functional problem solving

10 Best Problem-Solving Therapy Worksheets & Activities

Cognitive science tells us that we regularly face not only well-defined problems but, importantly, many that are ill defined (Eysenck & Keane, 2015).

Sometimes, we find ourselves unable to overcome our daily problems or the inevitable (though hopefully infrequent) life traumas we face.

Problem-Solving Therapy aims to reduce the incidence and impact of mental health disorders and improve wellbeing by helping clients face life’s difficulties (Dobson, 2011).

This article introduces Problem-Solving Therapy and offers techniques, activities, and worksheets that mental health professionals can use with clients.

Before you continue, we thought you might like to download our three Positive Psychology Exercises for free . These science-based exercises explore fundamental aspects of positive psychology, including strengths, values, and self-compassion, and will give you the tools to enhance the wellbeing of your clients, students, or employees.

This Article Contains:

What is problem-solving therapy, 14 steps for problem-solving therapy, 3 best interventions and techniques, 7 activities and worksheets for your session, fascinating books on the topic, resources from positivepsychology.com, a take-home message.

Problem-Solving Therapy assumes that mental disorders arise in response to ineffective or maladaptive coping. By adopting a more realistic and optimistic view of coping, individuals can understand the role of emotions and develop actions to reduce distress and maintain mental wellbeing (Nezu & Nezu, 2009).

“Problem-solving therapy (PST) is a psychosocial intervention, generally considered to be under a cognitive-behavioral umbrella” (Nezu, Nezu, & D’Zurilla, 2013, p. ix). It aims to encourage the client to cope better with day-to-day problems and traumatic events and reduce their impact on mental and physical wellbeing.

Clinical research, counseling, and health psychology have shown PST to be highly effective in clients of all ages, ranging from children to the elderly, across multiple clinical settings, including schizophrenia, stress, and anxiety disorders (Dobson, 2011).

Can it help with depression?

PST appears particularly helpful in treating clients with depression. A recent analysis of 30 studies found that PST was an effective treatment with a similar degree of success as other successful therapies targeting depression (Cuijpers, Wit, Kleiboer, Karyotaki, & Ebert, 2020).

Other studies confirm the value of PST and its effectiveness at treating depression in multiple age groups and its capacity to combine with other therapies, including drug treatments (Dobson, 2011).

The major concepts

Effective coping varies depending on the situation, and treatment typically focuses on improving the environment and reducing emotional distress (Dobson, 2011).

PST is based on two overlapping models:

Social problem-solving model

This model focuses on solving the problem “as it occurs in the natural social environment,” combined with a general coping strategy and a method of self-control (Dobson, 2011, p. 198).

The model includes three central concepts:

Social problem-solving
The problem
The solution

The model is a “self-directed cognitive-behavioral process by which an individual, couple, or group attempts to identify or discover effective solutions for specific problems encountered in everyday living” (Dobson, 2011, p. 199).

Relational problem-solving model

The theory of PST is underpinned by a relational problem-solving model, whereby stress is viewed in terms of the relationships between three factors:

Stressful life events
Emotional distress and wellbeing
Problem-solving coping

Therefore, when a significant adverse life event occurs, it may require “sweeping readjustments in a person’s life” (Dobson, 2011, p. 202).

Enhance positive problem orientation
Decrease negative orientation
Foster ability to apply rational problem-solving skills
Reduce the tendency to avoid problem-solving
Minimize the tendency to be careless and impulsive

D’Zurilla’s and Nezu’s model includes (modified from Dobson, 2011):

Initial structuring Establish a positive therapeutic relationship that encourages optimism and explains the PST approach.
Assessment Formally and informally assess areas of stress in the client’s life and their problem-solving strengths and weaknesses.
Obstacles to effective problem-solving Explore typically human challenges to problem-solving, such as multitasking and the negative impact of stress. Introduce tools that can help, such as making lists, visualization, and breaking complex problems down.
Problem orientation – fostering self-efficacy Introduce the importance of a positive problem orientation, adopting tools, such as visualization, to promote self-efficacy.
Problem orientation – recognizing problems Help clients recognize issues as they occur and use problem checklists to ‘normalize’ the experience.
Problem orientation – seeing problems as challenges Encourage clients to break free of harmful and restricted ways of thinking while learning how to argue from another point of view.
Problem orientation – use and control emotions Help clients understand the role of emotions in problem-solving, including using feelings to inform the process and managing disruptive emotions (such as cognitive reframing and relaxation exercises).
Problem orientation – stop and think Teach clients how to reduce impulsive and avoidance tendencies (visualizing a stop sign or traffic light).
Problem definition and formulation Encourage an understanding of the nature of problems and set realistic goals and objectives.
Generation of alternatives Work with clients to help them recognize the wide range of potential solutions to each problem (for example, brainstorming).
Decision-making Encourage better decision-making through an improved understanding of the consequences of decisions and the value and likelihood of different outcomes.
Solution implementation and verification Foster the client’s ability to carry out a solution plan, monitor its outcome, evaluate its effectiveness, and use self-reinforcement to increase the chance of success.
Guided practice Encourage the application of problem-solving skills across multiple domains and future stressful problems.
Rapid problem-solving Teach clients how to apply problem-solving questions and guidelines quickly in any given situation.

Success in PST depends on the effectiveness of its implementation; using the right approach is crucial (Dobson, 2011).

Problem-solving therapy – Baycrest

The following interventions and techniques are helpful when implementing more effective problem-solving approaches in client’s lives.

First, it is essential to consider if PST is the best approach for the client, based on the problems they present.

Is PPT appropriate?

It is vital to consider whether PST is appropriate for the client’s situation. Therapists new to the approach may require additional guidance (Nezu et al., 2013).

Therapists should consider the following questions before beginning PST with a client (modified from Nezu et al., 2013):

Has PST proven effective in the past for the problem? For example, research has shown success with depression, generalized anxiety, back pain, Alzheimer’s disease, cancer, and supporting caregivers (Nezu et al., 2013).
Is PST acceptable to the client?
Is the individual experiencing a significant mental or physical health problem?

All affirmative answers suggest that PST would be a helpful technique to apply in this instance.

Five problem-solving steps

The following five steps are valuable when working with clients to help them cope with and manage their environment (modified from Dobson, 2011).

Ask the client to consider the following points (forming the acronym ADAPT) when confronted by a problem:

Attitude Aim to adopt a positive, optimistic attitude to the problem and problem-solving process.
Define Obtain all required facts and details of potential obstacles to define the problem.
Alternatives Identify various alternative solutions and actions to overcome the obstacle and achieve the problem-solving goal.
Predict Predict each alternative’s positive and negative outcomes and choose the one most likely to achieve the goal and maximize the benefits.
Try out Once selected, try out the solution and monitor its effectiveness while engaging in self-reinforcement.

If the client is not satisfied with their solution, they can return to step ‘A’ and find a more appropriate solution.

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Positive self-statements

When dealing with clients facing negative self-beliefs, it can be helpful for them to use positive self-statements.

Use the following (or add new) self-statements to replace harmful, negative thinking (modified from Dobson, 2011):

I can solve this problem; I’ve tackled similar ones before.
I can cope with this.
I just need to take a breath and relax.
Once I start, it will be easier.
It’s okay to look out for myself.
I can get help if needed.
Other people feel the same way I do.
I’ll take one piece of the problem at a time.
I can keep my fears in check.
I don’t need to please everyone.

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PST practitioners have many different techniques available to support clients as they learn to tackle day-to-day or one-off trauma.

5 Worksheets and workbooks

Problem-solving self-monitoring form.

Ask the client to complete the following:

Describe the problem you are facing.
What is your goal?
What have you tried so far to solve the problem?
What was the outcome?

Reactions to Stress

It can be helpful for the client to recognize their own experiences of stress. Do they react angrily, withdraw, or give up (Dobson, 2011)?

The Reactions to Stress worksheet can be given to the client as homework to capture stressful events and their reactions. By recording how they felt, behaved, and thought, they can recognize repeating patterns.

What Are Your Unique Triggers?

Helping clients capture triggers for their stressful reactions can encourage emotional regulation.

When clients can identify triggers that may lead to a negative response, they can stop the experience or slow down their emotional reaction (Dobson, 2011).

The What Are Your Unique Triggers ? worksheet helps the client identify their triggers (e.g., conflict, relationships, physical environment, etc.).

Problem-Solving worksheet

Imagining an existing or potential problem and working through how to resolve it can be a powerful exercise for the client.

Use the Problem-Solving worksheet to state a problem and goal and consider the obstacles in the way. Then explore options for achieving the goal, along with their pros and cons, to assess the best action plan.

Getting the Facts

Clients can become better equipped to tackle problems and choose the right course of action by recognizing facts versus assumptions and gathering all the necessary information (Dobson, 2011).

Use the Getting the Facts worksheet to answer the following questions clearly and unambiguously:

Who is involved?
What did or did not happen, and how did it bother you?
Where did it happen?
When did it happen?
Why did it happen?
How did you respond?

2 Helpful Group Activities

While therapists can use the worksheets above in group situations, the following two interventions work particularly well with more than one person.

Generating Alternative Solutions and Better Decision-Making

A group setting can provide an ideal opportunity to share a problem and identify potential solutions arising from multiple perspectives.

Use the Generating Alternative Solutions and Better Decision-Making worksheet and ask the client to explain the situation or problem to the group and the obstacles in the way.

Once the approaches are captured and reviewed, the individual can share their decision-making process with the group if they want further feedback.

Visualization

Visualization can be performed with individuals or in a group setting to help clients solve problems in multiple ways, including (Dobson, 2011):

Clarifying the problem by looking at it from multiple perspectives
Rehearsing a solution in the mind to improve and get more practice
Visualizing a ‘safe place’ for relaxation, slowing down, and stress management

Guided imagery is particularly valuable for encouraging the group to take a ‘mental vacation’ and let go of stress.

Ask the group to begin with slow, deep breathing that fills the entire diaphragm. Then ask them to visualize a favorite scene (real or imagined) that makes them feel relaxed, perhaps beside a gently flowing river, a summer meadow, or at the beach.

The more the senses are engaged, the more real the experience. Ask the group to think about what they can hear, see, touch, smell, and even taste.

Encourage them to experience the situation as fully as possible, immersing themselves and enjoying their place of safety.

Such feelings of relaxation may be able to help clients fall asleep, relieve stress, and become more ready to solve problems.

We have included three of our favorite books on the subject of Problem-Solving Therapy below.

1. Problem-Solving Therapy: A Treatment Manual – Arthur Nezu, Christine Maguth Nezu, and Thomas D’Zurilla

This is an incredibly valuable book for anyone wishing to understand the principles and practice behind PST.

Written by the co-developers of PST, the manual provides powerful toolkits to overcome cognitive overload, emotional dysregulation, and the barriers to practical problem-solving.

Find the book on Amazon .

2. Emotion-Centered Problem-Solving Therapy: Treatment Guidelines – Arthur Nezu and Christine Maguth Nezu

Another, more recent, book from the creators of PST, this text includes important advances in neuroscience underpinning the role of emotion in behavioral treatment.

Along with clinical examples, the book also includes crucial toolkits that form part of a stepped model for the application of PST.

