the RedRock game .

Does it make sense to invest in a Solve Preparation bundle?

Short answer: yes. If you just think about the financials, a job at McKinsey is worth millions in the long run. If you factor in experience, personal growth and exit opportunities, the investment is a no-brainer. And if this is not enough, we also offer a 30 days money back guaranteed no questions asked .

How our bundle can help you ace the test

Don't expect some magic tricks to game the system (because you can't), but rather an in-depth analysis of key areas crucial to boost your scores. This helps you to:

As noted, the bundle is based on interviews with real recent test takers and covers the current games in detail. Being familiar with the game rules, mechanics and potential strategies in advance will massively reduce the amount of new information you have to assimilate from scratch on test day, allowing you to focus on the actual problems at hand.

Despite the innovative environment, the Solve assessment tests candidates for the same skills evaluated in case interviews, albeit on a more abstract level. Our guide (part of the bundle) breaks these skills down and provides a clear route to develop them. You also benefit from the cumulative experience of our clients, as we have followed up to see which prep methods and game strategies were genuinely helpful. Playing with the simulator will allow you to further strengthen these skills.

A clear plan of how to prepare is instrumental for success. Our guide includes a detailed, flexible preparation strategy, leveraging a whole host of diverse prep activities to help you practice and build your skills as effectively as possible. Importantly, our guide helps you prioritise the most effective aspects of preparation to optimise for whatever timeframe you have to work in.

Overall, the MyConsultingCoach Solve bundle provides the tools for an efficient and effective preparation. Our guide is designed to be no-nonsense and straight to the point. It tells you what you need to know up front and - for those of you in a hurry - crucial sections are clearly marked to read first to help you prep ASAP. Our simulator helps you uncover the fundamental mechanics of the game.

For those of you starting early with more time to spare, there is also a fully detailed, more nuanced discussion in the guide of what the test is looking for and how you can design a more long-term prep to build up the skills you need - and how this can fit into your wider case interview prep.

Importantly, there is no fluff to bulk out the page count. The market is awash with guides at huge page counts, stuffed full of irrelevant material to boost overall document length. By contrast, we realise your time is better spent actually preparing than ploughing through a novel.

If this sounds right for you, you can purchase our PDF Solve bundle here:

McKinsey Solve Assessment Bundle

• Full guide to both the legacy version of the Solve assessment and the newer Redrock Case Study versions
• Solve Simulator: unlimited scenarios, solution checker and solution generator
• In-depth description of the different games and strategies to beat them
• Preparation strategies for the short, medium and long-term prep
• No fluff - straight to the point, with specific tips for those without much time
• Straight to your inbox
• 30 days money-back guarantee, no questions asked. Simply email us and we will refund the full amount.

The Next Step - Case Interviews

So, you pour in the hours to generate an amazing resume and cover letter. You prepare diligently for the Solve assessment, going through our PDF guide and implementing all the suggestions. On test day, you sit down and ace Solve. The result is an invitation to a live McKinsey case interview.

Now the real work begins…

Arduous as application writing and Solve prep might have seemed, preparing for McKinsey case interviews will easily be an order of magnitude more difficult.

Remember that McKinsey tells candidates not to prepare for Solve - but McKinsey explicitly expects applicants to have rigorously prepared for case interviews .

The volume of specific business knowledge and case-solving principles, as well as the sheer complexity of the cases you will be given, mean that there is no way around knuckling down, learning what you need to know and practicing on repeat.

If you want to get through your interviews and actually land that McKinsey offer, you are going to need to take things seriously, put in the time and learn how to properly solve case studies.

Unfortunately, the framework-based approach taught by many older resources is unlikely to cut it for you. These tend to falter when applied to difficult, idiosyncratic cases - precisely the kind of case you can expect from McKinsey!

The method MCC teaches is based specifically on the way McKinsey train incoming consultants. We throw out generic frameworks altogether and show you how to solve cases like a real management consultant on a real engagement.

You can start reading about the MCC method for case cracking here . To step your learning up a notch, you can move on to our Case Academy course .

And, if all this (rightfully) seems pretty daunting and you’d like to have an experienced consultant guide you through your whole prep from start to finish, we will be able to assist you. Click below to learn more!

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• Published: 31 August 2024

Development and validation of a higher-order thinking skills (HOTS) scale for major students in the interior design discipline for blended learning

• Dandan Li 1 ,
• Xiaolei Fan 2 &
• Lingchao Meng 3  

Scientific Reports volume  14 , Article number:  20287 ( 2024 ) Cite this article

Metrics details

• Environmental social sciences

Assessing and cultivating students’ HOTS are crucial for interior design education in a blended learning environment. However, current research has focused primarily on the impact of blended learning instructional strategies, learning tasks, and activities on the development of HOTS, whereas few studies have specifically addressed the assessment of these skills through dedicated scales in the context of blended learning. This study aimed to develop a comprehensive scale for assessing HOTS in interior design major students within the context of blended learning. Employing a mixed methods design, the research involved in-depth interviews with 10 education stakeholders to gather qualitative data, which informed the development of a 66-item soft skills assessment scale. The scale was administered to a purposive sample of 359 undergraduate students enrolled in an interior design program at a university in China. Exploratory and confirmatory factor analyses were also conducted to evaluate the underlying factor structure of the scale. The findings revealed a robust four-factor model encompassing critical thinking skills, problem-solving skills, teamwork skills, and practical innovation skills. The scale demonstrated high internal consistency (Cronbach's alpha = 0.948–0.966) and satisfactory convergent and discriminant validity. This scale provides a valuable instrument for assessing and cultivating HOTS among interior design major students in blended learning environments. Future research can utilize a scale to examine the factors influencing the development of these skills and inform instructional practices in the field.

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Introduction.

In the contemporary landscape of the twenty-first century, students face numerous challenges that necessitate the development of competitive skills, with a particular emphasis on the cultivation of HOTS 1 , 2 , 3 , this has become a crucial objective in educational reform. Notably, it is worth noting that the National Education Association (NEA, 2012) has clearly identified critical thinking and problem-solving, communication, collaboration, creativity, and innovation as key competencies that students must possess in the current era, which are considered important components of twenty-first century skills 4 , 5 , 6 , 7 . As learners in the fields of creativity and design, students in the interior design profession also need to possess HOTS to address complex design problems and the evolving demands of the industry 8 , 9 .

