Principles of Problem Solving

PPS-10  Awareness

(Adapted from MPS1 Don Woods 2003)

 

Pre-class assignment

  1. Read sections What is It?, Why Do It?, New Concepts, How to  Do It, and Learning Objectives
  2. Be able to describe the roles of Problem Solver and Listener when called on

 

What is it?

Awareness is the ability to describe your thought processes as you solve problems.

 

New Concepts

Awareness, Whimbey Pairs

 

Why Do It?

A good problem solver is aware of how their thoughts relate to the problem, recognize when they have hit a dead end, and have strategies for getting back on track.

 

Looking at what is going on in your head is called “Awareness”.  You will be learning a method that has been shown to help people be better problem solvers.

 

Thinking is a skill, like playing golf.  People who want to get better at golf sometimes watch their swing on video.  Analysis of the video can help them see what is going well and what is going poorly.  This exercise can be viewed videotaping your thought processes.  And like the video of your golf swing, viewing your thought processes  may not be pretty, but it should be useful.

 

How to Do It

The technique to do this (called TAPPS Whimbey pair) is to

  • Form into pairs
  • One person is the problem solver
  • One person is the listener

 

The Problem Solver

  • Gathers the needed tools (chair, table, pencil, paper, calculator …)
  • Reads the problem aloud
  • Tries to solve the problem while continually describing that internal process aloud
  • Avoid long silences, don’t worry as much about the quality of your words, just keep describing
  • Write things down, short term memory is a limited buffer.

 

The Listener

The listener is there to LISTEN, to encourage and keep the problem solver talking, not to solve the problem.  Thus, you will

  • Make encouraging noises (yes, go on, umhhhm)
  • Ask for clarification (I’m not sure I understand, could you go through that again)
  • Encourage accuracy (Are you sure, can you check that)

 

 

 

Learning Objectives and Assessment

1    Given an exercise, you will be able to verbally describe the mental processes you are using to solve the exercise such that there will be fewer than two silent periods of more than 10 s duration.

2    Given that you are the listener in the TAPPS Whimbey pair method, the feedback from the listener will be that you were within two scale ratings of “about what I wanted” on both the degree of interaction and the tone of the interaction.

3    Given that you are the problem solver in the TAPPS Whimbey pair method, the feedback from the listener will be that you are within two scale ratings of being active, methodical and careful and that you check and double check as you describe the process.

 

In-Class

Task 1

When told to begin:

·         Form Pairs

·         The 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 the role described above (How to Do It)

At end of allotted time:

·         Stop problem solution, even if you are not finished

·         Problem Solver evaluates self on their own Problem Solver Feedback Form (marks appropriate number with initials; writes comments)

·         Listener evaluates self on their own Listener Feedback Form

·         Listener evaluates problem solver on Problem Solver’s Awareness Evidence Form

·         Problem solver evaluates Listener on Listener’s Listener Feedback Form

 

Task 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 the role described above (How to Do It)

At end of allotted time

·         Stop problem solution, even if you are not finished

·         Problem Solver evaluates self on their own Problem Solver Feedback Form (marks appropriate number with initials; writes comments)

·         Listener evaluates self on own Listener Feedback Form

·         Listener evaluates problem solver on Problem Solver’s Awareness Evidence Form

·         Problem solver evaluates Listener on Listener’s Listener Feedback Form

 

Reflect

  • Each individual fills out the Personal Reflection form

 

Task 3

Repeat Tasks 1 and 2  with technical problem and

  • Problem Solver should focus on accuracy, not time.
  • Listener should be prompting with “Are you sure” comments.

PPS-10

Assignment 1

Submit a memo that assesses your progress from this exercise.  Assess with respect to the learning objectives.  You must submit evidence that supports your assessment (this can be attached to the memo).

 

Evidence may include the following:

  • Marked up problem
  • Scratch paper with problem solution notations
  • Awareness evidence form
  • Feedback listener form
  • Written work done in other classes

 

 

Memo Format:

 

MEMO

 

Date:   mm/dd/yy

To:      Course Instructor

From:  Student

Re:      Personal Assessment – MPS1

 

With respect to Learning Objective 1, the attached ____ Form shows that I have ….

