Principles of Problem
Solving
PPS12: Problem
Solving Workshop
(Adapted
from MPS 4,
Preclass assignment
What is It?
This is a practice session for the
Six Step Method. You will use the
Whimbey Pair technique from PPS10 Awareness to practice the method and to get
feedback on how you are doing.
New Concepts (from
PPS11)
Engage,
Explore, Define, Plan, Solve, Look Back.
Why Do It?
You can’t
master a skill unless you practice.
Feedback helps make sure you are practicing good techniques.
You are trying
to transition from the techniques of less successful problem solvers to the
techniques of more successful problem solvers.
You can review those techniques in this chart from PPS11.
Novices (less successful) 
Experts (more successful) 
Spend
little time reading the problem 
Spend 23
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? 
How to Do It
We use the
same Whimbey pair method from PPS10.
You will need to work in pairs with one problem solver and one listener
We will
emphasize two important techniques of the experts. First, experts tend to spend a lot of time
Monitoring
includes
The
Listener will use a Strategy Feedback Form to keep track of how long the
problem solver is spending in each stage of the problem solving process. The Listener will also indicate each
monitoring statement on the Feedback Form.
The Problem Solver should
The Listener should
InClass Exercise
Work on Problem 1
When told to begin:
At end of allotted time:
Work on Problem 2
When told to begin:
At end of allotted time:
Reflect
Problem Solvers Feedback Form (short
version)
Novices (less successful) 
Beginner (Need lots more practice) (12) 
Good Start (some progress, but could do
better) (34) 
Getting There (56) 
Almost There (just a
little more practice) (78) 
Expert (910) 
Experts (more successful) 
Spend
little time reading the problem 





Spend a
long time reading the problem 
Start
solution stage right away 





Spend up
to half the time defining the problem 
Don’t
think about thinking 





Monitor
thought processes regularly (1/min) 
Strategy Feedback Form
Problem Solver__________________ Listener _______________________
1.
Listener
should mark a continuous squiggly line from left to right to indicate the of
time spent in each step
·
xaxis
is time
·
time
zero is when the problem solver begins to read the problem)
2.
Mark
the occurrence of monitoring statements with a ▼.

Six Steps 






Three steps of “Define” 
Read 






Define the Stated Problem 







Explore 







Plan 
Plan 






Implement 
Do It 






Evaluate 
Look Back 






0
min 2 min 4 6 8 10 12
Problem Solver__________________ Listener _______________________
3.
Listener
should mark a continuous squiggly line from left to right to indicate the of
time spent in each step
·
xaxis
is time
·
time
zero is when the problem solver begins to read the problem)
4.
Mark
the occurrence of monitoring statements with a ▼.

Six Steps 






Three steps of “Define” 
Read 






Define the Stated Problem 







Explore 







Plan 
Plan 






Implement 
Do It 






Evaluate 
Look Back 






0
min 2 min 4 6 8 10 12
Problem Solvers Feedback Form
Novices (less successful) 
Beginner (Need lots more practice) (12) 
Good Start (some progress, but could do
better) (34) 
Getting There (56) 
Almost There (just a
little more practice) (78) 
Expert (910) 
Experts (more successful) 
Spend
little time reading the problem 





Spend a
long time reading the problem 
Start
solution stage right away 





Spend up
to half the time defining the problem 
Don’t
think about thinking 





Monitor
thought processes regularly (1/min) 
Reflection of the Problem Solver
What did I
learn from this?
Which of
the skills do I do pretty well? (List
Evidence)
Which skills could use some work?
(List Evidence)