History of Mathematics for Teachers of Grades 9-12

Date	CLASSWORK AND HOMEWORK Work is due at the beginning of class unless otherwise noted!
July 18 - Mon	Classwork Registration Discuss scheduling of course and syllabus What history have you covered in your own classroom? and Introductions Why history in the classroom? NCTM Standards on history. Hand out Who? How? What? A Strategy for Using History to Teach Mathematics Hand out selections from Math Through the Ages, History of numbers, primes and the Sieve of Eratosthenes Euclid's Book IX Prop 20 Triangle Measuring, irrationality of sqrt(2) and history. Project Mathematics' Early History of Mathematics Video Cantor diagonalization DodgeBall worksheet, Dr. Sarah's Cantor worksheet. Move to the computer lab. Intro to web searching and sum of cubes worksheet. Prepare to present your findings. NCTM Standards in grades 9-12 for Number and Operations Standard. Intro to the CD. Search for activities related to these standards and prepare to present your findings. Homework for Tuesday Linear equations homework and begin working on the Daily Journal and CD assignment.
July 19 - Tues	Classwork Linear equations: Egypt Rhind Papyrus, Babylon, China: Egyptian Multiplication/Division The origin of algebraic manipulation via Linear Equations in One Unknown - Islamic Method worksheet from the CD. Chinese method of double false position of solving two linear equations with two unknowns via Chinese Problems worksheet from the CD. System of Three Linear Equations - The Chinese Solution from Algebra Activities from Many Cultures Multicultural Origin of the Quadratic Formula worksheet from Algebra Activities from Many Cultures Brief history of the Pythagorean Theorem via web search: site and site MacTutor History of Mathematics Archive Scarecrow's Theorem Slide 1 Slide 2 Copyright Slide Cubic equations: Europe - leading to sqrt(-1) Solutions to the quintic Maple demo and fictional account of Galois Begin Wednesday's classwork. Homework for Wednesday Daily Journal reflections for the first two days should be completed. Your CD project topic must be approved by Dr. Sarah by Wednesday.
July 20 - Wed	Classwork What is geometry? Groups discuss and come back together. Brief history of early geometry knowledge including the Babylonians, Egyptians, Greeks (Thales, Pythagoras, Plato, Euclid), Chinese, and Africans. Mention the Timeline for Geometry: Multicultural Highpoints from Geometry Activities from Many Cultures Skim LAV 6 section of the CD on Origins of Length, Area, and Volume Measurement Mention CD LAV 80 on Thales' Shadow Measurement Activity Mention CD Trig 80 and LAV 88 on Eratosthenes' Size of the Earth and Trig 112 on Al-Biruni's Calculation on the Size of the Earth History of Euclid's elements including Euclid's 5th postulate (prop 29 and later). Sum of the Angles in a Triangle: Write out Proposition 32 in modern language. Discuss Euclid's historical proof, paper folding, and then an Intro to Geometric Constructions via a construction in Sketchpad. Dr. Sarah models the construction. Discuss the history (attributed to Pythagoras), and compare and contrast the activities, discussing the benefits and difficulties with using them in various classes. Then the group goes to the computer lab to try the Sketchpad construction. Pythagorean Theorem: Discuss the Yale tablet and Babylonian Pythagorean knowledge. Discuss the history of Euclid Book 1 Proposition 47 and of it's importance in measurement. Discuss Sketchpad demonstrations of the Pythagorean Theorem. From Sketchpad, under File/open, go to Desktop/205Math(yourcomputersnumber)/Applications(MacOS9)/Sketchpad/ Samples/Sketches/Geometry/Pythagoras.gsp Go through Behold Pythagoras! and Puzzled Pythagoras. Return to the classroom. Highlight the other proof from the video (Euclid's Pythagoras), and then Dr. Sarah's models the construction in Sketchpad. Mention CD activities LAV 124 Pythagorean Theorem, LAV 130 Practical Pythagorean Theorem, Geom 103 Pythagorean Project Hand out A Chinese Proof of the Theorem from Geometry Activities from Many Cultures in order to complement the Sketchpad Behold Pythagoras! activity Compare and contrast the methods used in the classroom. Non-Euclidean Geometry: Dynamic Geometry activities on the sphere and hyperbolic Poincare disk Walter Fendt's Java Applet and the sum of the angles and the Pythagorean Theorem Escher worksheet Sketchpad Hyperbolic Sum of Angles Sketchpad Hyperbolic Pythagorean Theorem Mention built in hyperbolic Sketchpad exploration and Brad Findell's Elliptic/Spherical Toolkit for Sketchpad Why Study Hyperbolic Geometry? and a brief history of non-Euclidean geometry. Crochet Model of Hyperbolic Geometry Hand out Explorers of Non-Euclidean Geometry from Geometry Activities from Many Cultures Mention CD Trig 151 on Spherical Trig Read through the Shape of the Universe and discuss Return to the computer lab. History of modern geometry via web searches. Return to the classroom. A brief history of geometry education. Brief history of the connections and differences between algebra and geometry The Proof video Mention the teacher's guide available at NOVA Online Powers of twelve activity Homework for Thursday Complete the CD assignment and work on the Daily Journal.
July 21 - Thur	Classwork Finish up classwork from Wednesday CD presentations Sharon Poly 50 Finding Cube Roots Gina Poly 33 Deriving the Quadratic Formula Emogene Trig 12 Angle Degree and Radian Measure Suzanne Geom 7 Checkerboard Challenge Joy Lav 33 Sticks, Stones, and Ropes Bob NegNums 55 Al-Khwarizmi's Negative Numbers Jeremy Lav 118 Euclid's Geometric Algebra Amelie ExpLog 36 Manhattan Purchase Cam Lav 71 Housing Jeanne NegNums 90 Excuse Me Do You Have the Time? Danielle Lav 111 Golden Mean Ben Franklin's Will Begin calculus: Discussion based on The Paradoxes of Zeno from From Agnesi to Zeno Quadrature of the lune Archimedes: Archimedes and pi via inscribed and circumscribed polygons. Hand out the Hypatia worksheet Examine the related NOVA website applet Archimedes finding the area of a parabola in terms of the area of a triangle and the quadrature of a parabola Archimedes computation of the area of a sphere as four times the length of the great circle via oranges Archimedes and the volume of a sphere. Read and discuss Measuring Volumes Applications of series: history of the approximation of Pi and the number of known digits of Pi. Apu and pi in Maple, and search for the world record on the number of digits. Discuss Bailey and Borwein's series. Calculus: Barrow, Newton, and Leibniz The spread of calculus: Agnesi and the witch of Agnesi Analytical Institutions Witch. Handout worksheet From Agnesi to Zeno Rigor in calculus and modern analysis Homework for Friday Complete the Daily Journal.
July 22 - Fri	Classwork Finish calculus Issues in current research on history of math and ethnomathematics and web searches CD presentation reflections Look at textbooks Melt evaluations Reflection assessment Hand out main web page Homework for Saturday July 30th Work on the final project.
July 30 - Sat	Final project due as a word-processed document or a PDF file, sent as an attachment in an email to [email protected]. Final projects as word files: Danielle Fractals Emogene Plato's Dialogue Meno Bob Historical Pi Jeremy Just How Big is the Earth Anyway? Gina Patterns of Operations for Integers Cam Aztec Mathematics Jeanne Shang Numerals and Counting Boards