Problem Solving in Calculus with Symbolic Geometry and CAS

Autor/inn/en	Todd, Philip; Wiechmann, James
Titel	Problem Solving in Calculus with Symbolic Geometry and CAS
Quelle	In: Australian Senior Mathematics Journal, 22 (2008) 2, S.49-56 (8 Seiten) PDF als Volltext (1); PDF als Volltext kostenfreie Datei (2) Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Computer Software; Geometry; Calculus; Algebra; Problem Solving; Mathematics Instruction; Computer Uses in Education; Symbols (Mathematics); Geometric Concepts; Secondary School Mathematics; College Mathematics + Suchen Sie Ihr Suchwort? Geometrie; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Problemlösen; Mathematics lessons; Mathematikunterricht; Computernutzung; Elementare Geometrie
Abstract	Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical expressions can be copied back and forth between a symbolic geometry system and a CAS thus making it an interesting new tool for exploring mathematics and solving problems. In this paper, the authors illustrate the use of a symbolic geometry system applied to two classic optimisation problems, both drawn from "100 Great Problems of Elementary Mathematics". The first problem, "Regiomontanus' Optimisation Problem", is suitable for students at the upper secondary level. The second, "Fagnano's Perimeter Minimisation Problem", does involve some partial derivatives, and so would be more suitable for students at tertiary level. Their symbolic geometry system is "Geometry Expressions" (Saltire Software, 2008). In order to illustrate the flexibility of the CAS interface, in the first problem the authors use "Mathematica" (Wolfram Research, 2008), and in the second problem, they use "Maple" (Maplesoft, 2008). (Contains 10 figures.) (ERIC).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10