problem solving 4 blocker

• Michael Asbury

Driving Continuous Improvement with 4-Blockers

Turn unhappy campers into your biggest fans.

Unhappy Campers

A long, long time ago at a company far, far away, the leadership was not happy with the performance of an expensive piece of automated equipment purchased & installed about 6 months earlier.

Their assumption was that implementing this capital project would solve the performance issues with one of their production constraints.

Unfortunately, the performance issues were not solved.

The process needed 75% more operators & additional overtime

Additional inspections were required

An additional programmer was needed to support the primary operator

Twice as much space was used for the process

Scrap and rework actually increased

Disruptions to the next process were even more frequent

To say they were “not happy” with the ROI and anticipated negative payback time would be a gross understatement.

That is when I was called in and explained to that "this project was going to succeed" and it was my responsibility to make it happen…like now!

Without any hesitation, I formed a small team of 5 people that understood the process, the inputs, and the quality requirements as well as the skills and authority to make the necessary changes. We held a weekly meeting to review the output versus our daily goal and the issues hindering additional flow. The key Continuous Improvement tool we used to communicate during this meeting is called a 4-Blocker . We used a simple Defect Log to track the daily output and defect types & locations, which was linked to the 4-Blocker graphs.

Within 2 months:

Throughput through the automated process doubled

Defects per unit reduced from 11 dpu to 0.01 dpu

Scrap became rare

Inspections were reduced

Headcount returned to normal (besides some periodic programming)

Overtime became rare

There was a buffer of units ready for the next operation

What is a 4-Blocker?

A 4-Blocker is a highly adaptable and effective 1-page collaboration tool that shows multiple views of a process over a given period of time.

The 1st Quadrant uses a line graph with output versus time to show a history of process output relative to a target & a bar chart displays the count of issues per day. A stretch goal target line may be added 10 to 20% above the current target.

The 2nd Quadrant provides a breakdown of type and location of issues in the form of a stacker bar graph arranged from high to low by occurrence. It could just as easily have been arranged by location with type stacked or with impact instead of occurrence.

The 3rd Quadrant is an area filled in during a review meeting in which team members rank the issues quantified in the 2nd quadrant, then discuss and identify the most likely root causes.

In the 4th Quadrant , actions that can reduce or prevent the recurrence of issues are identified and responsibilities with dates are assigned.

The actions taken should follow the PDCA model (Plan-Do-Check-Act) in which a test action is executed and then judgment made whether to adjust and test again or move on with full implementation. Lessons learned from successful actions in one area should be quickly implemented in the other target areas with appropriate modifications.

The periodic review meeting should be allowed to take 30-60min. Weekly is a good starting point. Reducing the frequency to monthly, or as needed, is recommended when the number of issues drops to a predefined level. The team members need to have the knowledge, skills, and authority to take appropriate actions related to the process with a sense of urgency.

Common Results within 60 days in the Target Area

Depending on the level of support and prioritization, the following results are not uncommon:

40-60% Less Rework

20-50% Less Scrap

40-50% Less Overtime

20-50% More Throughput

By utilizing some simple data and engaging teams Quality, Cost, and Throughput can ALL be rapidly improved.

We use a systematic approach to gain insight & understanding into organizations in order to make rapid improvements where it will have the most impact.

Our methodology is a combination of Lean Six Sigma & Theory of Constraints called TLS. TLS is like combining a grand slam and a slam dunk to create a new power move...  The Grand Slam Dunk !

You can think of us as strategic problem solvers. 

We really enjoy developing and executing strategic rapid improvement plans for organizations. It is great to see bottom line results come to fruition! 

Check out our self-study eLearning course if you would like to find out how to drive Data Driven Continuous Improvement for Rapid Improvement in your organization! If you're interested in our other courses, check out our course catalog .

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Examples of Problem Solving with 4 Block

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Using 4 Block (4 Corners) Template in Math

Print the 4 Block Math Template in PDF

In this article I explain how to use this graphic organizer in math which is sometimes referred to as: 4 corners, 4 block or 4 square.

This template works well for solving problems in math that require more than one step or with problems that could be solved by using different strategies. For younger learners, it would work well as a visual which provides a framework for thinking through the problem and showing the steps. We often hear "use pictures, numbers and words to solve problems". This graphic organizer lends itself to support problem solving in math.