Currently, blended learning has become an important instructional model in interior design education 10 , 11 . It serves as a teaching approach that combines traditional face-to-face instruction with online learning, providing students with a more flexible and personalized learning experience 12 , 13 . Indeed, several scholars have recognized the benefits of blended learning in providing students with diverse learning resources, activities, and opportunities for interaction, thereby fostering HOTS 14 , 15 , 16 , 17 . For example, blended learning, as evidenced by studies conducted by Anthony et al. 10 and Castro 11 , has demonstrated its efficacy in enhancing students' HOTS. The integration of online resources, virtual practices, and online discussions in blended learning fosters active student engagement and improves critical thinking, problem solving, and creative thinking skills. Therefore, teachers need to determine appropriate assessment methods and construct corresponding assessment tasks to assess students' expected learning outcomes. This decision requires teachers to have a clear understanding of students' learning progress and the development of various skills, whereas students have knowledge of only their scores and lack awareness of their individual skill development 18 , 19 .

Nevertheless, the precise assessment of students' HOTS in the blended learning milieu poses a formidable challenge. The dearth of empirically validated assessment tools impedes researchers from effectively discerning students' levels of cognitive aptitude and developmental growth within the blended learning realm 20 , 21 , 22 . In addition, from the perspective of actual research topics, current studies on blended learning focus mainly on the "concept, characteristics, mechanisms, models, and supporting technologies of blended learning 23 . " Research on "measuring students' HOTS in blended learning" is relatively limited, with most of the focus being on elementary, middle, and high school students 24 , 25 . Few studies have specifically examined HOTS measurement in the context of university students 26 , 27 , particularly in practical disciplines such as interior design. For example, Bervell et al. 28 suggested that the lack of high-quality assessment scales inevitably impacts the quality of research. Additionally, Schmitt 29 proposed the “Three Cs” principle for measurement, which includes clarity, coherence, and consistency. He highlighted that high-quality assessment scales should possess clear and specific measurement objectives, logically coherent items, and consistent measurement results to ensure the reliability and validity of the data. This reflects the importance of ensuring the alignment of the measurement goals of assessment scales with the research questions and the content of the discipline in the design of assessments.

The development of an assessment scale within the blended learning environment is expected to address the existing gap in measuring and assessing HOTS scores in interior design education. This scale not only facilitates the assessment of students' HOTS but also serves as a guide for curriculum design, instructional interventions, and student support initiatives. Ultimately, the integration of this assessment scale within the blended learning environment has the potential to optimize the development of HOTS among interior design students, empowering them to become adept critical thinkers, creative problem solvers, and competent professionals in the field.

Therefore, this study follows a scientific scale development procedure to develop an assessment scale specifically designed to measure the HOTS of interior design students in blended learning environments. This endeavor aims to provide educators with a reliable instrument for assessing students' progress in cultivating and applying HOTS, thus enabling the implementation of more effective teaching strategies and enhancing the overall quality of interior design education. The research questions are as follows:

What key dimensions should be considered when developing a HOTS assessment scale to accurately capture students' HOTS in an interior design major blended learning environment?

How can an advanced thinking skills assessment scale for blended learning in interior design be developed?

How can the reliability and validity of the HOTS assessment scale be verified and ensured, and is it reliable and effective in the interior design of major blended learning environments?

Key dimensions of HOTS assessment scale in an interior design major blended learning environment

The research results indicate that in the blended learning environment of interior design, this study identified 16 initial codes representing key dimensions for enhancing students' HOTS. These codes were further categorized into 8 main categories and 4 overarching themes: critical thinking, problem-solving, teamwork skills and practical innovation skills. They provide valuable insights for data comprehension and analysis, serving as a comprehensive framework for the HOTS scale. Analyzing category frequency and assessing its significance and universality in a qualitative dataset hold significant analytical value 30 , 31 . High-frequency terms indicate the central position of specific categories in participants' narratives, texts, and other data forms 32 . Through interviews with interior design experts and teachers, all core categories were mentioned more than 20 times, providing compelling evidence of their universality and importance within the field of interior design's HOTS dimensions. As shown in Table 1 .

Themes 1: critical thinking skills

Critical thinking skills constitute a key core category in blended learning environments for interior design and are crucial for cultivating students' HOTS. This discovery emphasizes the importance of critical thinking in interior design learning. This mainly includes the categories of logical reasoning and judgment, doubt and reflection, with a frequency of more than 8, highlighting the importance of critical thinking skills. Therefore, a detailed discussion of each feature is warranted. As shown in Table 2 .

Category 1: logical reasoning and judgment

The research results indicate that in a blended learning environment for interior design, logical reasoning and judgment play a key role in cultivating critical thinking skills. Logical reasoning refers to inferring reasonable conclusions from information through analysis and evaluation 33 . Judgment is based on logic and evidence for decision-making and evaluation. The importance of these concepts lies in their impact on the development and enhancement of students' HOTS. According to the research results, interior design experts and teachers unanimously believe that logical reasoning and judgment are very important. For example, as noted by Interviewee 1, “For students, logical reasoning skills are still very important. Especially in indoor space planning, students use logical reasoning to determine whether the layout of different functional areas is reasonable”. Similarly, Interviewee 2 also stated that “logical reasoning can help students conduct rational analysis of various design element combinations during the conceptual design stage, such as color matching, material selection, and lighting application”.

As emphasized by interviewees 1 and 2, logical reasoning and judgment are among the core competencies of interior designers in practical applications. These abilities enable designers to analyze and evaluate design problems and derive reasonable solutions from them. In the interior design industry, being able to conduct accurate logical reasoning and judgment is one of the key factors for success. Therefore, through targeted training and practice, students can enhance their logical thinking and judgment, thereby better addressing design challenges and providing innovative solutions.

