Spreadsheet Software as a Teaching Tool
for Introductory Mathematics Courses
Shuzo Takahashi
Arizona Winter School 2002
March 10, 2002
Abstract
I will talk about one way to use spreadsheets
(Excel) in teaching mathematics, in particular,
in teaching elementary probability theory to
business majors. Other applications (i.e., calculus)
will be briefly discussed.
Outline of Talk
 Overview of the Business Mathematics course
 The loan workout project and
its solution using Excel
 A fun approach to teaching expected value and a
graphical illustration of the meaning of expected
value using Excel.
 Possible use of Excel in teaching calculus
The Business Mathematics Course
at the University of Arizona
This course was developed jointly by
Professor Richard Thompson
Department of Mathematics
and
Professor Chris Lamoureux
Department of Finance
Business Mathematics
Business Mathematics is the foundation for students’
future career in business, showing them how to apply
the language of mathematics to business problems, and
how to use computers to do mathematics.
Business Mathematics
Business Mathematics centers around significant
business problems and the tools, both mathematical
and computer based, that are needed for their
solutions.
 Projects are the loan workout project, the stock
option pricing project, etc.
 Mathematical tools are elementary probability
theory, calculus, etc.
 Computer tools are Excel, PowerPoint, etc.
Business Mathematics
 Using the new tools, students work in teams to
complete projects and report their solutions
both orally and in written form.
 Student presentations will be given in the
current business style, using PowerPoint and
Excel.
Business Mathematics
All course material is in PowerPoint, Excel, Word,
and Media files.
Usefulness of Computer Text

Hyperlinks allow you to move easily between mathematical
instruction and computer calculation, graphing, and
simulations.

Computer animations clarify mathematical concepts.

Electronic searching can locate any given word or phrase.

You can customize your computer text by adding notes,
extra pages, or additional files.
Business Mathematics
Course Web Site
http://business.math.arizona.edu
Business Mathematics
Loan Workout Project
 You are loan officers of Acadia Bank.
 Acadia Bank has a commercial loan with a full
value of $4,000,000 outstanding to John
Sanders’ entrepreneurial venture.
 His business is not going well and he is not able
to pay interest on his loan.
 What are you going to do as loan officers?
Loan Workout Project
Acadia has to decide whether to foreclose on
the loan or to work out a new schedule of
payments.
 If Acadia forecloses on John’s loan, it will only
recover a foreclosure value of $2,100,000.
 If Acadia attempts a workout, and John's
venture succeeds, then the bank will be repaid
the full value of $4,000,000.
 If Acadia attempts a workout, and John's
venture fails, then the bank will only recover a
default value of $250,000.
Decision
How do you decide which one to choose?
 Foreclosure
 Workout
Expected Value
E(W) = Full Value  Pr(S) + Default Value  Pr(F)
 E(W) = Expected Value of Workout
 Pr(S) = The probability of success
 Pr(F) = The probability of failure
How to Calculate
Pr(S) and Pr(F)
 Historical data on past borrowers
 Certain information about John Sanders
 Current economic conditions
 Conditional Probability and Bayes’ Theorem
A Decision Method
 Compare Expected Value and Foreclosure Value.
 If Expected Value < Foreclosure Value,
then choose “Foreclosure.”
 If Expected Value > Foreclosure Value,
then choose “Workout.”
Solution
Questions
 What is the actual meaning of expected value?
 Is our decision method sound?
Issue
 Students tend to focus on their individual case.
 They are not able to recognize that the bank’s
profit is based on many similar loans as a whole.
A Fun Approach to Teaching
Expected Value
One lecture I gave in class.
Let's play!
Who wants to be a millionaire?
Game Situation
You have won $64,000 and are facing a tough
$125,000 question.
This means that you will receive $125,000 if you
answer the question correctly. But you will receive
only $32,000 if your answer is wrong. Also, you can
walk away with $64,000 if you decide not to answer
the question.
What would be the best strategy to take?
$125,000 Question
Which city is the birthplace of the famous
business math instructor Shuzo?
A. Wakayama
C. Kumayama
B. Iiyama
D. Matsuyama
$125,000 Question
Which city is the birthplace of the famous
business math instructor Shuzo?
A. Wakayama
C. Kumayama
B. Iiyama
D. Matsuyama
 Suppose that you decide to answer the question.
What is the expected value of the outcome?
 Do you answer the question or do you walk
away with $64,000?
$125,000 Question
Which city is the birthplace of the famous
business math instructor Shuzo?
A. Wakayama
C. Kumayama
B. Iiyama
D. Matsuyama
Expected Value
125,000  1/4 + 32,000  3/4 = 55,250
Walk Away
64,000
$125,000 Question
50:50
Which city is the birthplace of the famous
business math instructor Shuzo?
A. Wakayama
C. Kumayama
B. Iiyama
D. Matsuyama
Two Choices
B. Iiyama
C. Kumayama
Two Choices
B. Iiyama
C. Kumayama
 Suppose that you decide to answer the question.
What is the expected value of the outcome?
 Do you answer the question or do you walk away
with $64,000?
Two Choices
B. Iiyama
C. Kumayama
Expected Value
125,000  1/2 + 32,000  1/2 = 78,500
Walk Away
64,000
Does Teamwork Help?
Suppose all of you will have a turn playing the game.
You got together and agreed that you will divide the
total winnings equally. (We are assuming that each of
you is facing exactly the same situation described
above.)
Now think about what the best strategy is.
Should everyone walk away? In this case, everyone
gets $64,000. Or should everyone answer the question?
Game Simulation
Team Discussion
Now think about how this can be applied
to your project.
Project Simulation
Some Uses of Excel in
Teaching Calculus
 Graphing
Graphing
 Midpoint Sums
Sums
 Numerical Integration
Integration
 Slopes and Derivatives
Slopes