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