Category 2: skepticism and reflection

Skepticism and reflection play crucial roles in cultivating students' critical thinking skills in a blended learning environment for interior design. Doubt can prompt students to question and explore information and viewpoints, whereas reflection helps students think deeply and evaluate their own thinking process 34 . These abilities are crucial for cultivating students' higher-order thinking skills. According to the research findings, most interior design experts and teachers agree that skepticism and reflection are crucial. For example, as noted by interviewees 3, “Sometimes, when facing learning tasks, students will think about how to better meet the needs of users”. Meanwhile, Interviewee 4 also agreed with this viewpoint. As emphasized by interviewees 3 and 4, skepticism and reflection are among the core competencies of interior designers in practical applications. These abilities enable designers to question existing perspectives and practices and propose innovative design solutions through in-depth thinking and evaluation. Therefore, in the interior design industry, designers with the ability to doubt and reflect are better able to respond to complex design needs and provide clients with unique and valuable design solutions.

Themes 2: problem-solving skills

The research findings indicate that problem-solving skills constitute a key core category in blended learning environments for interior design and are crucial for cultivating students' HOTS. This discovery emphasizes the importance of problem-solving skills in interior design learning. Specifically, categories such as identifying and defining problems, as well as developing and implementing plans, have been studied more than 8 times, highlighting the importance of problem-solving skills. Therefore, it is necessary to discuss each function in detail to better understand and cultivate students' problem-solving skills. As shown in Table 3 .

Category 1: identifying and defining issues

The research findings indicate that in a blended learning environment for interior design, identifying and defining problems play a crucial role in fostering students' problem-solving skills. Identifying and defining problems require students to possess the ability to analyze and evaluate problems, enabling them to accurately determine the essence of the problems and develop effective strategies and approaches to solve them 35 . Interior design experts and teachers widely recognize the importance of identifying and defining problems as core competencies in interior design practice. For example, Interviewee 5 emphasized the importance of identifying and defining problems, stating, "In interior design, identifying and defining problems is the first step in addressing design challenges. Students need to be able to clearly identify the scope, constraints, and objectives of the problems to engage in targeted thinking and decision-making in the subsequent design process." Interviewee 6 also supported this viewpoint. As stressed by Interviewees 5 and 6, identifying and defining problems not only require students to possess critical thinking abilities but also necessitate broad professional knowledge and understanding. Students need to comprehend principles of interior design, spatial planning, human behavior, and other relevant aspects to accurately identify and define problems associated with design tasks.

Category 2: developing and implementing a plan

The research results indicate that in a blended learning environment for interior design, developing and implementing plans plays a crucial role in cultivating students' problem-solving abilities. The development and implementation of a plan refers to students identifying and defining problems, devising specific solutions, and translating them into concrete implementation plans. Specifically, after determining the design strategy, students refine it into specific implementation steps and timelines, including drawing design drawings, organizing PPT reports, and presenting design proposals. For example, Interviewee 6 noted, “Students usually break down design strategies into specific tasks and steps by refining them.” Other interviewees also unanimously support this viewpoint. As emphasized by respondent 6, developing and implementing plans can help students maintain organizational, systematic, and goal-oriented problem-solving skills, thereby enhancing their problem-solving skills.

Themes 3: teamwork skills

The research results indicate that teamwork skills constitute a key core category in blended learning environments for interior design and are crucial for cultivating students' HOTS. This discovery emphasizes the importance of teamwork skills in interior design learning. This mainly includes communication and coordination and division of labor and collaboration, which are mentioned frequently in the interview documents. Therefore, it is necessary to discuss each function in detail to better understand and cultivate students' teamwork skills. As shown in Table 4 .

Category 1: communication and coordination

The research results indicate that communication and collaboration play crucial roles in cultivating students' teamwork abilities in a blended learning environment for interior design. Communication and collaboration refer to the ability of students to effectively share information, understand each other's perspectives, and work together to solve problems 36 . Specifically, team members need to understand each other's resource advantages integrate and share these resources to improve work efficiency and project quality. For example, Interviewee 7 noted, “In interior design, one member may be skilled in spatial planning, while another member may be skilled in color matching. Through communication and collaboration, team members can collectively utilize this expertise to improve work efficiency and project quality.” Other interviewees also unanimously believe that this viewpoint can promote students' teamwork skills, thereby promoting the development of their HOTS. As emphasized by the viewpoints of these interviewees, communication and collaboration enable team members to collectively solve problems and overcome challenges. Through effective communication, team members can exchange opinions and suggestions with each other, provide different solutions, and make joint decisions. Collaboration and cooperation among team members contribute to brainstorming and finding the best solution.

Category 2: division of labor and collaboration

The research results indicate that in the blended learning environment of interior design, the division of labor and collaboration play crucial roles in cultivating students' teamwork ability. The division of labor and collaboration refer to the ability of team members to assign different tasks and roles in a project based on their respective expertise and responsibilities and work together to complete the project 37 . For example, Interviewee 8 noted, “In an internal design project, some students are responsible for space planning, some students are responsible for color matching, and some students are responsible for rendering production.” Other interviewees also support this viewpoint. As emphasized by interviewee 8, the division of labor and collaboration help team members fully utilize their respective expertise and abilities, promote resource integration and complementarity, cultivate a spirit of teamwork, and enable team members to collaborate, support, and trust each other to achieve project goals together.

Themes 4: practical innovation skills

The research results indicate that practical innovation skills constitute a key core category in blended learning environments for interior design and are crucial for cultivating students' HOTS. This discovery emphasizes the importance of practical innovation skills in interior design learning. This mainly includes creative conception and design expression, as well as innovative application of materials and technology, which are often mentioned in interview documents. Therefore, it is necessary to discuss each function in detail to better understand and cultivate students' practical innovation skills. As shown in Table 5 .