Using 4 Block for a Math Term or Concept

 Here is an example of using 4 block to help with the understanding of a term or concept in math. For this template, the term Prime Numbers is used.

A blank template is provided next.

Blank 4 Block Template

 Print this blank 4 block template in PDF.

This type of template can be used with terms in math. (Definition, Characteristics, Examples and non Examples.)  Use terms like Prime Numbers, Rectangles, Right Triangle, Polygons, Odd Numbers, Even Numbers, Perpendicular Lines, Quadratic Equations, Hexagon, Coefficient to name a few. 

However, it can also be used to solve problems like a typical 4 block problem. See the Handshake Problem example next.

4 Block using Handshake Problem

 Here is an example of the handshake problem being solve by a 10 year old. The problem was: If 25 people shake hands, how many handshakes will there be?

Without a framework to solve the problem, students often miss steps or don't answer the problem correctly. When the 4 block template is used regularly, learners improve in their ability to solve problems as it forces a way of thinking that works for solving problems.

• Graphic Organizers in Math
• The Frayer Model for Math
• Math Stumper: Use Two Squares to Make Separate Pens for Nine Pigs
• Study Tips for Math Homework and Math Tests
• Problem Solving in Mathematics
• First Grade Math: Word Problems
• Using Graphic Organizers for Special Education
• Popular Math Terms and Definitions
• How to Use Math Journals in Class
• Parentheses, Braces, and Brackets in Math
• Distance, Rate, and Time Worksheets
• The Typical 10th Grade Math Curriculum
• The Horse Problem: A Math Challenge
• Report Card Comments for Math
• The 10 Things That Worry Math Teachers the Most
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The World Of Math

Examples of Problem Solving with 4 Block

Using 4 Block (4 Corners) Template in Math Print the 4 Block Math Template in PDF In this article I explain how to use this graphic organizer in math which is sometimes referred to as: 4 corners, 4 block or 4 square. This template works well for solving problems in math that require more than one step or with problems that could be solved by using different strategies. For younger learners, it would work well as a visual which provides a framework for thinking through the problem and showing the steps. We often hear “use pictures, numbers and words to solve problems”. This graphic organizer lends itself to support problem solving in math.

Using 4 Block for a Math Term or Concept Here is an example of using 4 block to help with the understanding of a term or concept in math. For this template, the term Prime Numbers is used. A blank template is provided next.

Blank 4 Block Template Print this blank 4 block template in PDF. This type of template can be used with terms in math. (Definition, Characteristics, Examples and non Examples.) Use terms like Prime Numbers, Rectangles, Right Triangle, Polygons, Odd Numbers, Even Numbers, Perpendicular Lines, Quadratic Equations, Hexagon, Coefficient to name a few. However, it can also be used to solve problems like a typical 4 block problem. See the Handshake Problem example next.

4 Block using Handshake Problem Here is an example of the handshake problem being solve by a 10 year old. The problem was: If 25 people shake hands, how many handshakes will there be? Without a framework to solve the problem, students often miss steps or don’t answer the problem correctly. When the 4 block template is used regularly, learners improve in their ability to solve problems as it forces a way of thinking that works for solving problems.

Author: Arya Math

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Back to Basics: Using the 4 Blocker for Project Management Communication - DockYard

• Project Management

Client Partner

5 April 2022

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All experienced project managers know that keeping a project on track and flowing smoothly hinges on effective communication. And when you’re sending information from your team to an outside partner, it’s vital to provide it in a consistent, concise way that makes consumption easy and keeps decision making simple.

One of the ways I’ve achieved that throughout my career is with the 4 Blocker. The 4 Blocker is a one-page document that gives a stakeholder critical information at a glance. Not only does this give them a high-level understanding of the project, but it’s also helpful to ensure that the project management team shares information with clients uniformly, no matter who’s sending it.

While the 4 Blocker may have initially been a teaching tool for junior project managers, it’s also a helpful refresh for seasoned project managers who are far down the rabbit hole of long, narrative status updates (which may or may not even be read!).

Getting back to the basics challenges project managers to eliminate information overload. Usually, each block of information contains a limit of three bullet points. This framework encourages project managers to include only the most critical information in the update (ensuring the update can be consumed quickly and easily.)