3. Handbook of Cognitive-Behavioral Therapies – Keith Dobson and David Dozois

This is the fourth edition of a hugely popular guide to Cognitive-Behavioral Therapies and includes a valuable and insightful section on Problem-Solving Therapy.

This is an important book for students and more experienced therapists wishing to form a high-level and in-depth understanding of the tools and techniques available to Cognitive-Behavioral Therapists.

For even more tools to help strengthen your clients’ problem-solving skills, check out the following free worksheets from our blog.

Case Formulation Worksheet This worksheet presents a four-step framework to help therapists and their clients come to a shared understanding of the client’s presenting problem.
Understanding Your Default Problem-Solving Approach This worksheet poses a series of questions helping clients reflect on their typical cognitive, emotional, and behavioral responses to problems.
Social Problem Solving: Step by Step This worksheet presents a streamlined template to help clients define a problem, generate possible courses of action, and evaluate the effectiveness of an implemented solution.

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While we are born problem-solvers, facing an incredibly diverse set of challenges daily, we sometimes need support.

Problem-Solving Therapy aims to reduce stress and associated mental health disorders and improve wellbeing by improving our ability to cope. PST is valuable in diverse clinical settings, ranging from depression to schizophrenia, with research suggesting it as a highly effective treatment for teaching coping strategies and reducing emotional distress.

Many PST techniques are available to help improve clients’ positive outlook on obstacles while reducing avoidance of problem situations and the tendency to be careless and impulsive.

The PST model typically assesses the client’s strengths, weaknesses, and coping strategies when facing problems before encouraging a healthy experience of and relationship with problem-solving.

Why not use this article to explore the theory behind PST and try out some of our powerful tools and interventions with your clients to help them with their decision-making, coping, and problem-solving?

We hope you enjoyed reading this article. Don’t forget to download our three Positive Psychology Exercises for free .

Cuijpers, P., Wit, L., Kleiboer, A., Karyotaki, E., & Ebert, D. (2020). Problem-solving therapy for adult depression: An updated meta-analysis. European P sychiatry , 48 (1), 27–37.
Dobson, K. S. (2011). Handbook of cognitive-behavioral therapies (3rd ed.). Guilford Press.
Dobson, K. S., & Dozois, D. J. A. (2021). Handbook of cognitive-behavioral therapies (4th ed.). Guilford Press.
Eysenck, M. W., & Keane, M. T. (2015). Cognitive psychology: A student’s handbook . Psychology Press.
Nezu, A. M., & Nezu, C. M. (2009). Problem-solving therapy DVD . Retrieved September 13, 2021, from https://www.apa.org/pubs/videos/4310852
Nezu, A. M., & Nezu, C. M. (2018). Emotion-centered problem-solving therapy: Treatment guidelines. Springer.
Nezu, A. M., Nezu, C. M., & D’Zurilla, T. J. (2013). Problem-solving therapy: A treatment manual . Springer.

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Problem Solving, Using and Applying and Functional Mathematics

Problem solving.

The problem-solving process can be described as a journey from meeting a problem for the first time to finding a solution, communicating it and evaluating the route. There are many models of the problem-solving process but they all have a similar structure. One model is given below. Although implying a linear process from comprehension through to evaluation, the model is more of a flow backward and forward, revisiting and revising on the problem-solving journey.

Comprehension

Representation.

Can they represent the situation mathematically?
What is it that they are trying to find?
What do they think the answer might be (conjecturing and hypothesising)?
What might they need to find out before they can get started?

Planning, analysis and synthesis

Having understood what the problem is about and established what needs finding, this stage is about planning a pathway to the solution. It is within this process that you might encourage pupils to think about whether they have seen something similar before and what strategies they adopted then. This will help them to identify appropriate methods and tools. Particular knowledge and skills gaps that need addressing may become evident at this stage.

Execution and communication

During the execution phase, pupils might identify further related problems they wish to investigate. They will need to consider how they will keep track of what they have done and how they will communicate their findings. This will lead on to interpreting results and drawing conclusions.

Pupils can learn as much from reflecting on and evaluating what they have done as they can from the process of solving the problem itself. During this phase pupils should be expected to reflect on the effectiveness of their approach as well as other people's approaches, justify their conclusions and assess their own learning. Evaluation may also lead to thinking about other questions that could now be investigated.

Using and Applying Mathematics

Aspects of using and applying reflect skills that can be developed through problem solving. For example:

In planning and executing a problem, problem solvers may need to:

select and use appropriate and efficient techniques and strategies to solve problems
identify what further information may be required in order to pursue a particular line of enquiry and give reasons for following or rejecting particular approaches
break down a complex calculation problem into simpler steps before attempting a solution and justify their choice of methods
make mental estimates of the answers to calculations
present answers to sensible levels of accuracy; understand how errors are compounded in certain calculations.

During problem solving, solvers need to communicate their mathematics for example by:

discussing their work and explaining their reasoning using a range of mathematical language and notation
using a variety of strategies and diagrams for establishing algebraic or graphical representations of a problem and its solution
moving from one form of representation to another to get different perspectives on the problem
presenting and interpreting solutions in the context of the original problem
using notation and symbols correctly and consistently within a given problem
examining critically, improve, then justifying their choice of mathematical presentation
presenting a concise, reasoned argument.

Problem solvers need to reason mathematically including through:

exploring, identifying, and using pattern and symmetry in algebraic contexts, investigating whether a particular case may be generalised further and understanding the importance of a counter-example; identifying exceptional cases
understanding the difference between a practical demonstration and a proof
showing step-by-step deduction in solving a problem; deriving proofs using short chains of deductive reasoning
recognising the significance of stating constraints and assumptions when deducing results
recognising the limitations of any assumptions that are made and the effect that varying the assumptions may have on the solution to a problem.

Functional Mathematics

Functional maths requires learners to be able to use mathematics in ways that make them effective and involved as citizens, able to operate confidently in life and to work in a wide range of contexts. The key processes of Functional Skills reflect closely the problem solving model but within three phases:

Making sense of situations and representing them
Processing and using the mathematics
Interpreting and communicating the results of the analysis

Functional equation

A functional equation , roughly speaking, is an equation in which some of the unknowns to be solved for are functions . For example, the following are functional equations:

$f(x) + 2f\left(\frac1x\right) = 2x$

1.1 The Inverse of a Function
2.1 Cyclic Functions
2.2 Problem Examples
3.1 Injectivity and Surjectivity

Introductory Topics

The inverse of a function.

$f(x) = x^2 + 6$

Intermediate Topics

Cyclic functions.

$f(x)$

Now, if we multiply the first equation by 3 and the second equation by 4, and add the two equations, we have:

$-7f(y) = 3y^2 + \frac{4}{y^2}$

Problem Examples

2006 AMC 12A Problem 18
2007 AIME II Problem 14

Advanced Topics

Injectivity and surjectivity.

Cauchy Functional Equation ]

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How to improve your problem solving skills and build effective problem solving strategies

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Problem solving strategies

What skills do i need to be an effective problem solver, how can i improve my problem solving skills.

Problem solving strategies are methods of approaching and facilitating the process of problem-solving with a set of techniques , actions, and processes. Different strategies are more effective if you are trying to solve broad problems such as achieving higher growth versus more focused problems like, how do we improve our customer onboarding process?

Broadly, the problem solving steps outlined above should be included in any problem solving strategy though choosing where to focus your time and what approaches should be taken is where they begin to differ. You might find that some strategies ask for the problem identification to be done prior to the session or that everything happens in the course of a one day workshop.

The key similarity is that all good problem solving strategies are structured and designed. Four hours of open discussion is never going to be as productive as a four-hour workshop designed to lead a group through a problem solving process.

Good problem solving strategies are tailored to the team, organization and problem you will be attempting to solve. Here are some example problem solving strategies you can learn from or use to get started.

Use a workshop to lead a team through a group process

Often, the first step to solving problems or organizational challenges is bringing a group together effectively. Most teams have the tools, knowledge, and expertise necessary to solve their challenges – they just need some guidance in how to use leverage those skills and a structure and format that allows people to focus their energies.

Facilitated workshops are one of the most effective ways of solving problems of any scale. By designing and planning your workshop carefully, you can tailor the approach and scope to best fit the needs of your team and organization.

Problem solving workshop

Creating a bespoke, tailored process
Tackling problems of any size
Building in-house workshop ability and encouraging their use

Workshops are an effective strategy for solving problems. By using tried and test facilitation techniques and methods, you can design and deliver a workshop that is perfectly suited to the unique variables of your organization. You may only have the capacity for a half-day workshop and so need a problem solving process to match.

By using our session planner tool and importing methods from our library of 700+ facilitation techniques, you can create the right problem solving workshop for your team. It might be that you want to encourage creative thinking or look at things from a new angle to unblock your groups approach to problem solving. By tailoring your workshop design to the purpose, you can help ensure great results.

One of the main benefits of a workshop is the structured approach to problem solving. Not only does this mean that the workshop itself will be successful, but many of the methods and techniques will help your team improve their working processes outside of the workshop.

We believe that workshops are one of the best tools you can use to improve the way your team works together. Start with a problem solving workshop and then see what team building, culture or design workshops can do for your organization!

Run a design sprint

Great for:

aligning large, multi-discipline teams
quickly designing and testing solutions
tackling large, complex organizational challenges and breaking them down into smaller tasks

By using design thinking principles and methods, a design sprint is a great way of identifying, prioritizing and prototyping solutions to long term challenges that can help solve major organizational problems with quick action and measurable results.

Some familiarity with design thinking is useful, though not integral, and this strategy can really help a team align if there is some discussion around which problems should be approached first.

The stage-based structure of the design sprint is also very useful for teams new to design thinking. The inspiration phase, where you look to competitors that have solved your problem, and the rapid prototyping and testing phases are great for introducing new concepts that will benefit a team in all their future work.

It can be common for teams to look inward for solutions and so looking to the market for solutions you can iterate on can be very productive. Instilling an agile prototyping and testing mindset can also be great when helping teams move forwards – generating and testing solutions quickly can help save time in the long run and is also pretty exciting!

Break problems down into smaller issues

Organizational challenges and problems are often complicated and large scale in nature. Sometimes, trying to resolve such an issue in one swoop is simply unachievable or overwhelming. Try breaking down such problems into smaller issues that you can work on step by step. You may not be able to solve the problem of churning customers off the bat, but you can work with your team to identify smaller effort but high impact elements and work on those first.

This problem solving strategy can help a team generate momentum, prioritize and get some easy wins. It’s also a great strategy to employ with teams who are just beginning to learn how to approach the problem solving process. If you want some insight into a way to employ this strategy, we recommend looking at our design sprint template below!

Use guiding frameworks or try new methodologies

Some problems are best solved by introducing a major shift in perspective or by using new methodologies that encourage your team to think differently.

Props and tools such as Methodkit , which uses a card-based toolkit for facilitation, or Lego Serious Play can be great ways to engage your team and find an inclusive, democratic problem solving strategy. Remember that play and creativity are great tools for achieving change and whatever the challenge, engaging your participants can be very effective where other strategies may have failed.

LEGO Serious Play

Improving core problem solving skills
Thinking outside of the box
Encouraging creative solutions

LEGO Serious Play is a problem solving methodology designed to get participants thinking differently by using 3D models and kinesthetic learning styles. By physically building LEGO models based on questions and exercises, participants are encouraged to think outside of the box and create their own responses.