Category 1: creative conception and design expression

The research results indicate that in the blended learning environment of interior design, creative ideation and design expression play crucial roles in cultivating students' practical and innovative skills. Creative ideation and design expression refer to the ability of students to break free from traditional thinking frameworks and try different design ideas and methods through creative ideation, which helps stimulate their creativity and cultivate their ability to think independently and solve problems. For example, interviewee 10 noted that "blended learning environments combine online and offline teaching modes, allowing students to acquire knowledge and skills more flexibly. Through learning and practice, students can master various expression tools and techniques, such as hand-drawn sketches, computer-aided design software, model making, etc., thereby more accurately conveying their design concepts." Other interviewees also expressed the importance of this viewpoint, emphasizing the importance of creative ideas and design expression in blended learning environments that cannot be ignored. As emphasized by interviewee 10, creative ideation and design expression in the blended learning environment of interior design can not only enhance students' creative thinking skills and problem-solving abilities but also strengthen their application skills in practical projects through diverse expression tools and techniques. The cultivation of these skills is crucial for students' success in their future careers.

Category 2: innovative application of materials and technology

Research findings indicate that the innovative application of materials and technology plays a crucial role in developing students' practical and creative skills within a blended learning environment for interior design. The innovative application of materials and technology refers to students' exploration and utilization of new materials and advanced technologies, enabling them to overcome the limitations of traditional design thinking and experiments with diverse design methods and approaches. This process not only stimulates their creativity but also significantly enhances their problem-solving skills. Specifically, the innovative application of materials and technology involves students gaining a deep understanding of the properties of new materials and their application methods in design, as well as becoming proficient in various advanced technological tools and equipment, such as 3D printing, virtual reality (VR), and augmented reality (AR). These skills enable students to more accurately realize their design concepts and effectively apply them in real-world projects.

For example, Interviewee 1 stated, "The blended learning environment combines online and offline teaching modes, allowing students to flexibly acquire the latest knowledge on materials and technology and apply these innovations in real projects." Other interviewees also emphasized the importance of this view. Therefore, the importance of the innovative application of materials and technology in a blended learning environment cannot be underestimated. As emphasized by interviewee 1, the innovative application of materials and technologies is crucial in the blended learning environment of interior design. This process not only enables students to flexibly acquire the latest materials and technical knowledge but also enables them to apply these innovations to practice in practical projects, thereby improving their practical abilities and professional ethics.

In summary, through research question 1 research, the dimensions of the HOTS assessment scale in blended learning for interior design include four main aspects: critical thinking skills, problem-solving skills, teamwork skills, and practical innovation skills. Based on the assessment scales developed by previous scholars in various dimensions, the researcher developed a HOTS assessment scale suitable for blended learning environments in interior design and collected feedback from interior design experts through interviews.

Development of the HOTS assessment scale

The above research results indicate that the dimensions of the HOTS scale mainly include critical thinking, problem-solving, teamwork skills and practical innovation skills. The dimensions of a scale represent the abstract characteristics and structure of the concept being measured. Since these dimensions are often abstract and difficult to measure directly, they need to be converted into several concrete indicators that can be directly observed or self-reported 38 . These concrete indicators, known as dimension items, operationalize the abstract dimensions, allowing for the measurement and evaluation of various aspects of the concept. This process transforms the abstract dimensions into specific, measurable components. The following content is based on the results of research question 1 to develop an advanced thinking skills assessment scale for mixed learning in interior design.

Dimension 1: critical thinking skills

The research results indicate that critical thinking skills constitute a key core category in blended learning environments for interior design and are crucial for cultivating students' HOTS. Critical thinking skills refer to the ability to analyze information objectively and make a reasoned judgment 39 . Scholars tend to emphasize this concept as a method of general skepticism, rational thinking, and self-reflection 7 , 40 . For example, Goodsett 26 suggested that it should be based on rational skepticism and careful thought about external matters as well as open self-reflection about internal thoughts and actions. Moreover, the California Critical Thinking Disposition Inventory (CCTDI) is widely used to measure critical thinking skills, including dimensions such as seeking truth, confidence, questioning and courage to seek truth, curiosity and openness, as well as analytical and systematic methods 41 . In addition, maturity means continuous adjustment and improvement of a person's cognitive system and learning activities through continuous awareness, reflection, and self-awareness 42 . Moreover, Nguyen 43 confirmed that critical thinking and cognitive maturity can be achieved through these activities, emphasizing that critical thinking includes cognitive skills such as analysis, synthesis, and evaluation, as well as emotional tendencies such as curiosity and openness.

In addition, in a blended learning environment for interior design, critical thinking skills help students better understand, evaluate, and apply design knowledge and skills, cultivating independent thinking and innovation abilities 44 . If students lack these skills, they may accept superficial information and solutions without sufficient thinking and evaluation, resulting in the overlooking of important details or the selection of inappropriate solutions in the design process. Therefore, for the measurement of critical thinking skills, the focus should be on cognitive skills such as analysis, synthesis, and evaluation, as well as curiosity and open mindedness. The specific items for critical thinking skills are shown in Table 6 .

Dimension 2: problem-solving skills

Problem-solving skills constitute a key core category in blended learning environments for interior design and are crucial for cultivating students' HOTS. Problem-solving skills involve the ability to analyze and solve problems by understanding them, identifying their root causes, and developing appropriate solutions 45 . According to the 5E-based STEM education approach, problem-solving skills encompass the following abilities: problem identification and definition, formulation of problem-solving strategies, problem representation, resource allocation, and monitoring and evaluation of solution effectiveness 7 , 46 . Moreover, D'zurilla and Nezu 47 and Tan 48 indicated that attitudes, beliefs, and knowledge skills during problem solving, as well as the quality of proposed solutions and observable outcomes, are demonstrated. In addition, D'Zurilla and Nezu devised the Social Problem-Solving Inventory (SPSI), which comprises seven subscales: cognitive response, emotional response, behavioral response, problem identification, generation of alternative solutions, decision-making, and solution implementation. Based on these research results, the problem-solving skills dimension questions designed in this study are shown in Table 7 .