 

With respect to Learning Objective 2, I am able to ….  Evidence for this includes attached example from Math xyz and ___ Form in which three examples of …. are shown.


Problem Solver Feedback Form

Both the Problem Solver, PS, and the Listener will fill in this form. 

 

Each will write their initials near the number that best represents their assessment.

 

Comments can be made by either person.

 

 

1st Problem

Problem Solver: ________________             Listener:___________________

 

1. Number of silent periods longer than ten seconds

5                      4                      3                      2                      1                      0

 

2. PS was focused on accuracy

No check of                                   Some checking                       All assumptions and

answers                                                                                        answers checked

5                         4                         3                            2                         1

 

3. The PS was “active” in writing/charting

No written                                      Some marking                                    Significant use of

notes                                             notes, pictures                                    notes, tables, pictures

5                         4                         3                            2                         1

 

Comments:

 

 

 

2nd Problem

Problem Solver: ________________             Listener:___________________

 

1. Number of silent periods longer than ten seconds

5                      4                      3                      2                      1                      0

 

2. PS was focused on accuracy

No check of                                   Some checking                       All assumptions and

answers                                                                                        answers checked

5                         4                         3                            2                         1

 

3. The PS was “active” in writing/charting

No written                                      Some marking                                    Significant use of

notes                                             notes, pictures                                    notes, tables, pictures

5                         4                         3                            2                         1

 

Comments:

 

 

 


Awareness Feedback Form

 

Problem solving style

During this experience, you observed someone else solving problems and you became aware of what you did when you solved problems. Here are some characteristics that may be observed. Without consultation with your partner, characterize yourself by putting your initials on the following scales. Then swap Forms and characterize your partner.  The numbers are just a scale, 10 is not best, nor is 1.

 

Initial response is:

0       1          2          3          4          5          6          7          8          9         10       

OK, let’s get at this                                                  Oh, it’s one of those problems

Can’t I try another one?

Emphasis is on:

0       1          2          3          4          5          6          7          8          9         10       

Speed                                                                                                           Accuracy

 

You:

0       1          2          3          4          5          6          7          8          9         10       

Work quickly through                                                           Check and double check

 the problem, sometimes                                                     so it takes a long time to

assuming previous ideas are OK                                        complete the problem

 

You:

0       1          2          3          4          5          6          7          8          9         10       

Maintain a holistic view.                                                       Quickly identify parts and

solve the whole problem,                                                     break into parts

do not consider subproblems                                              tackle these one at a time

 

When stuck you:

0       1          2          3          4          5          6          7          8          9         10       

Go back and check things                                                   Make a good guess

Through again and continue

 

You do your thinking:

0          1          2          3          4          5          6          7          8          9         10       

In your head                                                                            With pencil and paper

 

 


PPS-10 Feedback for the Listener Form:

Both the Problem Solver, PS, and the Listener will fill in this form. 

 

Each will write their initials near the number that best represents their assessment.

 

1st Problem

Problem Solver: ____________         Listener:_____________

 

1. The listener

      Was Silent                                                Kept the                                      Talked too much

      No Feedback                                 PS Talking                                   Distracted PS

5                         4                         3                            2                         1

 

2. The listener’s asked the PS to check

      Never                                             Sometimes                                Too often

                                                            About right                                  

5                         4                         3                            2                         1

 

3.. The listener’s emphasis was on:

      Listening                                        Helping PS                              Solving the Problem

                                                            Verbalize and Check                              

5                         4                         3                            2                         1

 

2nd Problem

Problem Solver: ____________         Listener:_____________

 

1. The listener

      Was Silent                                                Kept the                                      Talked too much

      No Feedback                                 PS Talking                                   Distracted PS

5                         4                         3                            2                         1

 

2. The listener’s asked the PS to check

      Never                                             Sometimes                                Too often

                                                            About right                                  

5                         4                         3                            2                         1

 

3.. The listener’s emphasis was on:

      Listening                                        Helping PS                              Solving the Problem

                                                            Verbalize and Check                              

5                         4                         3                            2                         1


PPS 10 Awareness – Activities

1. In a different language, luk eir lail means “heavy little package”, bo lail means “heavy man” and luk jo means “pretty package”. How would you say little man in this language?

