History of Mathematics for Teachers of Grades 9-12

  • Syllabus
  • Date

            Work is due at the beginning of class unless otherwise noted!

    July 18 - Mon
    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 greenwaldsj@appstate.edu.
    • 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