The document has two focus areas:

• The introduction, and
• The substance

The Introduction

The introduction consists of project staples:

The project name

A one-sentence description: The goal for what the team should accomplish by the end of the project. It’s important to keep this front and center so everyone stays on task. This centers everyone around a specific goal to avoid scope creep or misunderstandings.

Dates, which should include your

Target End Date : The date you anticipate the project will be completed.

Next Release Date : This section is important for teams that work in sprints, like we do at DockYard. This is where you’ll list the date at the end of a sprint when you’ll release your work to the client for a demo, further discussion, etc.

Status Date : The date you’re sending the 4 Blocker to the client for review

The Substance

The substance of the 4 Blocker consists of:

Upcoming milestones: These are points within the timeline that your team has identified as important markers to ensure you’re on the right track as you progress through the project.

Key achievements: These are items or tasks the team agreed during the previous sprint were important to complete, and which they’ve checked off during the current sprint.

Next steps: These items are the next block of work the team will complete in the upcoming sprint.

Action items & decisions: When meeting with the client, sometimes they need to decide how to proceed. Capture these tasks for visibility and accountability for the upcoming sprint.

As with any documentation, The 4 Blocker can be adjusted depending on the organization, frequency of updates, or specific measurements desired. Regardless of what form you decide to use, however, it’s important that the project team use the same template consistently so all clients receive uniform information regardless of the project.

Sometimes the basics are exactly what your team needs to get back on track. Relying on the 4 Blocker is a simple, effective way to make sure you, your team, and your client get all the most important information quickly and reliably.

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How to write a project 4-blocker

1) a description of what's the scope of the project ( WHAT ) 2) a list of the milestones achieved ( ACHIEVEMENTS ) 3) a summary of the risks and the opps you have identified and you are managing with the team ( SPOTLIGHT ) 4) an outlook on the next milestones ( WHAT'S NEXT ).

• Block #1 (left hand side, on the top):
• Block #2 (right hand side, on the top):
• Block #3 (left hand side, on the bottom):
• Block #4 (right hand side, on the bottom):

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What Is a 4 Blocker? (Plus How To Create One in 6 Steps)

What is a 4 blocker.

A single-sheet tool called a “four blocker” separates content or project updates into various sections. This helps organize the information and encourages collaboration. The use of four blockers during meetings may also help attendees concentrate on the most crucial updates and steer clear of less crucial topics. They might enable you to conduct fewer or shorter meetings without compromising your ability to give your team important information.

The following are examples of typical quadrants, though exact titles and contents may differ:

A four blocker provides a summary of a project’s key components. Although it covers almost all project topics, it’s crucial that each quadrant’s information be brief. This supports the presentation’s effectiveness by emphasizing the key points that everyone should take away from it. Its goal is to facilitate and support presentation discussions, not to include all the specifics.

How to create a 4 blocker

The steps to create a four blocker are as follows:

1. Prepare the document

Prepare the document youll use for the four blocker. Think about putting the document on a shared platform so that others can easily view and update the chart and promote teamwork. Using line tools, divide the document into four equal quadrants, and then add text boxes to each section. Consider including the date of the meeting you are creating the four blocker for as a resource and put the name of the project at the top of the document.

2. Explain the project scope

Use Quadrant 1 to review the scope of the project. Make a list with bullets that highlights the most crucial project information and another list that discusses the most crucial delivery deadlines or commitments. You may also mention details about the contractor, such as their background and the date the contract was awarded.

Consider adding graphic elements in the quadrant. You could, for instance, make a timeline that depicts the project’s scope and key dates. Making a line graph that depicts the overall development of the project to this point is another choice.

3. Review the project status

Dedicate Quadrant 2 to discussing the progress of the project. List the major accomplishments of the teams and include information about any significant meetings you had with the stakeholders. Additionally, discussing the budget or potential problems the team might face could be helpful. Think about including background information that might be influencing the project’s progress.

Think about including graphic elements in this quadrant, too. You might, as an illustration, include a graph showing the development of milestones or deliverables. Another choice to think about is categorizing certain tasks according to their health by using different colors, like green, red, and yellow. With this approach, you can use green to denote completed tasks or tasks that are moving along well, yellow to denote tasks that may have potential problems, and red to denote causes for concern.

4. Discuss the opportunities

Include the potential risks and opportunities you may have encountered during the project in Quadrant 3. Inform managers of new risks you’ve discovered and discuss risks you’ve already identified and the effectiveness of your efforts to mitigate them. Similarly, now might be a good time to talk about any other chances you’ve found for success or improvement.

