CAS – Computer Algebra Systems:
Articles, problems, ideas and resources.
One of my interests in mathematics and technology is the use of Computer Algebra Systems (CAS) in high school math. Mathematics today is done with technology such as CAS. Why is the use of CAS being taught? Why is it no a major feature of the math programs suggested by professional groups?
Algemetic The “Sound off” column from The Mathematics Teacher, February 2001.
DOING Math with a CAS for presentation first at the NCTM regional meeting September 21, 2006 in Chicago, IL. and at the USACAS Conference June 16, 2007 and most recently at the TTT Conference, Philadelphia, PA, March 7, 2013. Teaching how to do the same old things with a CAS is not the goal. First it is necessary to decide how to do math with a CAS. This talk includes thoughts and ideas on what will change and what will remain the same when you DO math with a CAS.. Slides (pptx) Handout with questions (docx) and solutions (docx)
The Golden Ratio in Quartic Polynomials I believe this to be an original result. The line containing the points of inflection of any 4-th degree polynomial intersects the polynomial in two other points whose coordinates are related to the points of inflection by the golden ratio and its conjugate. This version of this idea appeared on the NCTM’s On-Math site in the Winter 2004- 2005 column. Alexander Bogomolny expanded on this idea, his discussion is here. And see my post Lin McMullin’s Theorem
The Golden Ratio in Cubic Polynomials Once again the Golden Ratio makes an unexpected appearance, this time in cubic polynomials. The problem and its proof are in this article. Audrey Weeks, author of Calculus in Motion, has prepared a Geometers’ Sketchpad animation of the proof and result which can be downloaded here (open in GSP)
Half a Trapezoid is better than … An interesting geometry problem for CAS or by hand.
Two Cone Problem “Find the maximum sum of the volumes of two cones you make out of a construction paper disk of area S”
“How to Solve Any Triangle: First, Forget the Law of Sines and the Law of Cosines” From The Mathematics Teacher, September 2003.
Symbolic Logic on a CAS This article shows how to make truth tables and do other symbolic logic problems with a TI-92 (or a TI89, or Voyage 200).
CAS in High School Mathematics A discussion of the changes that will be necessary in the high school mathematic curriculum with the introduction of CAS. Originally presented at the NCTM regional meeting September 21, 2006 in Chicago, IL
Computer Algebra Systems in Secondary School Mathematics Education
An NCTM monograph on CAS use in high school.
Questions of the Month from AP* Central
These 8 questions originally appeared as the AP Calculus Question of the Month from May through December 2003. Links to AP Central. Many of them involve CAS work. (* AP and Advanced Placement Program are registered trademarks of The College Board, which was not involved in the production of and does not endorse any of the material here except those actually linked to AP Central)
1. Learning from Mistakes – Cylindrical Shells (May 2003) The solution has disappeared from AP Central. Click here for the solution.
2. Neighborhoods of Infinity (June 2003)
3. Calculus with Compass and Straight Edge? (July 2003)
4. My Favorite Function (August 2003)
5. Is There Anything Remaining from the Remainder Theorem? (September 2003)
6. What’s Normal for a Quadratic? (October 2003)
7. Fun Investigations with a CAS – Third Degree Polynomials Part I (November 2003)
8. Fun Investigations with a CAS – Third Degree Polynomials Part II (December 2003)