Principles of Problem Solving

PPS-12: Problem Solving Workshop

(Adapted from MPS 4, 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. Establish your Baseline on this skill on the Problem Solvers Feedback Form (page 5).
  3. Be able to Name the Six Steps, and describe what is done in each step

 

What is It?

This is a practice session for the Six Step Method.  You will use the Whimbey Pair technique from PPS-10 Awareness to practice the method and to get feedback on how you are doing.

 

New Concepts (from PPS-11)

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 PPS-11.

 

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?

 

How to Do It

We use the same Whimbey pair method from PPS-10.  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 Reading, Defining, and Exploring the problem.  Second, experts tend to monitor their progress relatively frequently (about once a minute). 

 

Monitoring includes

  • Assessing the benefit to be gained from an activity or calculation before doing it - If I calculate___, will that get me closer to a solution?  How will the answer to this question help me?
  • Assessing your location in the process - Is the problem defined?  Am I ready to move on?;  Where do I go from here?
  • Learning from errors If you find you have screwed up or have reached an impossible answer, you ask “What did I learn from that?”
  • Checking your work – Do the units work?; Did I include all the information?; Is this reasonable?

 

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

  • Assemble the Problem Statement, the Strategy Board (page 6), and a Marker (coin, eraser,…)
  • Read the Problem Statement aloud
  • Describe aloud your thoughts as you solve the problem
  • Move the Marker on the Strategy Board to indicate where you think you are in the problem solving process (You do not need to proceed linearly through the steps)
  • Try to use monitoring statements
    • I think I’m finished with that step.
    • How does this help?
    • What am I doing?
    • Are all the bases covered?

 

The Listener should

  • Not contribute to the solution
  • Make encouraging noises (ok, I see, umh hm, …)
  • Ask process questions (Have you finished that step?, Are you sure?)
  • Mark on the Strategy Feedback Form (page4) to indicate
    • Time spent in each stage
    • Use of monitoring statements

 

 

In-Class Exercise

Work on Problem 1

When told to begin:

  • Form Pairs (different than the last time)
  • First problem solver has last name later in the alphabet
  • Problem solver selects problem from the following list and tries to solve it
  • Listener plays there role as described above

At end of allotted time:

  • Stop problem solution, even if you are not finished
  • Problem Solver and Listener review the Strategy Feedback Form
  • Problem Solver evaluates self  on Problem Solver Feedback Form (p.3)
  • Listener evaluates Problem Solver (marks their own initials) on the same form.

 

 

Work on Problem 2

When told to begin:

  • Switch roles of problem solver and listener
  • Problem solver selects new problem from the following list and tries to solve it
  • Listener plays there role as described above

At end of allotted time:

  • Stop problem solution, even if you are not finished
  • Problem Solver and Listener review the Strategy Feedback Form
  • Problem Solver evaluates self on chart portion of the Problem Solver Feedback Form (p.3)
  • Listener evaluates Problem Solver on the same form.

 

Reflect

  • Each individual fills out the Chart and Reflection portion of the Problem Solver Feedback Form on Page 5.

 

Problem Solvers Feedback Form (short version)

 

Novices (less successful)

Beginner

(Need lots

more practice)

 

(1-2)

Good Start

(some progress, but could do better)

(3-4)

Getting There

 

 

 

(5-6)

Almost There

(just a little more practice)

(7-8)

Expert

 

 

 

 

(9-10)

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

·         x-axis 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

·         x-axis 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)

 

(1-2)

Good Start

(some progress, but could do better)

(3-4)

Getting There

 

 

 

(5-6)

Almost There

(just a little more practice)

(7-8)

Expert

 

 

 

 

(9-10)

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)