2. Salesmen who work for the ACME Wig Company are assigned to a different city each year. Henry began working for ACME in New York in 1965, and in the succeeding 4 years worked in Minneapolis, New Haven, Youngstown and Charleston in that order. Peter worked for ACME in New Haven in 1963 and in succeeding years worked in New York, Charleston, Minneapolis, and Youngstown. Fred worked for ACME in Charleston in 1967. The previous two years he worked first in New Haven and then in Minneapolis. John worked in Charleston in 1968. Before that he worked in New Haven, before that Youngstown and before that in New York.

Which ACME salesmen were in New Haven in 1967?

Which ones were in Minneapolis in 1966?

3. On a certain day, I ate lunch at Tommy’s, took out two books from the library (The Sea Wolf and Martin Eden, both by Jack London), visited a museum and had a cavity filled. Tommy’s is closed on Wednesday, the library is closed on weekends, the museum is only open Monday, Wednesday and Friday and my dentist has office hours Tuesday, Friday and Saturday. On which day of the week did I do all of these things?

4. Sally loaned $7 to Betty, but borrowed $15 from Estella and $32 from Joan. Moreover, Joan owes $3 to Estella and $7 to Betty. One day the girls got together at Betty’s house to straighten out their accounts.  Which girl left with $18 more than she came in with?

5. The number of cows owned by Farmer Smith is the number owned by Farmer Thompson divided by the number owned by Farmer Jones. Farmer Thompson, who owns 42 cows, would own 8 times as many cows as Farmer Jones if he owned 14 more cows. How many cows does Farmer Smith own?

1-5 reprinted courtesy of A. Whimbey and J. Lochhead.

6. Two skaters of equal weight are facing each other on a frozen pond. The ice is very smooth and practically frictionless. Neither skater is allowed to dig in his/her skates. Skater A is stronger than skater B. A pushes B. Describe what you think will happen.

a) they will move away from each other with equal velocity.

b) A will move forward and B will move backward. B really moves backwards very fast because B is weaker.

c) A will go backwards and B will go backwards but A won’t go as fast as B because the force of A’s push is greater than B’s. Indeed, A pushed B, B didn’t push A.

7. The value of gc in the American Engineering System is:

a) 32.2

b) 32.2 ft lb/lb s2

c) 32.2 ft lbf/lbm s2

d) 32.2 ft lbm/lbf s2

e) 32.2 ft/s2

f) depends on the location (for example the moon)

g) other

 

Problem Solving involves more than being able to do exercises at the end of the chapter.  You may be the master of all of those exercises and still not be very good at solving a typical problem on the factory floor.  Suppose you are stamping oil pans and the corners start tearing out.  You have the responsibility to fix the problem and probably don’t have the time to do Finite Element Analysis.  You need a strategy that doesn’t get honed in problems courses like statics and mechanics of materials.

 

This approach allows you to better deal with ambiguity and with problems that you haven’t encountered before.  One of the first steps is to look at what is currently happening in your head (and other people’s heads) while solving problems.  If you know the steps that you go through, you can troubleshoot your own problems of getting stuck.

 

RHPS 1 – Skills to Develop

1.                                                                                                                                                                                      Develop the ability to talk about your thought process

2.                                                                                                                                                                                      Shift to a focus on accuracy instead of on time.

3.                                                                                                                                                                                      Unburden your mind by writing things down.

4.                                                                                                                                                                                      Recognize that others solve problems differently than you do.

5.                                                                                                                                                                                      Acquire some skills at listening.

6.                                                                                                                                                                                      Acquire some skills at self assessment.

7.                                                                                                                                                                                      Acquire some skill at giving and receiving feedback.

8.                                                                                                                                                                                      Begin to realize that assessment is based on evidence

9.                                                                                                                                                                                      Begin to develop an environment of trust where risking is OK.

 

Pretest

Awareness:

How aware are you of what you do when you solve problems?

On a scale of 1-10, where

1 is Unaware, I just do it, 4 is Aware of some and 10 is Very aware: I can describe the details of how I do it.

Skill:

How skilled are you in doing this activity? On a scale of 1-10, where

1 is poor, 3 is fair, 5 is good, 7 is very good and 10 is excellent?

 

Write any comments that you might have prior to doing the unit in your journal.