EXPLORING CIRCLES BY USING COMPUTER

PROGRAMMING

Learning from pre-written computer programs is more engaging and rewarding than hand calculations and manual plotting Jerry Sommerville

Overview

  • Purpose
    Demonstrate math concepts using computer programming
  • Plan of Action
    Draw a smiley face with circles
    This demonstrates the behavior of a circle with offsets
    Use pre-written computer program to teach math ideas and simple programming language features
  • English and Music composition parallels
    Execution of Plan Explain math/language features in context of larger goal (smiley face)
    Learn how to dissect or experiment with program to understand steps
    Let the computer do the hard work
  • Evaluation of Results
    Which method is more engaging and more intuitive?
  • Presentation of Solution and Summary

Plan of Action

  • Language features
    Language has graphics primitives (able to draw)
    Language is easy to remember, intuitive
  • ‘Apostrophe(Comment)
  • STOP
    (Cease execution of steps)
  • SLEEP
    (Pause execution of steps)
  • Loop: For I = 1 to 5: Next I (Repeat execution of steps) PSET(X,Y) [put a point on the screen] SQR (Square root)

Circle equations

  • Circle equation:
    x^{2}+y^{2}=R^{2}

  • Circle equation with an offset (shifted to h, k position):
    (x-h)^{2}+(y-k)^{2}=R^{2}
    Where x, and y are variables (they change) Radius, R, and offsets h and k are constants (they don’t change)

  • Solve for y in terms of x
    \tt{\Delta y}=\tt{K}+\tt{S Q R}R(R^{2}\tt{\Delta}(x \tt{-} h)^{2}),

  • y=f(x), y is dependent upon x

  • Put this equation in a do loop and change y by changing x,

Execution of Plan

  • Run Entire Program
  • Use comments to explain phases using apostrophe.
  • Stop program to explain phases, use “STOP”
  • Pause program using “SLEEP”
  • Change constants and variables to understand trends
  • Edit program to explore other functions and language features

Evaluation of Results

  • When you compare manual (conventional) method vs. computer-assisted method:
  • Which method is more engaging?
  • Which method is more intuitive?
  • Which requires the most preparation time to teach?
  • Which enhances programming skills better?

Conclusions

  • Computer program reduces the burden upon math teachers to convey math concepts.
  • It encourages the development of programming skills because students see a purpose for them.
  • It teaches students to be purposeful (objective oriented) while meticulous (detail oriented).
  • CANVAS
    A term coined for this approach. Computers, Algebra, Numbers, Visual Aids for Science (C.A.N.V.A.S)
  • The computer screen is used like a canvas in art.