Dimension 3: teamwork skills

The research results indicate that teamwork skills constitute a key core category in blended learning environments for interior design and are crucial for cultivating students' HOTS. Teamwork skills refer to the ability to effectively collaborate, coordinate, and communicate with others in a team environment 49 . For example, the Teamwork Skills Assessment Tool (TWKSAT) developed by Stevens and Campion 50 identifies five core dimensions of teamwork: conflict management; collaborative problem-solving; communication; goal setting; performance management; decision-making; and task coordination. The design of this tool highlights the essential skills in teamwork and provides a structured approach for evaluating these skills. In addition, he indicated that successful teams need to have a range of skills for problem solving, including situational control, conflict management, decision-making and coordination, monitoring and feedback, and an open mindset. These skills help team members effectively address complex challenges and demonstrate the team’s collaboration and flexibility. Therefore, the assessment of learners' teamwork skills needs to cover the above aspects. As shown in Table 8 .

Dimension 4: practice innovative skills

The research results indicate that practical innovation skills constitute a key core category in blended learning environments for interior design, which is crucial for cultivating students' HOTS. The practice of innovative skills encompasses the utilization of creative cognitive processes and problem-solving strategies to facilitate the generation of original ideas, solutions, and approaches 51 . This practice places significant emphasis on two critical aspects: creative conception and design expression, as well as the innovative application of materials and technology. Tang et al. 52 indicated that creative conception and design expression involve the generation and articulation of imaginative and inventive ideas within a given context. With the introduction of concepts such as 21st-century learning skills, the "5C" competency framework, and core student competencies, blended learning has emerged as the goal and direction of educational reform. It aims to promote the development of students' HOTS, equipping them with the essential qualities and key abilities needed for lifelong development and societal advancement. Blended learning not only emphasizes the mastery of core learning content but also requires students to develop critical thinking, complex problem-solving, creative thinking, and practical innovation skills. To adapt to the changes and developments in the blended learning environment, this study designed 13 preliminary test items based on 21st-century learning skills, the "5C" competency framework, core student competencies, and the TTCT assessment scale developed by Torrance 53 . These items aim to assess students' practice of innovative skills within a blended learning environment, as shown in Table 9 .

The researchers' results indicate that the consensus among the interviewed expert participants is that the structural integrity of the scale is satisfactory and does not require modification. However, certain measurement items have been identified as problematic and require revision. The primary recommendations are as follows: Within the domain of problem-solving skills, the item "I usually conduct classroom and online learning with questions and clear goals" was deemed biased because of its emphasis on the "online" environment. Consequently, the evaluation panel advised splitting this item into two separate components: (1) "I am adept at frequently adjusting and reversing a negative team atmosphere" and (2) "I consistently engage in praising and encouraging others, fostering harmonious relationships. “The assessment process requires revisions and adjustments to specific projects, forming a pilot test scale consisting of 66 observable results from the original 65 items. In addition, there were other suggestions about linguistic formulation and phraseology, which are not expounded upon herein.

Verify the effectiveness of the HOTS assessment scale

The research results indicate that there are significant differences in the average scores of the four dimensions of the HOTS, including critical thinking skills (A1–A24 items), problem-solving skills (B1–B13 items), teamwork skills (C1–C16 items), and practical innovation skills (D1–D13 items). Moreover, this also suggests that each item has discriminative power. Specifically, this will be explained through the following aspects.

Project analysis based on the CR value

The critical ratio (CR) method, which uses the CR value (decision value) to remove measurement items with poor discrimination, is the most used method in project analysis. The specific process involves the use of the CR value (critical value) to identify and remove such items. First, the modified pilot test scale data are aggregated and sorted. Individuals representing the top and bottom 27% of the distribution were subsequently selected, constituting 66 respondents in each group. The high-score group comprises individuals with a total score of 127 or above (including 127), whereas the low-score group comprises individuals with a total score of 99 or below (including 99). Finally, an independent sample t test was conducted to determine the significant differences in the mean scores for each item between the high-score and low-score groups. The statistical results are presented in Table 10 .

The above table shows that independent sample t tests were conducted for all the items; their t values were greater than 3, and their p values were less than 0.001, indicating that the difference between the highest and lowest 27% of the samples was significant and that each item had discriminative power.

In summary, based on previous research and relevant theories, the HOTS scale for interior design was revised. This revision process involved interviews with interior design experts, teachers, and students, followed by item examination and homogeneity testing via the critical ratio (CR) method. The results revealed significant correlations ( p  < 0.01) between all the items and the total score, with correlation coefficients (R) above 0.4. Therefore, the scale exhibits good accuracy and internal consistency in capturing measured HOTS. These findings provide a reliable foundation for further research and practical applications.

Pilot study exploratory factor analysis

This study used SPSS (version 28) to conduct the KMO and Bartlett tests on the scale. The total HOTS test scale as well as the KMO and Bartlett sphericities were first calculated for the four subscales to ensure that the sample data were suitable for factor analysis 7 . The overall KMO value is 0.946, indicating that the data are highly suitable for factor analysis. Additionally, Bartlett's test of sphericity was significant, further supporting the appropriateness of conducting factor analysis ( p  < 0.05). All the values are above 0.7, indicating that the data for these subscales are also suitable for factor analysis. According to Javadi et al. 54 , these results suggest the presence of shared factors among the items within the subscales, as shown in Table 11 .

For each subscale, exploratory factor analysis was conducted to extract factors with eigenvalues greater than 1 while eliminating items with communalities less than 0.30, loadings less than 0.50, and items that cross multiple (more than one) common factors 55 , 56 . Additionally, items that were inconsistent with the assumed structure of the measure were identified and eliminated to ensure the best structural validity. These principles were applied to the factor analysis of each subscale, ensuring that the extracted factor structure and observed items are consistent with the hypothesized measurement structure and analysis results, as shown in the table 55 , 58 . In the exploratory factor analysis (EFA), the latent variables were effectively interpreted and demonstrated a significant response, with cumulative explained variances of the common factors exceeding 60%. This finding confirms the alignment between the scale structure, comprising the remaining items, and the initial theoretical framework proposed in this study. Additionally, the items were systematically reorganized to construct the final questionnaire. Consequently, items A1 to A24 were associated with the critical thinking skills dimension, items B25 to B37 were linked to problem-solving skills, items C38 to C53 were indicative of teamwork skills, and items D54 to D66 were reflective of practical innovation skills. As shown in Table 12 below.

