History of Mathematics for Teachers of Grades 9-12

  • Syllabus
  • Date

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

    July 17 - Mon
    July 18 - Tues
    • Classwork Algebra
      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 Linear Eqs 32-33.
      Chinese method of double false position of solving two linear equations with two unknowns via Chinese Problems worksheet from the CD NegNums 42-44.
      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
      History of Plimpton 322 via web search (Plimpton 322)
      Brief history of the Pythagorean Theorem via a web search (history of the pythagorean theorem): site and site
      Additional History of Math sites:
      MacTutor History of Mathematics Archive (Pythagorean site:www-groups.dcs.st-and.ac.uk/)
      Mathematicians of the African Diaspora
      Convergence: where mathematics, history and teaching interact
      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 Choose an NCTM standard related to algebra or geometry. Write down that standard. Then find an activity related to that standard that is not from our CD. You may find an activity in one of the books or from a web search. Specify how the activity relates to the standard that you chose. Continue working on the Reflective Journal and CD assignments. Your CD project topic must be approved by Dr. Sarah by Wednesday. Provide the Chapter and page number in addition to the title of the activity.

    July 19 - Wed
    • Classwork Geometry
    • 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/Sketchpad/ Samples/Sketches/Geometry/Pythagoras.gsp Go through Behold Pythagoras! and Puzzled Pythagoras.
      **Return to the classroom. (Highlight Euclid's Proof), discuss the historical differences in proofs, and then Dr. Sarah's models the Pythagorean Theorem 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.
      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 and the related DXC history and history of writers in the classroom
    • Homework for Thursday Complete the CD assignment.

    July 20 - Thur
    • Classwork CD presentations and Precursors to Calculus
    • Finish up classwork from Wednesday
    • CD presentations
    • Ben Franklin's Will
    • Begin calculus: Discussion based on The Paradoxes of Zeno from From Agnesi to Zeno
    • 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
      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.
      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
      The Archimedes Palimpsest
      Analytic Geometry Notes
      Create timeline - include names, year, and accomplishments
    • Homework for Friday Study for Assessment. Complete the Reflective Journal Assignment.

    July 21 - Fri
    July 29 - Sat