Spreadsheet Software as a Teaching Tool for Introductory Mathematics Courses

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Spreadsheet Software as a Teaching Tool for
Introductory Mathematics Courses
Shuzo Takahashi Arizona Winter School
2002 March 10, 2002
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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.
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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

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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
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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.
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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.

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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.

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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.

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Business Mathematics
Course Web Site http//business.math.arizona.edu
Business Mathematics
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Loan Workout Project

• You are loan officers of Acadia Bank.
• Acadia Bank has a commercial loan with a
  fullvalue 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?

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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 Johns 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.

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Decision
How do you decide which one to choose?

• Foreclosure
• Workout

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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

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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

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A Decision Method

• Compare Expected Value and Foreclosure Value.
• If Expected Value lt Foreclosure Value, then
  choose Foreclosure.
• If Expected Value gt Foreclosure Value,then
  choose Workout.

Solution
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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 banks
  profit is based on many similar loans as a whole.

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A Fun Approach to Teaching Expected Value
One lecture I gave in class.
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Let's play!
Who wants to be a millionaire?
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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?
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125,000 Question
Which city is the birthplace of the famous
business math instructor Shuzo?
A. Wakayama B. Iiyama C. Kumayama D. Matsuyama
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125,000 Question
Which city is the birthplace of the famous
business math instructor Shuzo?
A. Wakayama B. Iiyama C. Kumayama 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?

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125,000 Question
Which city is the birthplace of the famous
business math instructor Shuzo?
A. Wakayama B. Iiyama C. Kumayama D. Matsuyama
Expected Value 125,000 ? 1/4 32,000 ? 3/4
55,250 Walk Away 64,000
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125,000 Question
5050
Which city is the birthplace of the famous
business math instructor Shuzo?
A. Wakayama B. Iiyama C. Kumayama D. Matsuyama
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Two Choices
B. Iiyama C. Kumayama
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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?

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Two Choices
B. Iiyama C. Kumayama
Expected Value 125,000 ? 1/2 32,000 ? 1/2
78,500 Walk Away 64,000
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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
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Team Discussion
Now think about how this can be applied to your
project.
Project Simulation
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Some Uses of Excel in Teaching Calculus

• Graphing
• Midpoint Sums
• Numerical Integration
• Slopes and Derivatives

Graphing
Sums
Integration
Slopes