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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: [email protected]@etsu.edu
[email protected]@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