Collaborate LEGO Serious Play exercises are also used to encourage communication and build problem solving skills in a group. By using this problem solving process, you can often help different kinds of learners and personality types contribute and unblock organizational problems with creative thinking.

Problem solving strategies like LEGO Serious Play are super effective at helping a team solve more skills-based problems such as communication between teams or a lack of creative thinking. Some problems are not suited to LEGO Serious Play and require a different problem solving strategy.

Card Decks and Method Kits

New facilitators or non-facilitators
Approaching difficult subjects with a simple, creative framework
Engaging those with varied learning styles

Card decks and method kids are great tools for those new to facilitation or for whom facilitation is not the primary role. Card decks such as the emotional culture deck can be used for complete workshops and in many cases, can be used right out of the box. Methodkit has a variety of kits designed for scenarios ranging from personal development through to personas and global challenges so you can find the right deck for your particular needs.

Having an easy to use framework that encourages creativity or a new approach can take some of the friction or planning difficulties out of the workshop process and energize a team in any setting. Simplicity is the key with these methods. By ensuring everyone on your team can get involved and engage with the process as quickly as possible can really contribute to the success of your problem solving strategy.

Source external advice

Looking to peers, experts and external facilitators can be a great way of approaching the problem solving process. Your team may not have the necessary expertise, insights of experience to tackle some issues, or you might simply benefit from a fresh perspective. Some problems may require bringing together an entire team, and coaching managers or team members individually might be the right approach. Remember that not all problems are best resolved in the same manner.

If you’re a solo entrepreneur, peer groups, coaches and mentors can also be invaluable at not only solving specific business problems, but in providing a support network for resolving future challenges. One great approach is to join a Mastermind Group and link up with like-minded individuals and all grow together. Remember that however you approach the sourcing of external advice, do so thoughtfully, respectfully and honestly. Reciprocate where you can and prepare to be surprised by just how kind and helpful your peers can be!

Mastermind Group

Solo entrepreneurs or small teams with low capacity
Peer learning and gaining outside expertise
Getting multiple external points of view quickly

Problem solving in large organizations with lots of skilled team members is one thing, but how about if you work for yourself or in a very small team without the capacity to get the most from a design sprint or LEGO Serious Play session?

A mastermind group – sometimes known as a peer advisory board – is where a group of people come together to support one another in their own goals, challenges, and businesses. Each participant comes to the group with their own purpose and the other members of the group will help them create solutions, brainstorm ideas, and support one another.

Mastermind groups are very effective in creating an energized, supportive atmosphere that can deliver meaningful results. Learning from peers from outside of your organization or industry can really help unlock new ways of thinking and drive growth. Access to the experience and skills of your peers can be invaluable in helping fill the gaps in your own ability, particularly in young companies.

A mastermind group is a great solution for solo entrepreneurs, small teams, or for organizations that feel that external expertise or fresh perspectives will be beneficial for them. It is worth noting that Mastermind groups are often only as good as the participants and what they can bring to the group. Participants need to be committed, engaged and understand how to work in this context.

Coaching and mentoring

Focused learning and development
Filling skills gaps
Working on a range of challenges over time

Receiving advice from a business coach or building a mentor/mentee relationship can be an effective way of resolving certain challenges. The one-to-one format of most coaching and mentor relationships can really help solve the challenges those individuals are having and benefit the organization as a result.

A great mentor can be invaluable when it comes to spotting potential problems before they arise and coming to understand a mentee very well has a host of other business benefits. You might run an internal mentorship program to help develop your team’s problem solving skills and strategies or as part of a large learning and development program. External coaches can also be an important part of your problem solving strategy, filling skills gaps for your management team or helping with specific business issues.

Now we’ve explored the problem solving process and the steps you will want to go through in order to have an effective session, let’s look at the skills you and your team need to be more effective problem solvers.

Problem solving skills are highly sought after, whatever industry or team you work in. Organizations are keen to employ people who are able to approach problems thoughtfully and find strong, realistic solutions. Whether you are a facilitator , a team leader or a developer, being an effective problem solver is a skill you’ll want to develop.

Problem solving skills form a whole suite of techniques and approaches that an individual uses to not only identify problems but to discuss them productively before then developing appropriate solutions.

Here are some of the most important problem solving skills everyone from executives to junior staff members should learn. We’ve also included an activity or exercise from the SessionLab library that can help you and your team develop that skill.

If you’re running a workshop or training session to try and improve problem solving skills in your team, try using these methods to supercharge your process!

Active listening

Active listening is one of the most important skills anyone who works with people can possess. In short, active listening is a technique used to not only better understand what is being said by an individual, but also to be more aware of the underlying message the speaker is trying to convey. When it comes to problem solving, active listening is integral for understanding the position of every participant and to clarify the challenges, ideas and solutions they bring to the table.

Some active listening skills include:

Paying complete attention to the speaker.
Removing distractions.
Avoid interruption.
Taking the time to fully understand before preparing a rebuttal.
Responding respectfully and appropriately.
Demonstrate attentiveness and positivity with an open posture, making eye contact with the speaker, smiling and nodding if appropriate. Show that you are listening and encourage them to continue.
Be aware of and respectful of feelings. Judge the situation and respond appropriately. You can disagree without being disrespectful.
Observe body language.
Paraphrase what was said in your own words, either mentally or verbally.
Remain neutral.
Reflect and take a moment before responding.
Ask deeper questions based on what is said and clarify points where necessary.

Active Listening #hyperisland #skills #active listening #remote-friendly This activity supports participants to reflect on a question and generate their own solutions using simple principles of active listening and peer coaching. It’s an excellent introduction to active listening but can also be used with groups that are already familiar with it. Participants work in groups of three and take turns being: “the subject”, the listener, and the observer.

Analytical skills

All problem solving models require strong analytical skills, particularly during the beginning of the process and when it comes to analyzing how solutions have performed.

Analytical skills are primarily focused on performing an effective analysis by collecting, studying and parsing data related to a problem or opportunity.

It often involves spotting patterns, being able to see things from different perspectives and using observable facts and data to make suggestions or produce insight.

Analytical skills are also important at every stage of the problem solving process and by having these skills, you can ensure that any ideas or solutions you create or backed up analytically and have been sufficiently thought out.

Nine Whys #innovation #issue analysis #liberating structures With breathtaking simplicity, you can rapidly clarify for individuals and a group what is essentially important in their work. You can quickly reveal when a compelling purpose is missing in a gathering and avoid moving forward without clarity. When a group discovers an unambiguous shared purpose, more freedom and more responsibility are unleashed. You have laid the foundation for spreading and scaling innovations with fidelity.

Collaboration

Trying to solve problems on your own is difficult. Being able to collaborate effectively, with a free exchange of ideas, to delegate and be a productive member of a team is hugely important to all problem solving strategies.

Remember that whatever your role, collaboration is integral, and in a problem solving process, you are all working together to find the best solution for everyone.

Marshmallow challenge with debriefing #teamwork #team #leadership #collaboration In eighteen minutes, teams must build the tallest free-standing structure out of 20 sticks of spaghetti, one yard of tape, one yard of string, and one marshmallow. The marshmallow needs to be on top. The Marshmallow Challenge was developed by Tom Wujec, who has done the activity with hundreds of groups around the world. Visit the Marshmallow Challenge website for more information. This version has an extra debriefing question added with sample questions focusing on roles within the team.

Communication

Being an effective communicator means being empathetic, clear and succinct, asking the right questions, and demonstrating active listening skills throughout any discussion or meeting.

In a problem solving setting, you need to communicate well in order to progress through each stage of the process effectively. As a team leader, it may also fall to you to facilitate communication between parties who may not see eye to eye. Effective communication also means helping others to express themselves and be heard in a group.

Bus Trip #feedback #communication #appreciation #closing #thiagi #team This is one of my favourite feedback games. I use Bus Trip at the end of a training session or a meeting, and I use it all the time. The game creates a massive amount of energy with lots of smiles, laughs, and sometimes even a teardrop or two.

Creative problem solving skills can be some of the best tools in your arsenal. Thinking creatively, being able to generate lots of ideas and come up with out of the box solutions is useful at every step of the process.

The kinds of problems you will likely discuss in a problem solving workshop are often difficult to solve, and by approaching things in a fresh, creative manner, you can often create more innovative solutions.

Having practical creative skills is also a boon when it comes to problem solving. If you can help create quality design sketches and prototypes in record time, it can help bring a team to alignment more quickly or provide a base for further iteration.

The paper clip method #sharing #creativity #warm up #idea generation #brainstorming The power of brainstorming. A training for project leaders, creativity training, and to catalyse getting new solutions.

Critical thinking

Critical thinking is one of the fundamental problem solving skills you’ll want to develop when working on developing solutions. Critical thinking is the ability to analyze, rationalize and evaluate while being aware of personal bias, outlying factors and remaining open-minded.

Defining and analyzing problems without deploying critical thinking skills can mean you and your team go down the wrong path. Developing solutions to complex issues requires critical thinking too – ensuring your team considers all possibilities and rationally evaluating them.

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Data analysis

Though it shares lots of space with general analytical skills, data analysis skills are something you want to cultivate in their own right in order to be an effective problem solver.

Being good at data analysis doesn’t just mean being able to find insights from data, but also selecting the appropriate data for a given issue, interpreting it effectively and knowing how to model and present that data. Depending on the problem at hand, it might also include a working knowledge of specific data analysis tools and procedures.

Having a solid grasp of data analysis techniques is useful if you’re leading a problem solving workshop but if you’re not an expert, don’t worry. Bring people into the group who has this skill set and help your team be more effective as a result.

Decision making

All problems need a solution and all solutions require that someone make the decision to implement them. Without strong decision making skills, teams can become bogged down in discussion and less effective as a result.

Making decisions is a key part of the problem solving process. It’s important to remember that decision making is not restricted to the leadership team. Every staff member makes decisions every day and developing these skills ensures that your team is able to solve problems at any scale. Remember that making decisions does not mean leaping to the first solution but weighing up the options and coming to an informed, well thought out solution to any given problem that works for the whole team.

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

Dependability

Most complex organizational problems require multiple people to be involved in delivering the solution. Ensuring that the team and organization can depend on you to take the necessary actions and communicate where necessary is key to ensuring problems are solved effectively.

Being dependable also means working to deadlines and to brief. It is often a matter of creating trust in a team so that everyone can depend on one another to complete the agreed actions in the agreed time frame so that the team can move forward together. Being undependable can create problems of friction and can limit the effectiveness of your solutions so be sure to bear this in mind throughout a project.

Team Purpose & Culture #team #hyperisland #culture #remote-friendly This is an essential process designed to help teams define their purpose (why they exist) and their culture (how they work together to achieve that purpose). Defining these two things will help any team to be more focused and aligned. With support of tangible examples from other companies, the team members work as individuals and a group to codify the way they work together. The goal is a visual manifestation of both the purpose and culture that can be put up in the team’s work space.

Emotional intelligence

Emotional intelligence is an important skill for any successful team member, whether communicating internally or with clients or users. In the problem solving process, emotional intelligence means being attuned to how people are feeling and thinking, communicating effectively and being self-aware of what you bring to a room.