Quadrant 3 is an opportunity to raise your concerns with management. Think about enlisting their assistance in addressing these issues, and be sure to mention what steps you’ve already taken to address them. Share your plans for the following time you intend to review potential project risks to close out this section of the discussion. It might be beneficial to go over your specific review methodologies and any potential issues you foresee.

5. Establish an action plan

Discuss your next course of action in Quadrant 4 to complete your four blocks. List the upcoming key milestones and meetings for the project. Make sure to draw attention to crucial dates, particularly those that pertain to the problems discussed in Quadrant 3 Consider creating a chart to organize this information. You can describe the task or milestone, identify the responsible party, and indicate the deadline in the chart. This could ensure precision and eliminate uncertainty regarding who is in charge of what aspects of the project.

6. Review your 4 blocker

Check the document for accuracy after finishing your four blocks. Make sure to provide the appropriate updates and milestones and to include all the pertinent information you need to discuss in the meeting. It’s crucial to confirm that the document you create supports holding an effective meeting that lasts no longer than an hour. Finalize your four blocker, then distribute it as necessary.

4 Blocker PowerPoint Template | How To Use and Present

How do you present blockers on a project?

The 4 Blocker is a one-page document that provides key information to a stakeholder quickly. This not only gives them a broad understanding of the project but also helps to make sure that the project management team communicates with clients consistently regardless of who is sending the information.

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9-Square (Prioritization Tool)

Last updated by Jeff Hajek on October 19, 2020

The 9-square is a prioritization tool in Lean problem solving that helps you organize your improvement ideas. After completing a brainstorming session in which you compile a large number of viable options, you have to decide which ones to implement. To use the 9-square, rank each problem in two categories: impact and ease of implementation.

Create a 3 x 3 grid, with low, medium, and high impact as the vertical scale. Hard, medium, and easy to implement go on the horizontal scale. Place your options into the appropriate boxes. At this point, there may be little hard information, but you should be able to make an educated guess as to which square each idea should fall into.

The 9-square gives a visual representation of where projects fall relative to each other. I normally code each idea with a letter and write the corresponding letters on the grid—otherwise in a big project the 9-square quickly becomes cluttered. Alternately, I use a large grid on the wall and place sticky notes in the appropriate location. You end up with something like this example.

In some cases, the decision of which idea to try is not perfectly clear. You might have to choose between two similarly valued proposals. For example, would you rather do a medium impact, but easy project (F), or a high impact project that will require medium effort (B)? You will run into a few of these situations, but generally, you’ll end up with the most desirable project being at the top right, and the worst options at the lower left.

In this example, determining the sequence (except for the second and third spot) is a rather easy task. For the ones that are not crystal clear, you can always do a little research, or you can just pick one. The cost of getting the perfect answer might actually outweigh the difference in the benefit between the two choices.

Remember, though, this is a very, very rough prioritization tool. It is based on educated guesses and assumptions, so it should only be used in low-risk or low-cost situation. Don’t choose a new ERP using a 9-square. You can, however, pick between a few locations for a parts rack, or from among several ideas on how to improve phone service in a small call center. When the stakes are higher, you need a tool that is more data driven.

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A Humble Programmer

Conceptual blockbusting - a guide to better ideas.

the programmer’s main problem was not so much technical as psychological: he couldn’t make progress because he was trying to solve the wrong problem. We finally solved his problem by breaking through his conceptual block and solving an easier problem. Conceptual Blockbusting by James L. Adams studies this kind of leap and is generally a pleasant prod towards more creative thinking. Although it was not written with programmers in mind, many of its lessons are particularly appropriate for programming problems. Adams defines conceptual blocks as “metal walls that block the problem-solver from correctly perceiving a problem or conceiving its solution”. - Programming Pearls, by Jon Bentley

texts below are from © Conceptual Blockbusting 4th Edition, by James L. Adams

Chapter One Introduction

We spend little time monitoring our own thinking and comparing it with a more sophisticated ideal.

Thinking form

Conceptual blocks still control us. Much of thinking is quite automatic.

The following puzzle, which originates with Carl Duncker, is taken from The Arc of Creation by Arthur Koestler.