In addition, the criterion for extracting principal components in factor analysis is typically based on eigenvalues, with values greater than 1 indicating greater explanatory power than individual variables. The variance contribution ratio reflects the proportion of variance explained by each principal component relative to the total variance and signifies the ability of the principal component to capture comprehensive information. The cumulative variance contribution ratio measures the accumulated proportion of variance explained by the selected principal components, aiding in determining the optimal number of components to retain while minimizing information loss. The above table shows that four principal components can be extracted from the data, and their cumulative variance contribution rate reaches 59.748%.

However, from the scree plot (as shown in Fig.  1 ), the slope flattens starting from the fifth factor, indicating that no distinct factors can be extracted beyond that point. Therefore, retaining four factors seems more appropriate. The factor loading matrix is the core of factor analysis, and the values in the matrix represent the factor loading of each item on the common factors. Larger values indicate a stronger correlation between the item variable and the common factor. For ease of analysis, this study used the maximum variance method to rotate the initial factor loading matrix, redistributing the relationships between the factors and original variables and making the correlation coefficients range from 0 to 1, which facilitates interpretation. In this study, factor loadings with absolute values less than 0.4 were filtered out. According to the analysis results, the items of the HOTS assessment scale can be divided into four dimensions, which is consistent with theoretical expectations.

Gravel plot of factors.

Through the pretest of the scale and selection of measurement items, 66 measurement items were ultimately determined. On this basis, a formal scale for assessing HOTS in a blended learning environment was developed, and the reliability and validity of the scale were tested to ultimately confirm its usability.

Confirmatory factor analysis of final testing

Final test employed that AMOS (version 26.0), a confirmatory factor analysis (CFA) was conducted on the retested sample data to validate the stability of the HOTS structural model obtained through exploratory factor analysis. This analysis aimed to assess the fit between the measurement results and the actual data, confirming the robustness of the derived HOTS structure and its alignment with the empirical data. The relevant model was constructed based on the factor structure of each component obtained through EFA and the observed variables, as shown in the diagram. The model fit indices are presented in Fig.  2 (among them, A represents critical thinking skills, B represents problem-solving skills, C represents teamwork skills, and D represents practical innovation skills). The models strongly support the "4-dimensional" structure of the HOTS, which includes four first-order factors: critical thinking skills, problem-solving skills, teamwork skills, and practical innovation skills. Critical thinking skills play a pivotal role in the blended learning environment of interior design, connecting problem-solving skills, teamwork skills, and innovative practices. These four dimensions form the assessment structure of HOTS, with critical thinking skills serving as the core element, inspiring individuals to assess problems and propose innovative solutions. By providing appropriate learning resources, diverse learning activities, and learning tasks, as well as designing items for assessment scales, it is possible to delve into the measurement and development of HOTS in the field of interior design, providing guidance for educational and organizational practices. This comprehensive approach to learning and assessment helps cultivate students' HOTS and lays a solid foundation for their comprehensive abilities in the field of interior design. Thus, the CFA structural models provide strong support for the initial hypothesis of the proposed HOTS assessment structure in this study. As shown in Fig.  2 .

Confirmatory factor analysis based on 4 dimensions. *A represents the dimension of critical thinking. B represents the dimension of problem-solving skills. C represents the dimension of teamwork skills. D represents the dimension of practical innovation skills.

Additionally, χ2. The fitting values of RMSEA and SRMR are both below the threshold, whereas the fitting values of the other indicators are all above the threshold, indicating that the model fits well. As shown in Table 13 .

Reliability and validity analysis

The reliability and validity of the scale need to be assessed after the model fit has been determined through validation factor analysis 57 . Based on the findings of Marsh et al. 57 , the following conclusions can be drawn. In terms of hierarchical and correlational model fit, the standardized factor loadings of each item range from 0.700 to 0.802, all of which are greater than or equal to 0.7. This indicates a strong correspondence between the observed items and each latent variable. Furthermore, the Cronbach's α coefficients, which are used to assess the internal consistency or reliability of the scale, ranged from 0.948 to 0.966 for each dimension, indicating a high level of data reliability and internal consistency. The composite reliabilities ranged from 0.948 to 0.967, exceeding the threshold of 0.6 and demonstrating a substantial level of consistency (as shown in Table 14 ).

Additionally, the diagonal bold font represents the square root of the AVE for each dimension. All the dimensions have average variance extracted (AVE) values ranging from 0.551 to 0.589, all of which are greater than 0.5, indicating that the latent variables have strong explanatory power for their corresponding items. These results suggest that the scale structure constructed in this study is reliable and effective. Furthermore, according to the results presented in Table 15 , the square roots of the AVE values for each dimension are greater than the absolute values of the correlations with other dimensions, indicating discriminant validity of the data. Therefore, these four subscales demonstrate good convergent and discriminant validity, indicating that they are both interrelated and independent. This implies that they can effectively capture the content required to complete the HOTS test scale.

Discussion and conclusion

The assessment scale for HOTS in interior design blended learning encompasses four dimensions: critical thinking skills, problem-solving skills, teamwork skills, and practical innovation skills. The selection of these dimensions is based on the characteristics and requirements of the interior design discipline, which aims to comprehensively evaluate students' HOTS demonstrated in blended learning environments to better cultivate their ability to successfully address complex design projects in practice. Notably, multiple studies have shown that HOTSs include critical thinking, problem-solving skills, creative thinking, and decision-making skills, which are considered crucial in various fields, such as education, business, and engineering 20 , 59 , 60 , 61 . Compared with prior studies, these dimensions largely mirror previous research outcomes, with notable distinctions in the emphasis on teamwork skills and practical innovation skills 62 , 63 . Teamwork skills underscore the critical importance of collaboration in contemporary design endeavors, particularly within the realm of interior design 64 . Effective communication and coordination among team members are imperative for achieving collective design objectives.

