**Principles of Problem Solving**

**PPS-10 Awareness**

(Adapted
from MPS1 Don Woods 2003)

**Pre-class assignment**

- Read sections
**What is It?**,**Why Do It?**,**New Concepts**,**How to Do It**, and**Learning Objectives** - 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.

**1 ^{st} 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:

**2 ^{nd} 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.

**1 ^{st} 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

**2 ^{nd} 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

Which
ACME salesmen were in

Which
ones were in

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