Puzzle: One morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain. A narrow path, no more than a foot or two wide, spiraled around the mountain to a glittering temple at the summit. The monk ascended at varying rates of speed, stopping many times along the way to rest and eat dried fruit he carried with him. He reached the temple shortly before sunset. After several days of fasting and meditation he began his journey back along the same path, starting at sunrise and again walking at variable speeds with many pauses along the way His average speed descending was, of course, greater than his average climbing speed. Prove that there is a spot along the path that the monk will occupy on both trips at precisely the same time of day.

Solutions to Problems That Don’t Exist

Conceptual blocks.

mental walls that blocks the problem-solver from correctly perceiving a problem or conceiving its solutions .

Once again, please do the exercises and problems. The only way you will identify your own conceptual blocks is to try activities that are impeded by their existence.

Chapter Two Perceptual Blocks

Perceptual Blocks are obstacles that prevent the problem-solver from clearly perceiving either the problem itself or the information needed to solve the problem.

One: Detecting What You Expect - Stereotyping

Context is a key element in many memory techniques.

Two: Difficulty in isolating the Problem

Three: tendency to delimit the problem area poorly.

Puzzle : Draw no more than four straight lines(without lifting the pencil from the paper) which cross through all nine dots.

the widespread nature of this block is what makes this puzzle classic.

Four: Inability to See the Problem from Various Viewpoints

Five: saturation, six: failure to utilize all sensory inputs, chapter three emotional blocks, the mystery of emotion, the humanistic psychologists, fear of taking a risk, no appetite for chaos, judging rather than generating ideas, inability or unwillingness to incubate, lack of challenge versus excessive zeal, reality and fantasy, of flow and angst, chapter four cultural and environmental blocks, humor in problem-solving, reason and intuition, left-handed and right-handed thinking, primary and secondary creativity, everybody should be just like me, cyber is better.

Adria Anuzis looked at three aspects of communication, which she called personal(same location, personal interaction), cultural(commonalties of interest, background, and values), cyber(interacting electronically). she found that the most successful professional interaction made use of all three.

the best creative work comes from people who are not only electronically interconnected, but also share cultural values and interact personally in the same physical space.

Tradition and Change

Thinking through blocks, environmental blocks, supportive environments, accepting and incorporating criticism, autocratic bosses, non-support, chapter five intellectual and expressive blocks, choosing your problem-solving language, flexibility in your use of strategies, the computer, importance of correct information, expressive blocks, chapter six alternate thinking languages, visual thinking, other sensory languages, cognitive diversity, the problems of specialization, analysis-synthesis, convergence-divergence, deduction-induction, jung and the myers-briggs test, chapter seven kinds of blockbusters, a questioning attitude, working on the right problem, time and effort focusers, set breakers, using other people’s ideas, crossing disciplines, crossing cultures and changing environments, unconscious blockbusting, other paths for freeing the unconscious, chapter eight groups, the process, affiliation / ego needs, group membership, proper support, chapter nine organizations, control vs. creativity, the pattern of growth, tradition and past success, reward system and support, psychological rewards.

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How to use Toyota’s legendary A3 problem-solving technique

Georgina Guthrie

February 21, 2020

If you came home one day and found your kitchen taps on full-blast and your house full of water, what’s the first thing you’d do? Grab a bucket and start scooping — or turn off the tap?

When it comes to problem-solving, many of us take a rushed, reactionary approach rather than fixing the issue at the source. So in other words, we see the water, panic, and start scooping. If this sounds like something you’ve done recently, then don’t feel too bad: when the pressure’s high, we often jump towards the quickest fix, as opposed to the most effective one.

This is where the A3 technique comes in. It’s a problem-solving approach designed to efficiently address the root cause of issues.

What is the A3 technique?

The A3 technique is a structured way to solve problems. It’s part of the Lean methodology , developed by Toyota back in the mid-’40s. This doesn’t mean you need to implement a Lean way of working to take advantage of this process — it can work as a standalone exercise.

Granted, A3 isn’t an inspiring name, but the story of its origins is actually pretty interesting. Rumour has it that Taiichi Ohno, inventor of the Toyota Production System, refused to read past the first page of any report. In response, his team created A3 address and summarize problem-solving on one side of A3-sized paper. The A3 technique played a huge part in Toyota’s success and all kinds of industries have since adopted it. Here’s how to get started.