There are often differences of opinion when working through problem solving processes, and it can be easy to let things become impassioned or combative. Developing your emotional intelligence means being empathetic to your colleagues and managing your own emotions throughout the problem and solution process. Be kind, be thoughtful and put your points across care and attention.

Being emotionally intelligent is a skill for life and by deploying it at work, you can not only work efficiently but empathetically. Check out the emotional culture workshop template for more!

Facilitation

As we’ve clarified in our facilitation skills post, facilitation is the art of leading people through processes towards agreed-upon objectives in a manner that encourages participation, ownership, and creativity by all those involved. While facilitation is a set of interrelated skills in itself, the broad definition of facilitation can be invaluable when it comes to problem solving. Leading a team through a problem solving process is made more effective if you improve and utilize facilitation skills – whether you’re a manager, team leader or external stakeholder.

The Six Thinking Hats #creative thinking #meeting facilitation #problem solving #issue resolution #idea generation #conflict resolution The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

Flexibility

Being flexible is a vital skill when it comes to problem solving. This does not mean immediately bowing to pressure or changing your opinion quickly: instead, being flexible is all about seeing things from new perspectives, receiving new information and factoring it into your thought process.

Flexibility is also important when it comes to rolling out solutions. It might be that other organizational projects have greater priority or require the same resources as your chosen solution. Being flexible means understanding needs and challenges across the team and being open to shifting or arranging your own schedule as necessary. Again, this does not mean immediately making way for other projects. It’s about articulating your own needs, understanding the needs of others and being able to come to a meaningful compromise.

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

Working in any group can lead to unconscious elements of groupthink or situations in which you may not wish to be entirely honest. Disagreeing with the opinions of the executive team or wishing to save the feelings of a coworker can be tricky to navigate, but being honest is absolutely vital when to comes to developing effective solutions and ensuring your voice is heard.

Remember that being honest does not mean being brutally candid. You can deliver your honest feedback and opinions thoughtfully and without creating friction by using other skills such as emotional intelligence.

Explore your Values #hyperisland #skills #values #remote-friendly Your Values is an exercise for participants to explore what their most important values are. It’s done in an intuitive and rapid way to encourage participants to follow their intuitive feeling rather than over-thinking and finding the “correct” values. It is a good exercise to use to initiate reflection and dialogue around personal values.

Initiative

The problem solving process is multi-faceted and requires different approaches at certain points of the process. Taking initiative to bring problems to the attention of the team, collect data or lead the solution creating process is always valuable. You might even roadtest your own small scale solutions or brainstorm before a session. Taking initiative is particularly effective if you have good deal of knowledge in that area or have ownership of a particular project and want to get things kickstarted.

That said, be sure to remember to honor the process and work in service of the team. If you are asked to own one part of the problem solving process and you don’t complete that task because your initiative leads you to work on something else, that’s not an effective method of solving business challenges.

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

Impartiality

A particularly useful problem solving skill for product owners or managers is the ability to remain impartial throughout much of the process. In practice, this means treating all points of view and ideas brought forward in a meeting equally and ensuring that your own areas of interest or ownership are not favored over others.

There may be a stage in the process where a decision maker has to weigh the cost and ROI of possible solutions against the company roadmap though even then, ensuring that the decision made is based on merit and not personal opinion.

Empathy map #frame insights #create #design #issue analysis An empathy map is a tool to help a design team to empathize with the people they are designing for. You can make an empathy map for a group of people or for a persona. To be used after doing personas when more insights are needed.

Being a good leader means getting a team aligned, energized and focused around a common goal. In the problem solving process, strong leadership helps ensure that the process is efficient, that any conflicts are resolved and that a team is managed in the direction of success.

It’s common for managers or executives to assume this role in a problem solving workshop, though it’s important that the leader maintains impartiality and does not bulldoze the group in a particular direction. Remember that good leadership means working in service of the purpose and team and ensuring the workshop is a safe space for employees of any level to contribute. Take a look at our leadership games and activities post for more exercises and methods to help improve leadership in your organization.

Leadership Pizza #leadership #team #remote-friendly This leadership development activity offers a self-assessment framework for people to first identify what skills, attributes and attitudes they find important for effective leadership, and then assess their own development and initiate goal setting.

In the context of problem solving, mediation is important in keeping a team engaged, happy and free of conflict. When leading or facilitating a problem solving workshop, you are likely to run into differences of opinion. Depending on the nature of the problem, certain issues may be brought up that are emotive in nature.

Being an effective mediator means helping those people on either side of such a divide are heard, listen to one another and encouraged to find common ground and a resolution. Mediating skills are useful for leaders and managers in many situations and the problem solving process is no different.

Conflict Responses #hyperisland #team #issue resolution A workshop for a team to reflect on past conflicts, and use them to generate guidelines for effective conflict handling. The workshop uses the Thomas-Killman model of conflict responses to frame a reflective discussion. Use it to open up a discussion around conflict with a team.

Planning

Solving organizational problems is much more effective when following a process or problem solving model. Planning skills are vital in order to structure, deliver and follow-through on a problem solving workshop and ensure your solutions are intelligently deployed.

Planning skills include the ability to organize tasks and a team, plan and design the process and take into account any potential challenges. Taking the time to plan carefully can save time and frustration later in the process and is valuable for ensuring a team is positioned for success.

3 Action Steps #hyperisland #action #remote-friendly This is a small-scale strategic planning session that helps groups and individuals to take action toward a desired change. It is often used at the end of a workshop or programme. The group discusses and agrees on a vision, then creates some action steps that will lead them towards that vision. The scope of the challenge is also defined, through discussion of the helpful and harmful factors influencing the group.

Prioritization

As organisations grow, the scale and variation of problems they face multiplies. Your team or is likely to face numerous challenges in different areas and so having the skills to analyze and prioritize becomes very important, particularly for those in leadership roles.

A thorough problem solving process is likely to deliver multiple solutions and you may have several different problems you wish to solve simultaneously. Prioritization is the ability to measure the importance, value, and effectiveness of those possible solutions and choose which to enact and in what order. The process of prioritization is integral in ensuring the biggest challenges are addressed with the most impactful solutions.

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

Project management

Some problem solving skills are utilized in a workshop or ideation phases, while others come in useful when it comes to decision making. Overseeing an entire problem solving process and ensuring its success requires strong project management skills.

While project management incorporates many of the other skills listed here, it is important to note the distinction of considering all of the factors of a project and managing them successfully. Being able to negotiate with stakeholders, manage tasks, time and people, consider costs and ROI, and tie everything together is massively helpful when going through the problem solving process.

Record keeping

Working out meaningful solutions to organizational challenges is only one part of the process. Thoughtfully documenting and keeping records of each problem solving step for future consultation is important in ensuring efficiency and meaningful change.

For example, some problems may be lower priority than others but can be revisited in the future. If the team has ideated on solutions and found some are not up to the task, record those so you can rule them out and avoiding repeating work. Keeping records of the process also helps you improve and refine your problem solving model next time around!

Personal Kanban #gamestorming #action #agile #project planning Personal Kanban is a tool for organizing your work to be more efficient and productive. It is based on agile methods and principles.

Research skills

Conducting research to support both the identification of problems and the development of appropriate solutions is important for an effective process. Knowing where to go to collect research, how to conduct research efficiently, and identifying pieces of research are relevant are all things a good researcher can do well.

In larger groups, not everyone has to demonstrate this ability in order for a problem solving workshop to be effective. That said, having people with research skills involved in the process, particularly if they have existing area knowledge, can help ensure the solutions that are developed with data that supports their intention. Remember that being able to deliver the results of research efficiently and in a way the team can easily understand is also important. The best data in the world is only as effective as how it is delivered and interpreted.

Customer experience map #ideation #concepts #research #design #issue analysis #remote-friendly Customer experience mapping is a method of documenting and visualizing the experience a customer has as they use the product or service. It also maps out their responses to their experiences. To be used when there is a solution (even in a conceptual stage) that can be analyzed.

Risk management

Managing risk is an often overlooked part of the problem solving process. Solutions are often developed with the intention of reducing exposure to risk or solving issues that create risk but sometimes, great solutions are more experimental in nature and as such, deploying them needs to be carefully considered.

Managing risk means acknowledging that there may be risks associated with more out of the box solutions or trying new things, but that this must be measured against the possible benefits and other organizational factors.

Be informed, get the right data and stakeholders in the room and you can appropriately factor risk into your decision making process.

Decisions, Decisions… #communication #decision making #thiagi #action #issue analysis When it comes to decision-making, why are some of us more prone to take risks while others are risk-averse? One explanation might be the way the decision and options were presented. This exercise, based on Kahneman and Tversky’s classic study , illustrates how the framing effect influences our judgement and our ability to make decisions . The participants are divided into two groups. Both groups are presented with the same problem and two alternative programs for solving them. The two programs both have the same consequences but are presented differently. The debriefing discussion examines how the framing of the program impacted the participant’s decision.

Team-building

No single person is as good at problem solving as a team. Building an effective team and helping them come together around a common purpose is one of the most important problem solving skills, doubly so for leaders. By bringing a team together and helping them work efficiently, you pave the way for team ownership of a problem and the development of effective solutions.

In a problem solving workshop, it can be tempting to jump right into the deep end, though taking the time to break the ice, energize the team and align them with a game or exercise will pay off over the course of the day.

Remember that you will likely go through the problem solving process multiple times over an organization’s lifespan and building a strong team culture will make future problem solving more effective. It’s also great to work with people you know, trust and have fun with. Working on team building in and out of the problem solving process is a hallmark of successful teams that can work together to solve business problems.

9 Dimensions Team Building Activity #ice breaker #teambuilding #team #remote-friendly 9 Dimensions is a powerful activity designed to build relationships and trust among team members. There are 2 variations of this icebreaker. The first version is for teams who want to get to know each other better. The second version is for teams who want to explore how they are working together as a team.

Time management

The problem solving process is designed to lead a team from identifying a problem through to delivering a solution and evaluating its effectiveness. Without effective time management skills or timeboxing of tasks, it can be easy for a team to get bogged down or be inefficient.

By using a problem solving model and carefully designing your workshop, you can allocate time efficiently and trust that the process will deliver the results you need in a good timeframe.

Time management also comes into play when it comes to rolling out solutions, particularly those that are experimental in nature. Having a clear timeframe for implementing and evaluating solutions is vital for ensuring their success and being able to pivot if necessary.

Improving your skills at problem solving is often a career-long pursuit though there are methods you can use to make the learning process more efficient and to supercharge your problem solving skillset.

Remember that the skills you need to be a great problem solver have a large overlap with those skills you need to be effective in any role. Investing time and effort to develop your active listening or critical thinking skills is valuable in any context. Here are 7 ways to improve your problem solving skills.

Share best practices

Remember that your team is an excellent source of skills, wisdom, and techniques and that you should all take advantage of one another where possible. Best practices that one team has for solving problems, conducting research or making decisions should be shared across the organization. If you have in-house staff that have done active listening training or are data analysis pros, have them lead a training session.

Your team is one of your best resources. Create space and internal processes for the sharing of skills so that you can all grow together.

