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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 MathematicsBusiness 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
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.
All course material is in PowerPoint, Excel, Word, and Media files.
Usefulness of Computer Text
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?
Loan Workout Project
Loan Workout ProjectAcadia 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.
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.
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?
Game Situation
$125,000 QuestionWhich city is the birthplace of the famous business math instructor Shuzo?
A. Wakayama B. IiyamaC. 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?
$125,000 QuestionWhich city is the birthplace of the famous business math instructor Shuzo?
A. Wakayama B. IiyamaC. Kumayama D. Matsuyama
Expected Value 125,000 1/4 + 32,000 3/4 = 55,250
Walk Away64,000
$125,000 QuestionWhich city is the birthplace of the famous business math instructor Shuzo?
A. Wakayama B. IiyamaC. Kumayama D. Matsuyama
50:50$125,000 Question
Which city is the birthplace of the famous business math instructor Shuzo?
A. Wakayama B. IiyamaC. Kumayama D. Matsuyama
B. IiyamaC. Kumayama
Two Choices
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?
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
Does Teamwork Help?