How to solve a problem with A3

The first thing to remember is this: A3 is collaborative and relies on good communication. It’s not something you should do by yourself.

There are three main roles involved:

• Owner (that’s you or someone under your charge)

As you’ve probably guessed, these aren’t roles that already exist in your company; you must create them for the purpose of this process. Here’s what they mean.

The owner is responsible for leading the exercise. They are the lynchpin between the two other roles, fostering good communication and keeping documents up to date. It’s tempting to think of the owner as the head of this trio, but that’s not true: everyone is equal here.

The mentor is someone with solid  problem-solving experience. It’s their job to coach the owner and steer them towards finding a solution. It’s not their job to find the answers themselves.

And finally, there are the  responders . This is someone (or a group of people) who have a vested interest in the outcome of the A3 project. Responders might include the client, stakeholders, or managers. A potential problem here is gaining access to them: if you work somewhere with a strict hierarchy — and you’re somewhere near the bottom of that structure — you may face challenges. There’s no easy way around this. Essentially, you need your organization to support this way of working and make it easy for you to access those at the top if needed.

How to create an A3 report

True to its origins, the A3 report is a one-page document. It typically contains 5-7 sections that systematically lead you towards a solution. These are the most commonly used steps, but feel free to modify them.

• Background:  Explain your project in a few sentences, including its context.
• Problem statement:  Explain the current problem. You can use process mapping to see the different tasks that surround the issue. This isn’t essential, but it will make it easier for you to locate the root cause.
• Goals:  Define your desired outcome, and include metrics for measuring success. You won’t know everything until you reach the end, so you may find you need to come back and refine stages 1-3.
• Root cause analysis:  This is a big stage of the process. You need to work out what you think the root problem is. You can use different methods to help you here, including 5 whys or a fault tree analysis .
• Countermeasures:  Once you’ve worked out your root cause, you can start proposing solutions.
• Implementation:  Work out how you’ll implement these solutions, including an action list with clearly defined roles and responsibilities. Project management software is a useful tool here because it can help everyone on the team track each other’s progress in real-time.
• Follow-up:  Using your metrics for success, decide whether the problem was solved. Report your results back to the team/organization. In the spirit of Lean (continuous improvement), you should go back and modify your plan if the results weren’t as expected. And if they were, you should make this process the new standard.

Final thoughts

A3 is an efficient, methodical way to solve problems at their source. When issues rear their head, rising stress can lead people to panic. Having a clearly designed system in place to guide you towards a solution minimizes the chances of people settling for a ‘quick fix’ or failing to act altogether.

Beyond being a guiding light in times of pressure, A3 is a great team-building exercise because it encourages individuals to work together towards a common goal — across all areas of the organization. Combine this with collaborative tools designed to help teams track progress and work together more effectively, and you’ll be unstoppable.

Solve problems like a pro with Root Cause Corrective Action

Lean to Six Sigma: process improvement methodologies explained

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6.8: Blocks to Problem Solving

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• Mehgan Andrade and Neil Walker
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Sometimes, previous experience or familiarity can even make problem solving more difficult. This is the case whenever habitual directions get in the way of finding new directions – an effect called fixation.

Functional Fixedness

Functional fixedness concerns the solution of object-use problems. The basic idea is that when the usual way of using an object is emphasised, it will be far more difficult for a person to use that object in a novel manner. An example for this effect is the candle problem : Imagine you are given a box of matches, some candles and tacks. On the wall of the room there is a cork- board. Your task is to fix the candle to the cork-board in such a way that no wax will drop on the floor when the candle is lit. – Got an idea?

Explanation: The clue is just the following: when people are confronted with a problem

and given certain objects to solve it, it is difficult for them to figure out that they could use them in a different (not so familiar or obvious) way. In this example the box has to be recognized as a support rather than as a container.

A further example is the two-string problem: Knut is left in a room with a chair and a pair of pliers given the task to bind two strings together that are hanging from the ceiling. The problem he faces is that he can never reach both strings at a time because they are just too far away from each other. What can Knut do?

Solution: Knut has to recognize he can use the pliers in a novel function – as weight for a pendulum. He can bind them to one of the strings, push it away, hold the other string and just wait for the first one moving towards him. If necessary, Knut can even climb on the chair, but he is not that small, we suppose…

Mental Fixedness

Functional fixedness as involved in the examples above illustrates a mental set - a person’s tendency to respond to a given task in a manner based on past experience. Because Knut maps an object to a particular function he has difficulties to vary the way of use (pliers as pendulum's weight). One approach to studying fixation was to study wrong-answer verbal insight problems. It was shown that people tend to give rather an incorrect answer when failing to solve a problem than to give no answer at all.