Ask for help and attend training

Once you’ve figured out you have a skills gap, the next step is to take action to fill that skills gap. That might be by asking your superior for training or coaching, or liaising with team members with that skill set. You might even attend specialized training for certain skills – active listening or critical thinking, for example, are business-critical skills that are regularly offered as part of a training scheme.

Whatever method you choose, remember that taking action of some description is necessary for growth. Whether that means practicing, getting help, attending training or doing some background reading, taking active steps to improve your skills is the way to go.

Learn a process

Problem solving can be complicated, particularly when attempting to solve large problems for the first time. Using a problem solving process helps give structure to your problem solving efforts and focus on creating outcomes, rather than worrying about the format.

Tools such as the seven-step problem solving process above are effective because not only do they feature steps that will help a team solve problems, they also develop skills along the way. Each step asks for people to engage with the process using different skills and in doing so, helps the team learn and grow together. Group processes of varying complexity and purpose can also be found in the SessionLab library of facilitation techniques . Using a tried and tested process and really help ease the learning curve for both those leading such a process, as well as those undergoing the purpose.

Effective teams make decisions about where they should and shouldn’t expend additional effort. By using a problem solving process, you can focus on the things that matter, rather than stumbling towards a solution haphazardly.

Create a feedback loop

Some skills gaps are more obvious than others. It’s possible that your perception of your active listening skills differs from those of your colleagues.

It’s valuable to create a system where team members can provide feedback in an ordered and friendly manner so they can all learn from one another. Only by identifying areas of improvement can you then work to improve them.

Remember that feedback systems require oversight and consideration so that they don’t turn into a place to complain about colleagues. Design the system intelligently so that you encourage the creation of learning opportunities, rather than encouraging people to list their pet peeves.

While practice might not make perfect, it does make the problem solving process easier. If you are having trouble with critical thinking, don’t shy away from doing it. Get involved where you can and stretch those muscles as regularly as possible.

Problem solving skills come more naturally to some than to others and that’s okay. Take opportunities to get involved and see where you can practice your skills in situations outside of a workshop context. Try collaborating in other circumstances at work or conduct data analysis on your own projects. You can often develop those skills you need for problem solving simply by doing them. Get involved!

Use expert exercises and methods

Learn from the best. Our library of 700+ facilitation techniques is full of activities and methods that help develop the skills you need to be an effective problem solver. Check out our templates to see how to approach problem solving and other organizational challenges in a structured and intelligent manner.

There is no single approach to improving problem solving skills, but by using the techniques employed by others you can learn from their example and develop processes that have seen proven results.

Try new ways of thinking and change your mindset

Using tried and tested exercises that you know well can help deliver results, but you do run the risk of missing out on the learning opportunities offered by new approaches. As with the problem solving process, changing your mindset can remove blockages and be used to develop your problem solving skills.

Most teams have members with mixed skill sets and specialties. Mix people from different teams and share skills and different points of view. Teach your customer support team how to use design thinking methods or help your developers with conflict resolution techniques. Try switching perspectives with facilitation techniques like Flip It! or by using new problem solving methodologies or models. Give design thinking, liberating structures or lego serious play a try if you want to try a new approach. You will find that framing problems in new ways and using existing skills in new contexts can be hugely useful for personal development and improving your skillset. It’s also a lot of fun to try new things. Give it a go!

Encountering business challenges and needing to find appropriate solutions is not unique to your organization. Lots of very smart people have developed methods, theories and approaches to help develop problem solving skills and create effective solutions. Learn from them!

Books like The Art of Thinking Clearly , Think Smarter, or Thinking Fast, Thinking Slow are great places to start, though it’s also worth looking at blogs related to organizations facing similar problems to yours, or browsing for success stories. Seeing how Dropbox massively increased growth and working backward can help you see the skills or approach you might be lacking to solve that same problem. Learning from others by reading their stories or approaches can be time-consuming but ultimately rewarding.

A tired, distracted mind is not in the best position to learn new skills. It can be tempted to burn the candle at both ends and develop problem solving skills outside of work. Absolutely use your time effectively and take opportunities for self-improvement, though remember that rest is hugely important and that without letting your brain rest, you cannot be at your most effective.

Creating distance between yourself and the problem you might be facing can also be useful. By letting an idea sit, you can find that a better one presents itself or you can develop it further. Take regular breaks when working and create a space for downtime. Remember that working smarter is preferable to working harder and that self-care is important for any effective learning or improvement process.

Want to design better group processes?

Over to you

Now we’ve explored some of the key problem solving skills and the problem solving steps necessary for an effective process, you’re ready to begin developing more effective solutions and leading problem solving workshops.

Need more inspiration? Check out our post on problem solving activities you can use when guiding a group towards a great solution in your next workshop or meeting. Have questions? Did you have a great problem solving technique you use with your team? Get in touch in the comments below. We’d love to chat!

James Smart is Head of Content at SessionLab. He’s also a creative facilitator who has run workshops and designed courses for establishments like the National Centre for Writing, UK. He especially enjoys working with young people and empowering others in their creative practice.

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7.3 Problem Solving

Learning objectives.

By the end of this section, you will be able to:

Describe problem solving strategies
Define algorithm and heuristic
Explain some common roadblocks to effective problem solving and decision making

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

Problem-Solving Strategies

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them ( Table 7.2 ). For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Method	Description	Example
Trial and error	Continue trying different solutions until problem is solved	Restarting phone, turning off WiFi, turning off bluetooth in order to determine why your phone is malfunctioning
Algorithm	Step-by-step problem-solving formula	Instructional video for installing new software on your computer
Heuristic	General problem-solving framework	Working backwards; breaking a task into steps

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

When one is faced with too much information
When the time to make a decision is limited
When the decision to be made is unimportant
When there is access to very little information to use in making the decision
When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Everyday Connection

Solving puzzles.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( Figure 7.7 ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

Here is another popular type of puzzle ( Figure 7.8 ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Take a look at the “Puzzling Scales” logic puzzle below ( Figure 7.9 ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

Pitfalls to Problem Solving

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but they just need to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to overcome the problem ( Figure 7.10 ). During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Link to Learning

Check out this Apollo 13 scene about NASA engineers overcoming functional fixedness to learn more.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in Table 7.3 .

Bias	Description
Anchoring	Tendency to focus on one particular piece of information when making decisions or problem-solving
Confirmation	Focuses on information that confirms existing beliefs
Hindsight	Belief that the event just experienced was predictable
Representative	Unintentional stereotyping of someone or something
Availability	Decision is based upon either an available precedent or an example that may be faulty

Watch this teacher-made music video about cognitive biases to learn more.

Were you able to determine how many marbles are needed to balance the scales in Figure 7.9 ? You need nine. Were you able to solve the problems in Figure 7.7 and Figure 7.8 ? Here are the answers ( Figure 7.11 ).

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/psychology-2e/pages/1-introduction

Authors: Rose M. Spielman, William J. Jenkins, Marilyn D. Lovett
Publisher/website: OpenStax
Book title: Psychology 2e
Publication date: Apr 22, 2020
Location: Houston, Texas
Book URL: https://openstax.org/books/psychology-2e/pages/1-introduction
Section URL: https://openstax.org/books/psychology-2e/pages/7-3-problem-solving

© Jun 26, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Functional Problem-Solving Resource!

by sashabro89 | May 17, 2019 | Uncategorized | 0 comments

Photo by Artem Beliaikin on Pexels.com

Sick of playing board games or reading hypothetical scenarios for your speech/language therapy students to problem-solve? Tired of pulling out those dull picture cards? Well, I have finally found a problem-solving resource that is actually engaging and very practical: GCF Global . Under the Everyday Life section, there are activities about grocery shopping, making change, using an ATM, reading a map, fire safety, and tons of other practical areas. Of course it’s ideal if you work in a district where you can take your Life Skills students out to utilize buses and grocery shop; however, these virtual activities will allow students to practice the skills on a computer or iPad in the event they cannot go on such trips. It might also be a good activity to supplement field trips by allows students to practice the necessary skills beforehand on the computer before needing to complete them in real life.

I often stop and start these videos to ask questions and guide life skills students. What section would this food item be in? Where might we get a map for the subway or bus station? What is another way people get can directions on how to get somewhere via car or bus (many kids say they use their phone GPS, which I tell them is a perfectly ok way to get around). Below are some pre-simulation and post-simulation lesson ideas.

Extension and Lesson Ideas for Functional Problem-Solving

Grocery Shopping : Practice categorizing food according to the section you’d likely find it in the grocery store. Discuss how to ask for help from a grocery clerk or staff person. Practice requesting & using a grocery store card at the checkout line.

Buses, Trains : Discuss where and how to get bus passes, how to ask for help if lost. Practice using phone GPS to look up how to get to desired locations via buses/trains/subways. Problem-solve what they would do if their phone died or malfunctioned and they had to find another way around.

Money : Bring in some foods or other interesting items and have students “buy” them with real money (they don’t need to actually pay, but you should let them practice buying with real coins/dollars for functionality).

Classifieds, Job Applications : Discuss and learn about the different websites you can use to look for a job (Monster, Indeed). Practice looking up jobs on these websites. Print out or practice completing segments of job applications for high school and post-high school jobs. Role-play using the phone or email to ask questions about a job and follow-up with information. Simulate job interview question and answer.

Paying Bills, Tax Documents : Role-play calling about an incorrect bill or paying a bill via phone. Role-play calling the IRS about a taxes issue/error. Call your own electricity/internet provider and have students listen in and study how to select the right options to get to a representative.

Hope your Life Skills Support students enjoy this great website! Tune in for the next post on how to comprehend lengthy noun phrases in text!

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Functional Fixedness (Definition + Examples)

If you're here, you are probably researching functional fixedness to help you solve a problem or write a paper. Have no fear since this page aims to give you everything you need to know, including a few functional fixedness examples!

What is Functional Fixedness?

Functional fixedness is a mental obstacle that makes us see objects exclusively functioning traditionally. We cannot get past these fixed functions of objects or tools. This stunts our creativity and may hold us back from seeing an object's full potential.

Why Do We Experience Functional Fixedness?

Functional fixedness, like other biases and heuristics, streamlines our cognitive processes, aiding us in rapidly understanding the world around us. By learning from previous knowledge and experiences, we can navigate situations more efficiently. For instance, consider the teacup you encounter every morning. Instead of pondering its potential uses each day, you intuitively recognize it as a vessel for your tea. This immediate association, a sort of "mental shortcut," ensures you don't waste precious morning minutes deliberating its function.

These mental shortcuts, termed heuristics in psychology, are invaluable. They save time and effort by enabling us to know how to interact with familiar objects instantly. However, herein lies a double-edged sword. While it's undoubtedly helpful to identify a teacup primarily for tea drinking, being trapped within this singular perspective can be limiting. Recognizing an object's primary purpose is vital, but an inability to think beyond that predefined context can pose distinct disadvantages.

Heuristics and Functional Fixedness: Cognitive Pathways in Decision-Making

In cognitive psychology, understanding how humans make decisions and solve problems is central to comprehending the complex nature of the human mind. Heuristics and functional fixedness are two concepts that illustrate the shortcuts and potential pitfalls our minds take in this process. Let's delve into these concepts and explore their relationship.

Heuristics: Mental Shortcuts to Quicker Decisions

Heuristics are mental shortcuts that our brain uses to simplify complex decision-making processes. Instead of analyzing all available data when deciding, the brain uses heuristics to quickly arrive at a solution based on patterns and previous experiences. While these shortcuts can be incredibly efficient, they can sometimes lead to errors or biases.