Moreover, practical innovation skills aim to increase students' capacity for creatively applying theoretical knowledge in practical design settings. Innovation serves as a key driver of advancement in interior design, necessitating students to possess innovative acumen and adaptability to evolving design trends for industry success. Evaluating practical innovation skills aims to motivate students toward innovative thinking, exploration of novel concepts, and development of unique design solutions, which is consistent with the dynamic and evolving nature of the interior design sector. Prior research suggests a close interplay between critical thinking, problem-solving abilities, teamwork competencies, and creative thinking, with teamwork skills acting as a regulatory factor for critical and creative thought processes 7 , 65 . This interconnected nature of HOTS provides theoretical support for the construction and validation of a holistic assessment framework for HOTS.

After the examination by interior design expert members, one item needed to be split into two items. The results of the CR (construct validity) analysis of the scale items indicate that independent sample t tests were subsequently conducted on all the items. The t values were greater than 3, with p values less than 0.001, indicating significant differences between the top and bottom 27% of the samples and demonstrating the discriminant validity of each item. This discovery highlights the diversity and effectiveness of the scale's internal items, revealing the discriminatory power of the scale in assessing the study subjects. The high t values and significant p values reflect the substantiality of the internal items in distinguishing between different sample groups, further confirming the efficacy of these items in evaluating the target characteristics. These results provide a robust basis for further refinement and optimization of the scale and offer guidance for future research, emphasizing the importance of scale design in research and providing strong support for data interpretation and analysis.

This process involves evaluating measurement scales through EFA, and it was found that the explanatory variance of each subscale reached 59.748%, and the CR, AVE, Cronbach's alpha, and Pearson correlation coefficient values of the total scale and subscales were in a better state, which strongly demonstrates the structure, discrimination, and convergence effectiveness of the scale 57 .

The scale structure and items of this study are reliable and effective, which means that students in the field of interior design can use them to test their HOTS level and assess their qualities and abilities. In addition, scholars can use this scale to explore the relationships between students' HOTS and external factors, personal personalities, etc., to determine different methods and strategies for developing and improving HOTS.

Limitations and future research

The developed mixed learning HOTS assessment scale for interior design also has certain limitations that need to be addressed in future research. The first issue is that, owing to the requirement of practical innovation skills, students need to have certain practical experience and innovative abilities. First-grade students usually have not yet had sufficient opportunities for learning and practical experience, so it may not be possible to evaluate their abilities effectively in this dimension. Therefore, when this scale is used for assessment, it is necessary to consider students' grade level and learning experience to ensure the applicability and accuracy of the assessment tool. For first-grade students, it may be necessary to use other assessment tools that are suitable for their developmental stage and learning experience to evaluate other aspects of their HOTS 7 . Future research should focus on expanding the scope of this dimension to ensure greater applicability.

The second issue is that the sample comes from ordinary private undergraduate universities in central China and does not come from national public universities or key universities. Therefore, there may be regional characteristics in the obtained data. These findings suggest that the improved model should be validated with a wider range of regional origins, a more comprehensive school hierarchy, and a larger sample size. The thirdly issue is the findings of this study are derived from self-reported data collected from participants through surveys. However, it is important to note that the literature suggests caution in heavily relying on such self-reported data, as perception does not always equate to actions 66 . In addition, future research can draw on this scale to evaluate the HOTS of interior design students, explore the factors that affect their development, determine their training and improvement paths, and cultivate skilled talent for the twenty-first century.

This study adopts a mixed method research approach, combining qualitative and quantitative methods to achieve a comprehensive understanding of the phenomenon 67 . By integrating qualitative and quantitative research methods, mixed methods research provides a comprehensive and detailed exploration of research questions, using multiple data sources and analytical methods to obtain accurate and meaningful answers 68 . To increase the quality of the research, the entire study followed the guidelines for scale development procedures outlined by Professor Li after the data were obtained. As shown in Fig.  3

Scale development program.

Basis of theory

This study is guided by educational objectives such as 21st-century learning skills, the "5C" competency framework, and students' core abilities 4 . The construction process of the scale is based on theoretical foundations, including Bloom's taxonomy. Drawing from existing research, such as the CCTDI 41 , SPSI 69 , and TWKSAT scales, the dimensions and preliminary items of the scale were developed. Additionally, to enhance the validity and reliability of the scale, dimensions related to HOTS in interior design were obtained through semi-structured interviews, and the preliminary project adapted or directly cited existing research results. The preliminary items were primarily adapted or directly referenced from existing research findings. Based on existing research, such as the CCTDI, SPSI, TWKSAT, and twenty-first century skills frameworks, this study takes "critical thinking skills, problem-solving skills, teamwork skills, and practical innovative skills" as the four basic dimensions of the scale.

Participants and procedures

This study is based on previous research and develops a HOTS assessment scale to measure the thinking levels of interior design students in blended learning. By investigating the challenges and opportunities students encounter in blended learning environments and exploring the complexity and diversity of their HOTS, this study aims to obtain comprehensive insights. For research question 1, via the purposive sampling method, 10 interior design experts are selected to investigate the dimensions and evaluation indicators of HOTS in blended learning of interior design. The researcher employed a semi structured interview method, and a random sampling technique was used to select 10 senior experts and teachers in the field of interior design, holding the rank of associate professor or above. This included 5 males and 5 females. As shown in Table 16 .

For research question 2 and 3, the research was conducted at an undergraduate university in China, in the field of interior design and within a blended learning environment. In addition, a statement confirms that all experimental plans have been approved by the authorized committee of Zhengzhou University of Finance and Economics. In the process of practice, the methods used were all in accordance with relevant guidelines and regulations, and informed consent was obtained from all participants. The Interior Design Blended Learning HOTS assessment scale was developed based on sample data from 350 students who underwent one pre-test and retest. The participants in the study consisted of second-, third-, and fourth-grade students who had participated in at least one blended learning course. The sample sizes were 115, 118, and 117 for the respective grade levels, totaling 350 individuals. Among the participants, there were 218 male students and 132 female students, all of whom were within the age range of 19–22 years. Through purposeful sampling, this study ensured the involvement of relevant participants and focused on a specific university environment with diverse demographic characteristics and rich educational resources.