A typical example: People are told that on a lake the area covered by water lilies doubles every 24 hours and that it takes 60 days to cover the whole lake. Then they are asked how many days it takes to cover half the lake. The typical response is '30 days' (whereas 59 days is correct).

These wrong solutions are due to an inaccurate interpretation, hence representation, of the problem. This can happen because of sloppiness (a quick shallow reading of the problemand/or weak monitoring of their efforts made to come to a solution). In this case error feedback should help people to reconsider the problem features, note the inadequacy of their first answer, and find the correct solution. If, however, people are truly fixated on their incorrect representation, being told the answer is wrong does not help. In a study made by P.I. Dallop and R.L. Dominowski in 1992 these two possibilities were contrasted. In approximately one third of the cases error feedback led to right answers, so only approximately one third of the wrong answers were due to inadequate monitoring. [6] Another approach is the study of examples with and without a preceding analogous task. In cases such like the water-jug task analogous thinking indeed leads to a correct solution, but to take a different way might make the case much simpler:

Imagine Knut again, this time he is given three jugs with different capacities and is asked to measure the required amount of water. Of course he is not allowed to use anything despite the jugs and as much water as he likes. In the first case the sizes are 127 litres, 21 litres and 3 litres while 100 litres are desired. In the second case Knut is asked to measure 18 litres from jugs of 39, 15 and three litres size.

In fact participants faced with the 100 litre task first choose a complicate way in order tosolve the second one. Others on the contrary who did not know about that complex task solved the 18 litre case by just adding three litres to 15.

Pitfalls to Problem Solving

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” 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 she just needs 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. 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 where the group of NASA engineers are given the task of overcoming functional fixedness.

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 non-industrialized cultures (German & Barrett, 2005).

Common obstacles to solving problems

The example also illustrates two common problems that sometimes happen during problem solving. One of these is functional fixedness : a tendency to regard the functions of objects and ideas as fixed (German & Barrett, 2005). Over time, we get so used to one particular purpose for an object that we overlook other uses. We may think of a dictionary, for example, as necessarily something to verify spellings and definitions, but it also can function as a gift, a doorstop, or a footstool. For students working on the nine-dot matrix described in the last section, the notion of “drawing” a line was also initially fixed; they assumed it to be connecting dots but not extending lines beyond the dots. Functional fixedness sometimes is also called response set , the tendency for a person to frame or think about each problem in a series in the same way as the previous problem, even when doing so is not appropriate to later problems. In the example of the nine-dot matrix described above, students often tried one solution after another, but each solution was constrained by a set response not to extend any line beyond the matrix.

Functional fixedness and the response set are obstacles in problem representation , the way that a person understands and organizes information provided in a problem. If information is misunderstood or used inappropriately, then mistakes are likely—if indeed the problem can be solved at all. With the nine-dot matrix problem, for example, construing the instruction to draw four lines as meaning “draw four lines entirely within the matrix” means that the problem simply could not be solved. For another, consider this problem: “The number of water lilies on a lake doubles each day. Each water lily covers exactly one square foot. If it takes 100 days for the lilies to cover the lake exactly, how many days does it take for the lilies to cover exactly half of the lake?” If you think that the size of the lilies affects the solution to this problem, you have not represented the problem correctly. Information about lily size is not relevant to the solution, and only serves to distract from the truly crucial information, the fact that the lilies double their coverage each day. (The answer, incidentally, is that the lake is half covered in 99 days; can you think why?)

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11.8: Base Four Blocks

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Longs (4L), Flats (4F) and Blocks (4B)

This page contains a set of Base Four blocks.Use the unit blocks from Material Card 4 with this set of Base Blocks. Cut along all solid line segments. Each piece is labeled. A Base Four Long is 1 cm by 4 cm and is labeled "4L". A Base Four Flat is 4 cm by 4 cm and is labeled"4F". The Base Four Block is 4 cm by 4 cm by 4 cm and is labeled "4B". Fold this 3-dimensional block along the dark dotted lines; then tape to make a cube.