For instance, the availability heuristic suggests that people base the likelihood of an event on how easily they can recall similar events from memory. This might lead someone to overestimate the risk of shark attacks after seeing a news story on one, even if such events are rare statistically.

Functional Fixedness: Stuck in Established Patterns

On the other hand, functional fixedness is a cognitive bias that limits our ability to see alternative uses for objects or methods beyond their traditional or known functions. It is the tendency to be "fixed" in our understanding of how something should function, based largely on prior experiences and knowledge.

For example, viewing a newspaper strictly as a medium for reading news might prevent someone from considering its use as a tool for cleaning windows, packing material, or even craftwork.

Comparing the Two

While both heuristics and functional fixedness relate to cognitive shortcuts and biases, they manifest differently:

Nature of the Process : Heuristics are general decision-making shortcuts that can apply to various situations and help us navigate the world more efficiently. In contrast, functional fixedness is about seeing objects or methods in a limited scope based on their familiar functions.
Outcome : Heuristics can often lead to reasonably accurate outcomes due to their basis in frequent experiences. However, they can also result in cognitive biases and errors. Functional fixedness, meanwhile, typically leads to limited problem-solving abilities and curtails creativity.
Advantages & Pitfalls : Heuristics help speed up decision-making in a world brimming with information. They're essential for daily function. However, their reliance on past patterns can sometimes misguide us. On the other hand, functional fixedness primarily presents as an obstacle to innovative thinking and creative problem-solving.

Interrelation in Cognitive Processes

Despite their differences, heuristics and functional fixedness can sometimes intersect. For instance, one might use a heuristic to quickly decide how to use an object based on its most familiar function, leading to functional fixedness. Conversely, functional fixedness might cause someone to default to a heuristic way of problem-solving, relying on established patterns rather than seeking innovative solutions.

While both heuristics and functional fixedness highlight the brain's propensity for simplification and efficiency, they also underscore the importance of awareness in our cognitive processes. We can foster more thoughtful, creative, and informed decision-making by recognizing when we might be relying too heavily on mental shortcuts or getting stuck in established patterns.

Examples of Functional Fixedness Holding Us Back

Say you have a blunt kitchen knife that you need to sharpen. However, you don’t own a knife sharpener. Would you think of using the unglazed ring around the bottom of your teacup? After all, it has the same surface as a sharpening stone. Coming up with this alternative use for a teacup would quickly solve your problem. Otherwise, you would have to look for a “real” knife sharpener while using your cup only for drinking tea.

The moment we see an object, the motor cortex in our brains activates in anticipation of using it in a standard way. That means we don’t need to hesitate about reaching for a teacup when we feel like having tea. But that also means when you're looking for a knife sharpener, you're likely to glaze over that teacup because you don't take a mental shortcut from teacups to knife sharpeners. (Well, now you might!)

Being aware of functional fixedness is important because overcoming it could be the key to solving a problem.

Schemas, Prior Knowledge, and Functional Fixedness in Psychology

In the vast landscape of cognitive psychology, understanding how humans process information and navigate their world is paramount. Schemas and prior knowledge play pivotal roles in shaping our perceptions and responses to various situations, and their influence on cognitive biases like functional fixedness cannot be understated.

Schemas: Blueprint of Our Understanding

A schema is a mental framework or structure that organizes and interprets information in our brains. It's like a blueprint for categorizing and understanding the world around us. Schemas are created from accumulated experiences, cultural background, and learned knowledge. For instance, we have schemas about what constitutes a typical "bird" or how a usual "restaurant" operates. When we encounter information or experiences that fit into our existing schemas, it reinforces them. Conversely, when we encounter anomalies, we adjust our schema (accommodation) or try to fit this new information into our existing schemas (assimilation), as posited by Jean Piaget, a renowned developmental psychologist.

The Role of Prior Knowledge

Our past experiences significantly shape our present and future actions. Prior knowledge serves as a foundation upon which we build new knowledge. When faced with a situation, our brain quickly taps into the repository of prior experiences to find a suitable response or solution. This prior knowledge is a guidepost, helping us navigate familiar situations swiftly and efficiently.

Linking to Functional Fixedness

However, the reliance on schemas and prior knowledge can sometimes limit our cognitive flexibility, leading to functional fixedness. When too deeply entrenched in our pre-existing understanding of an object's function, we can become "fixed" in our approach, hindering our ability to see alternative uses or solutions. Our brain defaults to follow the well-trodden path of past experiences and established schemas. This is where functional fixedness comes into play. For example, if our schema of a "book" is strictly an object for reading, we might overlook its potential use as a doorstop or a makeshift monitor stand.

Functional fixedness, in many ways, is a byproduct of reliance on schemas and prior knowledge. While these cognitive structures help us process information efficiently, they can sometimes act as blinders, narrowing our field of vision and restricting creative problem-solving.

In the Broader Context of Cognitive Psychology

In psychology, schemas, prior knowledge, and functional fixedness are intertwined. They are all part of the broader cognitive structures and processes that dictate how we perceive, think, and act. Recognizing their interconnectedness can help us understand why we sometimes get stuck in particular patterns of thought and how we can potentially break free to foster innovation and creativity. By challenging our established schemas and being open to new experiences, we can mitigate the effects of functional fixedness and open the doors to a more flexible and adaptive way of thinking.

Examples of Overcoming Functional Fixedness in Everyday Life

You might identify these examples as "life hacks," but they are all forms of pushing past functional fixedness and seeing uses for everyday objects in new lights.

Want to keep your door open? Tie a rubber band around it!
Need to prop up your phone? Use upside-down sunglasses.
Place a pool noodle under your child's fitted sheet to prevent them from rolling out of bed.
Worried about your gear stick getting too hot in your car? Put a koozie over it!
Need a last-minute speaker? Cups (plastic and glass) and toilet paper rolls are great alternatives.
Preparing to serve condiments at a party but don't want to waste dishes? Place your condiments or sauces in a cupcake tin!
Use a shoe rack to hang cleaning supplies.
Clothespins are a great way to hold onto nails before you start hammering!
Did your flip-flop fall apart because the hole is too big? Use a bread clip to keep the strap in place. (Bread clips are also a great way to organize and separate cords.)
Looking for tiny things within your carpet? Roll some pantyhose or spandex over your vacuum to attract them without sucking them into your vacuum!
Use your seat warmer to keep food warm after you pick it up from a restaurant!
Hair straighteners make great collar irons in a pinch.
Don't have a juicer? Use tongs to get everything out of lemons or limes!

See how much you might have been missing out on? If all these hacks are within our grasp, what other uses could you consider for everyday items?

Who Discovered Functional Fixedness?

The term “functional fixedness” was coined in 1935 by German Gestalt therapist Karl Duncker who contributed to psychology with his extensive work on understanding cognition and problem-solving.

Duncker’s Candle Experiment

Duncker conducted a famous cognitive bias experiment that measured the influence of functional fixedness on our problem-solving abilities.

He handed the participants a box of thumbtacks, a candle, and matches. He then asked them to find a way to attach the lit candle to a wall so the wax wouldn’t drip on the floor. The solution consisted of removing the tacks from the box, tacking the box to the wall, and placing the candle upright in the box.

Pretty simple, right?

But most participants couldn’t solve this problem. They saw the box only as something that was used for holding tacks. Duncker observed a "mental block against using an object in a new way that is required to solve a problem" in these participants. To find a solution, they would first need to overcome the tendency towards the psychological obstacle holding them back—functional fixedness.

Functional Fixedness and Problem Solving

Functional fixedness is practical in everyday life and crucial in building expertise and specialization in fields where it’s important to come up with quick solutions. But as we saw in Duncker’s experiment, this cognitive constraint is the enemy of creativity. Functional fixedness stops us from seeing alternative solutions and makes problem-solving more difficult.

Functional fixedness can become a genuine problem among professionals. Research shows that functional fixedness is one of large organizations' most significant barriers to innovation. If your job is to produce innovative solutions, being able to think “outside the box” is a must.

So why do we become limited when it comes to using objects?

Children, especially those under 5, are not as biased as adults. As we know only too well, toddlers won’t hesitate to turn a wall into a blank canvas for their works of art. But because they are constantly being corrected, children become more functionally fixed over time. Eventually, they realize that paper is the only acceptable support to draw on.

As we gain more experience and knowledge, we become increasingly fixated on the predetermined use of objects and tools. And the more we practice using them in certain ways, the harder it is to see other alternatives.

Knowledge and experience replace imagination and our ability to see an object for anything other than its original purpose.

How to Overcome Functional Fixedness?

The good news is that functional fixedness is not a psychological disorder that needs therapeutic intervention. We can train our minds to overcome the mental set, a problem-solving approach based on past experiences.

There are a few methods that can help break down functional fixedness and develop creative thinking:

Practicing creative thinking

The more often you try to see novel uses for everyday objects, the easier the process will eventually become. Let’s go back to the teacup. What other usages except for drinking tea (and sharpening knives) can you think of? With a bit of imagination, the same cup can become a paperweight, candle holder, cookie-cutter, bird feeder, and even a phone sound amplifier.

Practicing helps develop our ability to think creatively. It encourages something called divergent thinking, a term defined in 1967 by the American psychologist J. P. Guilford.

Contrary to convergent thinking , which focuses on finding a single solution, divergent thinking is a creative process where a problem is solved using strategies that deviate from commonly used ones.

Changing the context

Getting a fresh perspective is often useful when considering alternate approaches to a task. In a professional setting, this can mean brainstorming in a group or involving individuals from other disciplines to share their points of view.

Considering a problem from a different angle prompts us to think creatively.

Focusing on features instead of function

Another way of breaking away from habitual ways of looking at objects is to consider what they are made of instead of concentrating on their function. List an item's different characteristics, and you might come up with its alternative uses. A teacup is made of ceramic, which can be broken down into pieces to create a mosaic.

This approach helps combat functional fixedness by focusing on the object itself while distancing ourselves from the mechanics of its intended use.

Other Biases and Heuristics That Hold Us Back

Functional fixedness is not the only "mental shortcut" holding us back. If we allow ourselves to think beyond what appears to be the "obvious answer," we may do more than we could have ever imagined!

Bandwagon Effect

It's easy to agree with what other people think. Meetings go much faster when everyone agrees right away. Plus, if one person likes the idea, it's probably not so bad, right? Well, this isn't always the case. Sometimes, the bandwagon effect encourages us to go along with what everyone else is doing. (It's easy for us to "hop on the bandwagon," as they say." Will you and your colleagues find a better solution if you debate a few more options? Are you just agreeing to something because everyone else is?

Dunning-Kruger Effect

Think you know a lot about a subject? Think again. The Dunning-Kruger Effect suggests that the less we know about a subject, the more confident we are in our abilities. Let's say you go to a rock climbing gym for the first time. You look at the wall and think, "I can get the hang of this quickly!" After a few sessions, you learn that there are different grips and ways of moving your body that you would have never thought of before! The initial false sense of confidence is a result of the Dunning-Kruger Effect.

