Principles of Problem Solving

PPS-11: Problem Solving – Six Step Method

(Adapted from MPS 2, Don Woods 2003)

Pre-class assignment

1. Read sections What is It?, Why Do It?, New Concepts, How to  Do It, and Skills to Develop
2. Be able to Name the Six Steps, and describe what is done in each step

What is It?

The Six Step Method for Problem Solving is a formal set of steps that help the problem solver stay focused and organized.  These steps were developed by Donald Woods at McMaster University for the McMaster Problem Solving Program.  That was adapted from the four step approach of Polya (Define, Plan, Solve, Look Back).

New Concepts

Engage, Explore, Define, Plan, Solve, Look Back.

Why Do It?

When researchers compare novice and expert problem solvers, a number of striking differences are seen (Woods MPS 4).

 Novices (less successful) Experts (more successful) Spend little time reading the problem Spend 2-3 times as long reading the problem Start solution stage right away or fix on one idea and run with it Spend up to half the time understanding and defining the problem, remain open to alternate paths Go straight to equations and numbers Draw pictures and sketches to help describe the problem Memorize Equations Learn fundamentals Hunt for an equation that uses up the givens Focus on an organized strategy based on principles Don’t think about thinking Monitor their thought processes regularly to see if they are on track, etc. Don’t assess potential of approach, jumps from idea to idea. Ask What will this calculation tell me?, How will the answer to this be useful? Abandon ideas without reflection Hits blind alleys and asks What did I learn?

Application of the six step approach through a number of units of instruction has been shown to improve problem solving skills of students at McMaster University.  Perhaps more impressive is that McMaster alumni identify the McMaster Problem solving program as among the most useful things they learned in engineering school.

How to Do It

In this unit, we define the Six Steps.  In later units, we will practice all or parts of the stages.  The Six Steps are

1. Engage
2. Define Stated Problem
3. Explore
4. Plan a Solution
5. Do it
6. Evaluate

While this appears to be a linear process, it is not.  You can expect to go back from time to time as you hit blind alleys.  You may also cycle through the steps multiple times as you solve.

Consider a skier

You have just gotten off the ski lift and are standing at the top of a slope that is looking pretty darn steep.  You begin to wonder what you are doing here and if you are going to make it down in one piece.  You know that if you are tentative, you’ll crash.

This is the point at which you take some deep breaths, and say to yourself, “Calm down, I can do this.  What do I remember about skiing?  What did the instructor say this morning?  O.K., I can get to the bottom in one piece if I just need to keep my hands forward to get my weight right, shift weight to turn, and turn a lot to keep my speed down.  If I start to lose it, fall uphill.  If I just do what I learned, I can do this.  It might even be fun, as well as terrifying.”

1) Engage: I want to and I can

Without confidence and desire at the beginning, the skier is likely to get hurt (see picture).  Similarly, a good problem solver starts by reducing stress and developing a positive attitude.

In this first stage of problem solving, we:

• Manage our stress (deep breathing, positive self talk)
• Maintain our confidence and motivation
• Be willing to risk
• Monitor our thoughts

2) Define the Stated Problem

For the skier, getting to the bottom of the hill in one piece is the problem.  For most engineering problems encountered in school, you will have to read some text and extract the important information – the problem, the knowns, and the constraints before you can begin.  For other problems, you may need to parse your boss’s words or dignose the problem on your own.

In this stage we:

• Systematically classify information
• Recognize that some information may be inferred rather than explicit
• Organize the information in a way that will be useful
• Be thorough in reviewing the problem statement
• Extract the words relevant to the problem
• Begin to translate the words into symbols and pictures

3) Explore: Create an Internal Idea of the problem

In this stage you poke through all those boxes of knowledge that you have stashed in the attic of your brain.  You thought you wouldn’t need that stuff once the course was over, but here it comes again.

Here the skier racks their brain to recall everything they know that will help them survive the trip.  You are considering everything you know about problems like this one and problems in general.  You are trying to stay focused on principles and fundamentals rather than equations.  You may ask “what if?” questions.

In this stage we:

• Continue to translate information into pictures and symbols
• Review resources – brain, book, Web, people
• Learn new stuff
• Apply rules of thumb
• Be creative/brainstorm
• Be willing to try and willing to be wrong

4) Plan a Solution

Now you need to decide.  Select an approach that is most likely to get you to the goal.  This is the point where the skier listed the important techniques.

Here we:

• Commit to a decision
• Outline a plan
• Resist using a calculator

5) Do It: Carry out the Plan

Now is the time to be the stereotypical engineer with that single-minded focus and attention to detail.  Keep track of your units, your conversions, and your notation because those things will save your engineering soul.  Keep monitoring the process - Is this reasonable, consistent, and logical?  The skier is now in motion, internally monitoring and correcting position and balance.

Now it is time to:

• Be organized and systematic
• Be detail oriented (AR)
• Check as you go

6) Evaluate:  Check and Look Back

At the bottom of the hill, you may be patting yourself on the back or kicking yourself in the butt.  If you try to do both, let me know; I want to watch.  At the end of a problem solution, you should also look back.  Certainly you are checking your work, but you are also mentally listing any lessons learned.  Reviewing what you did helps you anchor that knowledge so you will gain experience over time and not just get old.

In this stage:

• Overview your work. – Is it understandable, reasonable, consistent?
• Consider the big picture – Did you solve the problem?; How does this fit into other things you’ve done?; What other problems would be amenable to this solution.

Problems vs. Exercises

Note that many of the end-of-the-chapter problems that you do in engineering school are better described as exercises than problems.  In these exercises, the author of the book has given you a clearly defined situation to illustrate a topic, and you are mostly practicing the plan and solution for that topic.  Doing these exercises is more like free throw practice; you sharpen a particular skill, but don’t necessarily learn to solve problems on the basketball court.

Likewise, “problem solving” in textbooks is often about practicing particular techniques.  Good textbook “problem solvers” learn to recognize which class of problems an example falls into, and select a plan and solution from a palette of choices.  This is not a bad thing.  As people become more experienced with different classes of problems, more of them look like straightforward exercises.  This is why professors seem to be so quick at solving problems in their area, while at the same time you may feel completely lost.

The Six Step Method is intended to address the issue of being completely lost.  Because it is a more general technique, it can help you organize your thoughts and the information in the problem to get moving in useful directions.  It will be more useful as time goes on, because many of the problems you will face on the job are very difficult to recognize as textbook problems.