Using a computer for math Graham Seibert Copyright 2006 This is a segment of the draft version of a large syllabus. I need your feedback to improve it

Using a computer for mathUsing a computer for math

Graham SeibertGraham Seibert

Copyright 2006Copyright 2006

This is a segment of the draft version of a large syllabus. I need your feedback to improve it. There is a voice recorder capture your suggestions during the presentation.

Copyright 2006 Graham Seibert - MathCopyright 2006 Graham Seibert - Math 22

Not just doing arithmeticNot just doing arithmetic

Computation aside, Word and Excel Computation aside, Word and Excel documents can be useful for homeworkdocuments can be useful for homework

Word fonts and special characters, and Word fonts and special characters, and Equation Editor, are useful for writing mathEquation Editor, are useful for writing math

Excel and drawing packages are useful in Excel and drawing packages are useful in teaching for creating visual teaching for creating visual representations of mathematical representations of mathematical processes processes


The role of machines of any sort is The role of machines of any sort is controversial in teaching mathcontroversial in teaching math

Countries with the strongest math students Countries with the strongest math students (Japan, Belgium, Korea) avoid calculators(Japan, Belgium, Korea) avoid calculators((www.mathematicallycorrect.comwww.mathematicallycorrect.com))

Mechanical computation is no substitute forMechanical computation is no substitute for– Learning algorithmsLearning algorithms– Writing proofsWriting proofs– Developing numerate judgmentDeveloping numerate judgment

However, where machines are justified…However, where machines are justified…


Excel generally beats a calculatorExcel generally beats a calculator

You can lay a problem out step You can lay a problem out step by stepby stepYou can see intermediate You can see intermediate resultsresultsYou have access to a huge You have access to a huge variety of built-in functionsvariety of built-in functionsYou never have to copy and You never have to copy and rekey numbersrekey numbersThe program recalculates The program recalculates automaticallyautomaticallyExcel graphics are more Excel graphics are more refined and can be captured in refined and can be captured in documentsdocumentsHowever….However….


Excel has its limitationsExcel has its limitations

Graphing calculators more easily handle Graphing calculators more easily handle some algebraic functionssome algebraic functionsCan’t allow computer use on most tests: it Can’t allow computer use on most tests: it would be impossible to control cheatingwould be impossible to control cheating– Consider the issues with programmable Consider the issues with programmable

calculatorscalculators

There is a fine line between enhancing There is a fine line between enhancing insight into math and depriving a student insight into math and depriving a student of the insights that come with doing itof the insights that come with doing it


Excel graphs Excel graphs

Show almost Show almost anything, in 3D if anything, in 3D if necessarynecessary

Lots of gimmickry to Lots of gimmickry to add to visual appealadd to visual appeal

Copy and paste into Copy and paste into Word documentsWord documents

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 202

8

14

200.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

Tim

es retu

rn o

n in

vestm

ent

Years Invested Annual Interest Rate

Compound Interest

35.00-40.00

30.00-35.00

25.00-30.00

20.00-25.00

15.00-20.00

10.00-15.00

5.00-10.00

0.00-5.00


Equation EditorEquation Editor

Type in all of your Type in all of your math equationsmath equations

Math type is an extra-Math type is an extra-cost alternativecost alternative

( ) ( )

( ) ( )

( )( )

( ) ( )

( ) ( )

( )( )

( )

2

( )

2

11

(1 ) (1 )1 1

11

(1 ) (1 )1 1

Simplifying

DA B DA B

DA B DA B

DA BDA B

DA B DA B

DA B DA B

DA BDA B

DA B

DA B

d e d ee ed e d dc c c

d e e

d e d ee ed e d dc c c

d e e

( )

( )( )

( )

( )( )

( )

( )(

( )

2

( )

2

( )

the numerator

(1 ) (1 )1 1

( )(1 ) (1 )

1 1

(1 ) (1 )1 1

DA B

DA BDA B

DA B

DA BDA B

DA B

DA BDA

DA B

DA B

DA B

ded e dc c c

d e e

de DA Bd e dc c c

d e e

d e DAec c c

d e e

) 2B


Greek letters and math symbols in Greek letters and math symbols in Microsoft fontsMicrosoft fonts

Greek characters are Greek characters are available in most fontsavailable in most fonts

Common math symbols are Common math symbols are included in standard fonts; included in standard fonts; – Insert→Symbol→(scroll Insert→Symbol→(scroll

down to Mathematical down to Mathematical Operators).Operators). These are in These are in sequence; look for Character sequence; look for Character Codes starting with 2200Codes starting with 2200

Many more math symbols Many more math symbols are available in Unicode are available in Unicode fonts like Arial Unicode MSfonts like Arial Unicode MS

Type “2200” in here to see math symbols


Using Excel for classroom Using Excel for classroom illustration of math principlesillustration of math principles

Roll your own calculus: integration the way Roll your own calculus: integration the way Newton did itNewton did itExampleExample

Illustrating principles of statistics Illustrating principles of statistics ExampleExample

Using matrix arithmetic to solve Using matrix arithmetic to solve simultaneous equationssimultaneous equations

Using Excel Solver to solve systems of Using Excel Solver to solve systems of equations iterativelyequations iteratively


ConclusionConclusion

This has been mainly for teachersThis has been mainly for teachers

If you can use examples like this, I would If you can use examples like this, I would hope that some students would download hope that some students would download the spreadsheets to play with themthe spreadsheets to play with them

I have many more examples; ask meI have many more examples; ask me

Documents

Using a computer for math Graham Seibert Copyright 2006 This is a segment of the draft version of a large syllabus. I need your feedback to improve it