Confirmation Bias

Once we decide, we will likely search for "evidence" confirming that we are right. If you have decided to vote for a certain political candidate, for example, you may only seek out news articles and information that confirms that they are the best candidate for the job. If you decide to leave your job, you may start focusing on the worst parts of the job. Don't let the confirmation bias prevent you from seeing all sides of an argument!

Not all biases are inherently bad, but they can hold us back. When approaching a big decision or trying to solve a problem, evaluate how biases could influence your thinking. Can you push past them? Can you try something new and unexpected?

Jean Piaget’s Theory of Cognitive Development
The Psychology of Long Distance Relationships
Operant Conditioning (Examples + Research)
Beck’s Depression Inventory (BDI Test)
Variable Interval Reinforcement Schedule (Examples)

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Why do we have trouble thinking outside the box?

Functional fixedness, what is functional fixedness.

Functional fixedness describes why we're unable to use an object in ways beyond its traditional use. Functional fixedness is a phenomenon found in problem-solving psychology and affects an individual’s ability to innovate and be creative when solving challenges. 1

Where this bias occurs

Debias your organization.

Most of us work & live in environments that aren’t optimized for solid decision-making. We work with organizations of all kinds to identify sources of cognitive bias & develop tailored solutions.

Consider the term “thinking outside the box.” Functional fixedness describes the difficulty we experience when we attempt to be creative in our problem-solving and our outside of the box thinking. Commonly, functional fixedness is used to highlight this problem-solving barrier in instances such as when we strive to use an object for a purpose other than its traditional use.

As children, many people may remember the ease of being creative and using their imagination to transform objects and their intended uses into something more. What was once a chair or a cardboard box, children quickly turn into fortresses with pillows and blankets. As we age, though, this ease in innovation becomes more difficult for the average person. Imagine someone needs a paperweight but is unable to find one. Instead of using a heavy object they can easily find in the room, they are fixated on their need for a paperweight. They might not think of using an object like a hammer or a stapler, which is unconventional to its typical use.

Individual effects

Functional fixedness is a cognitive bias that negatively affects a person’s ability to problem-solve and innovate. The bias causes a person to look at a problem in only one specific way and it can prevent them from developing effective solutions to their challenge. Functional fixedness can impact all areas of one’s life, including their academic life, careers, and personal lives. A person’s inability to recognize alternative approaches constrains their creativity and limits their potential ideas when looking to solve a problem.

Systemic effects

Functional fixedness can prevent companies and societies from innovating and solving pressing challenges. Passiveness and familiarity stem from an individual’s need to maintain the status quo and do things as they have always been done. There is comfort in familiarity, and it’s a natural human tendency to do what is comfortable. 2

From a corporate level, functional fixedness has led to issues in developing breakthrough products and solutions for internal challenges. For nations, functional fixedness has resulted in a lack of innovative solutions to tackle more significant societal problems. Systemic issues arising from functional fixedness have real-world impacts and are a real pain point for societies, as leaders cannot look past traditional solutions to solve complex problems.

Why it happens

Functional fixedness occurs due to strong pre-conceived notions that people develop regarding objects and how they must solve challenges using those objects.

Researchers have found that functional fixedness is a bias that develops and strengthens as we age. When studying functional fixedness in children, a study done at the University of Essex found that 5-year-old children showed no initial signs of the bias in early development when problem-solving. Meanwhile, as early as the age of 7, children tended to treat objects as they were meant to be used, already developing the bias. 2 Younger participants present initial immunity to the bias due to their initial lack of problem-solving experience, allowing them to be more creative in their solutions. 1

Functional fixedness has also proven to develop more as individuals gain more experience with problem-solving. Ironically, the more practice we have with identifying solutions to a problem, the more difficult it is to identify alternative or more creative solutions. 3 Though individuals may be aware that their traditional method of solving a problem may be over-used and ineffective, they are typically still tempted to use the same problem-solving approach, due to their familiarity with it.

Why it is important

Problem-solving is a regular part of any individual’s life. Functional fixedness impairs an individual’s ability to innovate and creatively tackle problems by limiting their problem-solving capabilities.

Individuals who are aware of functional fixedness can work towards avoiding bias and improving their problem-solving abilities. By consciously working to think innovatively, and better tackle problems in their professional and personal lives, they can strive towards unique and innovative solutions.

How to avoid it

As with many cognitive biases, functional fixedness can appear when tackling challenges in many different areas of life. Avoiding functional fixedness requires a conscious effort on the individual’s part towards promoting innovative ways of thinking and problem-solving.

Abstract the Problem

The first step to overcoming functional fixedness is done by first developing an awareness of the problem and simplifying it. A practice referred to as “uncommitting,” describes simplifying a challenge and distilling it down to the problem’s essential elements. By eliminating the details of the problem, we allow ourselves to think more creatively about the solution. By focusing on identifying the problem, and not judging ideas too early in the problem-solving process, alternative perspectives and possible solutions can be identified. 3

Draw Inspiration from Unexpected Places

Researchers have found that when people look for inspiration from distant domains, they tend to generate more creative solutions to their problems, especially in comparison to those who draw inspiration from more closely related fields. 3 Solutions from the abstract and distantly-related industries provide novel fixes, which tend to deliver creative and successful solutions.

Opinions from Different Disciplines

Like drawing inspiration from different disciplines, reaching out to experts in various fields also serves as a solution to avoiding functional fixedness and better-solving problems within one’s domain. Crowdsourcing initiatives by large technology companies provide an excellent example of this fix in play. Samsung, Unilever, and Lego have used crowdsourcing campaigns to share internal company challenges and call for innovative solutions from those external to their company in different industries. Crowdsourcing initiatives have continued to gain traction due to the success companies have seen in their ability to garner innovative solutions at a low cost, aiding these companies to avoid functional fixedness. 4 Crowdsourcing has proven to be an innovative way to avoid functional fixedness, as participants from outside of corporations do not hold the same preconceived notions of internal employees within these companies. Without these preconceived notions and set standards and processes, crowdsourcing participants are able to avoid the restrictive innovative barriers typically developed in these traditional settings.

How it all started

Functional fixedness was first defined by the German psychologist Karl Duncker in 1945. Karl Duncker described functional fixedness as a mental block when using an object in a new way that is required to solve a problem. 5 The block Karl emphasizes in his famous experiment demonstrates how an individual’s ability to complete a task with specific components were limited, as they were unable to rationalize their use outside of their original purpose.

The famous experiment conducted by Karl Duncker is well-known in psychology for demonstrating functional fixedness. In this experiment, Duncker gave participants a book of matches, a candle and a box of thumbtacks, and asked them to attach the candle to the wall so that when it was lit, it would not drip onto the table below it. Initially, most of the participants attempted to attach the candle to the wall by directly using the tacks or by trying to glue the candle to the wall by melting it. Because the Duncker gave participants a box with thumbtacks in them, few of the participants thought of using the box as a candle-holder and attaching the box to the wall with the tacks. Since the experiment participants fixated on the functionality of the box being used to hold the thumbtacks, they were unable to conceptualize the box as a potential solution for holding the candle, thus solving the challenge.

Additionally, in 1952 the experiment was later conducted by giving one set of participants an empty box without the thumbtacks while giving the other set of participants the box with thumbtacks inside. Participants who were given the box without the thumbtacks inside of the box were two times as likely to solve the problem. 6 The box no longer was used to hold the thumbtacks; therefore, its functionality was not tied to one single use.

Example 1 - PepsiCo leverages orthopedic experts

PepsiCo provides a notable example of functional fixedness and how companies attempt to curtail their own biases when developing products. In this example, PepsiCo’s challenge was to reduce the amount of sodium in its potato chips, without altering the salty flavors that customers traditionally loved. PepsiCo first tried to identify a solution to their problem by looking at the food and snack industry for similar challenges faced by their competitors but found nothing notable to their challenge. PepsiCo then worked with a third-party consulting firm and shared their problem to a broad and diverse range of technical experts to find an innovative and feasible solution.

Experts called on included those from engineering services, energy companies, and those in medical fields. The most creative and applicable response came from the orthopedics department of a global research lab. Researchers had developed a method of creating nano-particles of salt, which was initially used to conduct advanced research on osteoporosis. The process provided a new perspective and partner for PepsiCo, which ultimately led to Pepsi being able to solve their challenge by overcoming functional fixedness. 2

Example 2 - Creatively designing power strips

Another example of functional fixedness showcases how individuals overcame the cognitive bias by simplifying their initial problem. The experiment conducted by researchers at Carnegie Mellon University required participants to design a power strip in which larger plugs would not block adjacent outlets. To promote creative design solutions, researchers gave one set of participants the initial design challenge, and the second set of participants an abstracted version of the problem. The second set of participants were asked to instead fit objects of different sizes into a container without blocking one another, and taking advantage of the container’s full capacity. The challenge was reframed to avoid functional fixedness by stripping away the objects’ details being power strips, plugs, and outlets. By doing this, researchers looked to see which set of participants would develop the most innovative results.

The researchers found that when participants given the abstracted challenge identified relevant but distant domains to aid in their problem-solving. The areas of comparison included landscaping, carpentry, Japanese aesthetics, and contortionism. Participants who were able to gain inspiration from these distant domains found the most novel and practical solutions to the design problem. The study proves that when preventing functional fixedness, and promoting creativity, the best solutions are developed. 4

Functional fixedness is a cognitive bias that limits a person’s ability to use an object in more ways than it is traditionally used and affects an individual’s ability to innovate and be creative when solving challenges.

Functional fixedness occurs due to strong pre-conceived notions that people develop in regards to objects and how they must solve challenges using those objects. These preconceived notions typically develop as we age, and as we gain experience in problem-solving.

PepsiCo encountered functional fixedness issues when looking for ways to reduce the amount of sodium in its potato chip products without altering the salty flavors that customers love. When the PepsiCo team was unable to innovate and solve the challenge due to their functional fixedness, they attempted to crowdsource solutions from across domains and were able to find a solution from the orthopedics department of a global research lab. A practice used in researching osteoporosis helped solve PepsiCo’s challenge and provided a creative solution for the company.

A study conducted at Carnegie Mellon University tested the quality of design solutions in participants without functional fixedness bias. The first set of participants had to design a power strip which ensured that larger plugs would not block adjacent outlets. The second set of students were asked to develop a similar simplified task. This entailed fitting objects of different sizes into a container so that they wouldn’t block one another to take advantage of the container’s full capacity. The researchers found that when participants were given the abstracted problem, they identified relevant domains to aid in their problem-solving. Participants were able to gain inspiration from these distant domains and found the most novel and practical solutions to the design problem.

Functional fixedness can be avoided by firstly being aware of the bias. Abstracting the initial problem, drawing inspiration from other domains, and even getting opinions from different types of experts in other industries can help avoid Functional fixedness in one’s quotidian life.