This approach enhances the reliability and generalizability of the research and contributes to a deeper understanding of the research question (as shown in Table 17 ).

Instruments

The tools used in this study include semi structured interview guidelines and the HOTS assessment scale developed by the researchers. For research question 1, the semi structured interview guidelines were reviewed by interior design experts to ensure the accuracy and appropriateness of their content and questions. In addition, for research question 2 and 3, the HOTS assessment scale developed by the researchers will be checked via the consistency ratio (CR) method to assess the consistency and reliability of the scale items and validate their effectiveness.

Data analysis

For research question 1, the researcher will utilize the NVivo version 14 software tool to conduct thematic analysis on the data obtained through semi structured interviews. Thematic analysis is a commonly used qualitative research method that aims to identify and categorize themes, concepts, and perspectives that emerge within a dataset 70 . By employing NVivo software, researchers can effectively organize and manage large amounts of textual data and extract themes and patterns from them.

For research question 2, the critical ratio (CR) method was employed to conduct item analysis and homogeneity testing on the items of the pilot test questionnaire. The CR method allows for the assessment of each item's contribution to the total score and the evaluation of the interrelationships among the items within the questionnaire. These analytical techniques served to facilitate the evaluation and validation of the scale's reliability and validity.

For research question 3, this study used SPSS (version 26), in which confirmatory factor analysis (CFA) was conducted on the confirmatory sample data via maximum likelihood estimation. The purpose of this analysis was to verify whether the hypothesized factor structure model of the questionnaire aligned with the actual survey data. Finally, several indices, including composite reliability (CR), average variance extracted (CR), average variance extracted (AVE), Cronbach's alpha coefficient, and the Pearson correlation coefficient, were computed to assess the reliability and validity of the developed scale and assess its reliability and validity.

In addition, exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) are commonly utilized techniques in questionnaire development and adaptation research 31 , 70 . The statistical software packages SPSS and AMOS are frequently employed for implementing these analytical techniques 71 , 72 , 73 . CFA is a data-driven approach to factor generation that does not require a predetermined number of factors or specific relationships with observed variables. Its focus lies in the numerical characteristics of the data. Therefore, prior to conducting CFA, survey questionnaires are typically constructed through EFA to reveal the underlying structure and relationships between observed variables and the latent structure.

In contrast, CFA tests the hypothesized model structure under specific theoretical assumptions or structural hypotheses, including the interrelationships among factors and the known number of factors. Its purpose is to validate the hypothesized model structure. Thus, the initial validity of the questionnaire structure, established through EFA, necessitates further confirmation through CFA 57 , 70 . Additionally, a sample size of at least 200 is recommended for conducting the validation factor analysis. In this study, confirmatory factor analysis was performed on a sample size of 317.

Data availability

All data generated or analyzed during this study are included in this published article. All the experimental protocols were approved by the Zhengzhou College of Finance and Economics licensing committee.

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An Adaptive Differential Evolution Algorithm Based on Data Preprocessing Method and a New Mutation Strategy to Solve Dynamic Economic Dispatch Considering Generator Constraints

• Published: 08 September 2024

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• Ruxin Zhao   ORCID: orcid.org/0000-0002-6810-2631 1 ,
• Wei Wang 1 ,
• Tingting Zhang 1 ,
• Chang Liu 2 ,
• Lixiang Fu 1 ,
• Jiajie Kang 1 ,
• Hongtan Zhang 1 ,
• Yang Shi 1 &
• Chao Jiang 1  

Differential evolution (DE) algorithm is a classical natural-inspired optimization algorithm which has a good. However, with the deepening of research, some researchers found that the quality of the candidate solution of the population in the differential evolution algorithm is poor and its global search ability is not enough when solving the global optimization problem. Therefore, in order to solve the above problems, we proposed an adaptive differential evolution algorithm based on the data processing method and a new mutation strategy (ADEDPMS). In this paper, the data preprocessing method is implemented by k -means clustering algorithm, which is used to divide the initial population into multiple clusters according to the average value of fitness, and select candidate solutions in each cluster according to different proportions. This method improves the quality of candidate solutions of the population to a certain extent. In addition, in order to solve the problem of insufficient global search ability in differential evolution algorithm, we also proposed a new mutation strategy, which is called “DE/current-to- \({p}_{1}\) best& \({p}_{2}\) best”. This strategy guides the search direction of the differential evolution algorithm by selecting individuals with good fitness, so that its search range is in the most promising candidate solution region, and indirectly increases the population diversity of the algorithm. We also proposed an adaptive parameter control method, which can effectively balance the relationship between the exploration process and the exploitation process to achieve the best performance. In order to verify the effectiveness of the proposed algorithm, the ADEDPMS is compared with five optimization algorithms of the same type in the past three years, which are AAGSA, DFPSO, HGASSO, HHO and VAGWO. In the simulation experiment, 6 benchmark test functions and 4 engineering example problems are used, and the convergence accuracy, convergence speed and stability are fully compared. We used ADEDPMS to solve the dynamic economic dispatch (ED) problem with generator constraints. It is compared with the optimization algorithms used to solve the ED problem in the last three years which are AEFA, AVOA, OOA, SCA and TLBO. The experimental results show that compared with the five latest optimization algorithms proposed in the past three years to solve benchmark functions, engineering example problems and the ED problem, the proposed algorithm has strong competitiveness in each test index.

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The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.

This work is supported by the National Natural Science Foundation of China (with number 61906164), by the Natural Science Foundation of Jiangsu Province of China (with number BK20190875).

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Ruxin Zhao, Wei Wang, Tingting Zhang, Lixiang Fu, Jiajie Kang, Hongtan Zhang, Yang Shi & Chao Jiang

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Zhao, R., Wang, W., Zhang, T. et al. An Adaptive Differential Evolution Algorithm Based on Data Preprocessing Method and a New Mutation Strategy to Solve Dynamic Economic Dispatch Considering Generator Constraints. Comput Econ (2024). https://doi.org/10.1007/s10614-024-10705-2

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