Teaching Mathematics Teaching Mathematics Using History and Fairy Using History and Fairy

TalesTalesDaryl Stephens and Robert Daryl Stephens and Robert

DavidsonDavidsonDepartment of Mathematical Department of Mathematical

SciencesSciencesEast Tennessee State UniversityEast Tennessee State University

Tennessee Association for Developmental Tennessee Association for Developmental EducationEducation

20th Annual Conference20th Annual ConferenceOctober 28, 2003 – Memphis, TennesseeOctober 28, 2003 – Memphis, Tennessee

Why integrate history and Why integrate history and stories into math class?stories into math class?

To humanize mathematicsTo humanize mathematics Connect real-life experiences with Connect real-life experiences with

mathematicsmathematics Show how people in the real world use Show how people in the real world use

mathmath Relax students and alleviate math Relax students and alleviate math

anxietyanxiety Solve problemsSolve problems Illustrate concepts by storiesIllustrate concepts by stories

MathematiciansMathematicians

Interesting TidbitsInteresting Tidbits

René Descartes René Descartes (March 31, 1596 – February 11, 1650)(March 31, 1596 – February 11, 1650)

Queen Christina

Elizabeth of Bohemia

Blaise PascalBlaise Pascal(June 19, 1623 – (June 19, 1623 –

August 19, August 19,

1662)1662)

Pierre de Fermat Pierre de Fermat (August 17, 1601 (August 17, 1601 – January 12, – January 12, 1665)1665)

Gerolamo CardanoGerolamo Cardano (September 24, (September 24, 1501 - September 1501 - September 21, 1576)21, 1576)

Niccolo Fontana Niccolo Fontana TartagliaTartaglia

(1499 or 1500 - (1499 or 1500 - December 13, 1557)December 13, 1557)

Robert RecordeRobert Recorde Ca. 1510-1558Ca. 1510-1558 Introduced Introduced == sign sign

Christoff Rudolff (1499?-Christoff Rudolff (1499?-1545?)1545?)

Introduced the radical sign, 1525, in a Introduced the radical sign, 1525, in a book called book called Die CossDie Coss. .

√√ Stretched-out Stretched-out rr Used a vertical bar as a decimal pointUsed a vertical bar as a decimal point Used a period for equalsUsed a period for equals Recognized the law Recognized the law b b nn · b · b mm = b = b n + mn + m

Credited with introducing Credited with introducing ++ and and ––

Michael Stifel (1486-1567)Michael Stifel (1486-1567)

““Greatest German algebraist of the 16Greatest German algebraist of the 16thth century”century”

Used Used ++ and and –– signs signs Also credited with modern radical signAlso credited with modern radical sign Concluded world would end on Concluded world would end on

10/3/1533.10/3/1533. Said Pope Leo X was the Beast in Rev.Said Pope Leo X was the Beast in Rev. Magic SquaresMagic Squares

Thomas Hariot (1560-1621)Thomas Hariot (1560-1621)

Introduced Introduced << and and >> as we use as we use them todaythem today

First to write exponents as we First to write exponents as we do (do (aa33 instead of instead of aaaaaa))

Helped Sir Walter Raleigh map Helped Sir Walter Raleigh map NCNC

Discovered sunspotsDiscovered sunspots Died of cancer from tobaccoDied of cancer from tobacco

William Oughtred (1574-William Oughtred (1574-1660)1660)

Introduced the Introduced the ×× for for multiplicationmultiplication

Introduced Introduced :::: for proportion for proportion and and ~~ for difference between for difference between

Clergyman who gave free Clergyman who gave free math lessonsmath lessons

Famous pupils: John Wallis, Famous pupils: John Wallis, Christopher Wren, Seth WardChristopher Wren, Seth Ward

Gottfried Wilhelm von LeibnizGottfried Wilhelm von Leibniz(1646-1716)(1646-1716)

Used both Used both •• and and for for multiplicationmultiplication

Calculating machine (first Calculating machine (first mechanical to multiply mechanical to multiply and divide)and divide)

Developed binary numeral Developed binary numeral systemsystem

Co-creator of calculusCo-creator of calculus

Johann Heinrich Rann (1622-Johann Heinrich Rann (1622-1676)1676)

Introduced the Introduced the ÷÷ symbol for division symbol for division (although this symbol was used by (although this symbol was used by many continental Europeans for many continental Europeans for subtraction).subtraction).