German, T. P., & Defeyter, M. A. (2000). Immunity to functional fixedness in young children. Psychonomic Bulletin & Review , 7 , 707-712. https://link.springer.com/article/10.3758/BF03213010
Zynga, A. (2014, August 07). The Cognitive Bias Keeping Us from Innovating. Retrieved July 13, 2020, from https://hbr.org/2013/06/the-cognitive-bias-keeping-us-from
Harley, A. (2017, July 30). Functional Fixedness Stops You From Having Innovative Ideas. Retrieved July 13, 2020, from https://www.nngroup.com/articles/functional-fixedness/
Norton, K. (2019, June 10). 12 Brands Using Crowdsourcing for Product Design Ideas. Retrieved July 13, 2020, from https://www.cadcrowd.com/blog/12-brands-using-crowdsourcing-for-product-design-ideas/
Duncker, K. (1945). On problem-solving. Psychological Monographs, 58 (5), I-113. doi:10.1037/h0093599
Adamson, R. E. (1952). Functional Fixedness As Related To Problem Solving: A Repetition Of Three Experiments. doi:10.21236/ad0006119

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Dan is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. Dan has a background in organizational decision making, with a BComm in Decision & Information Systems from McGill University. He has worked on enterprise-level behavioral architecture at TD Securities and BMO Capital Markets, where he advised management on the implementation of systems processing billions of dollars per week. Driven by an appetite for the latest in technology, Dan created a course on business intelligence and lectured at McGill University, and has applied behavioral science to topics such as augmented and virtual reality.

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Dr. Sekoul Krastev

Sekoul is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. A decision scientist with a PhD in Decision Neuroscience from McGill University, Sekoul's work has been featured in peer-reviewed journals and has been presented at conferences around the world. Sekoul previously advised management on innovation and engagement strategy at The Boston Consulting Group as well as on online media strategy at Google. He has a deep interest in the applications of behavioral science to new technology and has published on these topics in places such as the Huffington Post and Strategy & Business.

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Functional Problem Solving Cards

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This PDF contains 288 real-world task cards (with photos and illustrations) that can be used to target problem solving, reasoning, safety awareness, and more.

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Functional Activities Bundle: Rehab Discharge to Home

This packet was created to promote recovery of cognitive-linguistic deficits for individuals returning home or to an assisted/independent living facility. Use of functional real-world tasks in therapy helps generalize skills learned to everyday situations. Functional therapy is based on a patient-centered approach and it is important to consider your clients’ day-to-day responsibilities. This packet includes a case history form, functional activities, practice ideas, and compensatory strategies. To improve functionality and promote independence, modify materials based on individual needs and use real materials/scenarios when possible.

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The Functional Therapy Materials Bundle includes 350+ pages of functional activities and printable resources that target real world cognitive-linguistic skills.

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Client Intake Questionnaire
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Features and Functions
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Recipes and Ingredients
Scheduling – daily, monthly, yearly routines
Orientation – days, months, holidays
Medication – management
Calculating Coins
Balancing a Register
Sustaining Attention

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Functional maths - problem solving.

Although underpinning knowledge is tested in its own right, problem solving is a core element of Functional Skills mathematics yet should not obscure or add additional mathematical complexity beyond the level of the qualification. Defining problem solving is a challenge but the attributes below are helpful. Not all (in fact often just one) of the listed attributes must be present in a single task for it to be considered to be problem-solving.

Tasks that have little or no scaffolding: there is little guidance given to the student beyond a start point and a finish point. Questions do not explicitly state the mathematical process(es) required for the solution.
Tasks that provide for multiple representations, such as use of a sketch or a diagram as well as calculations.
The information is not given in mathematical form or in mathematical language; or there is a need for the results to be interpreted or methods evaluated, for example, in a real-world context.
Tasks have a variety of techniques that could be used.
The solution requires understanding of the processes involved rather than just application of the techniques.

Master Functional Skills Maths books from MarsCademy

A new series of comprehensive Functional Skills Maths books now available from talented mathematician and teacher Marsida Horeshka who you may already know from her popular Functional Skills maths site https://marscademy.com/ (previously known as Maths Made Fun). The three Entry Level books are now available on Amazon (and soon from other booksellers).

Oxford University Press - free FS worksheets to support ‘Maths the Basics’

An incredible collection of free worksheets from OUP. Designed to support the excellent book ‘Maths the Basics’ by June Haighton et al (see our separate entry about this book) but can be used independently. I haven’t looked at them all ( there are more than a 100 - plus answer sheets!) but they seem to cover Entry Level 3 to Level 2. In addition there are many other useful downloads including tips and hints for non-specialists on delivering Functional Skills maths, English and ICT and much more.

Theme Park L1 Functional Skills Maths Project

This is a resource I've designed to be a homework/classwork support for L1 Functional Skills maths (reform).

Editor's notes

A wonderful 104-page compilation of resources covering almost every aspect of Level 1 Reformed Functional Maths. With curriculum mapping and links to further resources. Note this project includes resources from many excellent free web sites - please read the notes on the front cover sheet and page 104 for further information.

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Functional Fixedness as a Cognitive Bias

Functional fixedness is a type of cognitive bias that involves a tendency to see objects as only working in a particular way. For example, you might view a thumbtack as something that can only be used to hold paper to a corkboard. But what other uses might the item have?

In many cases, functional fixedness can prevent people from seeing the full range of uses for an object. It can also impair our ability to think of novel solutions to problems .

How Functional Fixedness Influences Problem-Solving

Imagine that you need to drive a nail into a wall so you can hang a framed photo. Unable to find a hammer, you spend a significant amount of time searching your house to find the missing tool. A friend comes over and suggests using a metal wrench instead to pound the nail into the wall.

Why didn't you think of using the metal wrench? Psychologists suggest that something known as functional fixedness often prevents us from thinking of alternative solutions to problems and different uses for objects.

A Classic Example

Here's one well-known example of functional fixedness at work:

You have two candles, numerous thumbtacks, and a box of matches. Using only these items, try to figure out how to mount the candles to a wall.

How would you accomplish this? Many people might immediately start trying to use the thumbtacks to affix the candles to the wall. Due to functional fixedness, you might think of only one way to directly use the thumbtacks. There is another solution, however. Using the matches, melt the bottom part of each candle and then use the hot wax to stick the candle to the matchbox. Once the candles are attached to the box, use the thumbtacks to stick the box to the wall.

Functional fixedness is just one type of mental obstacle that can make problem-solving more difficult.

Functional fixedness isn't always a bad thing. In many cases, it can act as a mental shortcut allowing you to quickly and efficiently determine a practical use for an object.

For example, imagine that someone has asked you to open a toolbox and find a tool that can be used to loosen a screw. It would take a tremendous amount of time if you had to analyze every item in the box to determine how effective it might be at performing the task. Instead, you are able to quickly grab a screwdriver, the most obvious item for loosening a screw.

American Psychological Association. APA Dictionary of Psychology: functional fixedness . 2020.

Munoz-Rubke F, Olson D, Will R, James KH. Functional fixedness in tool use: Learning modality, limitations and individual differences . Acta Psychol (Amst). 2018;190:11-26. doi:10.1016/j.actpsy.2018.06.006

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

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Design of diffractive neural networks for solving different classification problems at different wavelengths.

1. Introduction

2. design of spectral dnns for solving several classification problems, 3. gradient method for designing spectral dnns, 4. design examples of spectral dnns, 4.1. sequential solution of the classification problems, 4.2. parallel solution of the classification problems, 5. discussion and conclusions, supplementary materials, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Click here to enlarge figure

Number of DOEs	Classification Problem	Wavelength (nm)	Sequential Regime		Parallel Regime
Number of DOEs	Classification Problem	Wavelength (nm)	Overall Accuracy (%)	Minimum Contrast	Overall Accuracy (%)	Minimum Contrast
One	: MNIST	457	96.41	0.17	96.25	0.18
	: FMNIST	532	84.11	0.10	83.71	0.11
	: EMNIST	633	90.87	0.13	90.56	0.14
Two	: MNIST	457	97.86	0.16	97.38	0.19
	: FMNIST	532	86.93	0.11	87.96	0.11
	: EMNIST	633	93.07	0.12	92.93	0.16
Three	: MNIST	457	97.89	0.20	97.41	0.21
	: FMNIST	532	89.75	0.11	89.10	0.13
	: EMNIST	633	93.22	0.19	92.95	0.17

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Motz, G.A.; Doskolovich, L.L.; Soshnikov, D.V.; Byzov, E.V.; Bezus, E.A.; Golovastikov, N.V.; Bykov, D.A. Design of Diffractive Neural Networks for Solving Different Classification Problems at Different Wavelengths. Photonics 2024 , 11 , 780. https://doi.org/10.3390/photonics11080780

Motz GA, Doskolovich LL, Soshnikov DV, Byzov EV, Bezus EA, Golovastikov NV, Bykov DA. Design of Diffractive Neural Networks for Solving Different Classification Problems at Different Wavelengths. Photonics . 2024; 11(8):780. https://doi.org/10.3390/photonics11080780

Motz, Georgy A., Leonid L. Doskolovich, Daniil V. Soshnikov, Egor V. Byzov, Evgeni A. Bezus, Nikita V. Golovastikov, and Dmitry A. Bykov. 2024. "Design of Diffractive Neural Networks for Solving Different Classification Problems at Different Wavelengths" Photonics 11, no. 8: 780. https://doi.org/10.3390/photonics11080780

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Enhanced robust output tracking of nonlinear systems with dynamic event-triggering using neural network-based method

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Published: 24 August 2024

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Zixian Chen 1 ,
Huiyan Zhang ORCID: orcid.org/0000-0003-3406-8954 2 , 3 ,
Peng Shi 2 , 3 , 4 ,
Yu Huang 1 &
Wudhichai Assawinchaichote 5

This paper investigates the problem of robust tracking control for a class of nonlinear systems using a novel three-layer fully connected feedforward neural network controller. The weights of the hidden and output layers of this neural network controller are obtained by solving linear matrix inequalities, while the weights of the input and hidden layers are optimized using a genetic algorithm. Notably, the fitness function for training the genetic algorithm is the square of the difference between the reference signal and the controlled system output signal within the whole period. Moreover, considering external disturbances and time delays of networks, a novel Lyapunov-Krasovskii functional is constructed to derive sufficient conditions for the asymptotic stability with an $H_{\infty }$ performance of the nonlinear system. Furthermore, to conserve communication resources and reduce the computational load of the neural network controller, a dynamic event-triggered scheme with a non-negative intermediate variable is implemented. Finally, the tracking effect of the nonlinear system on two types of reference signals is tested on an inverted pendulum model to illustrate and validate the effectiveness of the proposed controller.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 62003062; in part by the National Key R &D Program of China under Grant No. 2022YFE0107300, and in part by the Australian Research Council (DP240101140).

This work was supported in part by the Science and Technology Research Program of Chongqing Municipal Education Commission (No. KJZDK202300807), in part by the Australian Research Council (DP240101140), and in the part by the Graduate Student Scientific Research Innovation Project of China under Grant yjscxx2024-284-198.

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School of Mechanical Engineering, Chongqing Technology and Business University, Chongqing, 400067, China

Zixian Chen & Yu Huang

National Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing, 400067, China

Huiyan Zhang & Peng Shi

The University of Adelaide, Adelaide, SA, 5005, Australia

Research and Innovation Center, Obuda University, Budapest, 1034, Hungary

King Mongkut’s University of Technology Thonburi, Bangkok, Thailand

Wudhichai Assawinchaichote

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Chen, Z., Zhang, H., Shi, P. et al. Enhanced robust output tracking of nonlinear systems with dynamic event-triggering using neural network-based method. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-10125-9

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DOI : https://doi.org/10.1007/s11071-024-10125-9

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