Christian Kramp (1760-Christian Kramp (1760-1826)1826)

First to use the First to use the n! n! symbol for symbol for factorials in 1808factorials in 1808

Used because of printing problems Used because of printing problems with a previously-used symbolwith a previously-used symbol

Evariste Galois (1811 - Evariste Galois (1811 - 1832) 1832)

““Unfortunately what is little Unfortunately what is little recognized is that the most recognized is that the most worthwhile scientific books worthwhile scientific books are those in which the author are those in which the author clearly indicates what he clearly indicates what he does not know; for an author does not know; for an author most hurts his readers by most hurts his readers by concealing difficulties.”concealing difficulties.”

Died in a duel over a Died in a duel over a woman’s lovewoman’s love

Connecting Real-life Connecting Real-life ExperiencesExperiences

Real World ExamplesReal World Examples

Reading blueprintsReading blueprints Packing furniturePacking furniture ““Inequalities will never affect me!”Inequalities will never affect me!” Emily’s inequalitiesEmily’s inequalities Calculator projectCalculator project Cartesian inequalities and the tennis Cartesian inequalities and the tennis

courtcourt

Relax students and help Relax students and help alleviate math anxietyalleviate math anxiety

Math wasn’t created to make Math wasn’t created to make students miserable, but to students miserable, but to

solve problems!solve problems!

ReligionReligion PyramidsPyramids AstronomyAstronomy

PoliticsPolitics SputnikSputnik

MoneyMoney Geometry and Egyptian taxationGeometry and Egyptian taxation

Illustrate a point with a Illustrate a point with a storystory

The Key StoryThe Key Story

Try turning it upside Try turning it upside down!down!

Factor: 21Factor: 21x x 22 – – xx – 10 – 10 (3(3xx + 5)(7 + 5)(7xx – 2) doesn’t – 2) doesn’t

workwork Try switching around to Try switching around to (3(3xx + 2)(7 + 2)(7xx – 5) – 5)

Dr. Seuss’s Dr. Seuss’s The SneetchesThe Sneetches

FunctionsFunctions Composite Composite

functionsfunctions Inverse functions Inverse functions

The Cat in the BoxThe Cat in the Box

Dana Michel, Dana Michel,

Wonder Books, 1963Wonder Books, 1963 SubsetsSubsets Sets of numbersSets of numbers

Trolls and Negative Trolls and Negative ExponentsExponents

Working with Working with rational rational expressions with expressions with negative negative exponents such as:exponents such as:

7

1 4

4 6

2 9

x y

x y

““The Elephant and the The Elephant and the Squirrel”Squirrel”

Children’s story by Bill Sprague from Children’s story by Bill Sprague from A Treasury of Bedtime StoriesA Treasury of Bedtime Stories (ed. (ed. Judith Klugmann, Doubleday, 1960).Judith Klugmann, Doubleday, 1960).

Stop and look at other ways of Stop and look at other ways of solving problems besides the solving problems besides the obvious!obvious!

Your TurnYour Turn

Any stories you’d like to Any stories you’d like to share?share?

More informationMore informationThis presentation and a handout will This presentation and a handout will

be posted on Daryl’s web page late be posted on Daryl’s web page late next week.next week.

http://faculty.etsu.edu/stephenhttp://faculty.etsu.edu/stephen//Look for link on the page.Look for link on the page.

E-mail: E-mail: stephen@etsu.edustephen@etsu.edu

davidson@etsu.edudavidson@etsu.edu

CreditsCredits

Except for pictures of books, all Except for pictures of books, all images of people came from images of people came from Wikipedia (Wikipedia (www.wikipedia.comwww.wikipedia.com) or ) or The MacTutor History of Mathematics The MacTutor History of Mathematics archive (archive (http://www-gap.dcs.st-and.ac.uk/~hishttp://www-gap.dcs.st-and.ac.uk/~history/index.htmltory/index.html) and are in public domain) and are in public domain

Brown troll and key pictures by DarylBrown troll and key pictures by Daryl