





							COMPUTER ALGEBRA SYSTEMS - TECHNOLOGY IN MATHEMATICS EDUCATION

Cas as a “white Box”

Combining algebraic expressions: Students arrive at rules for combining algebraic terms by investigating what happens with like and unlike terms. The teacher can then direct the discussion on their rules and give other examples where the students using their conjectures do the example “by hand” and test their results with CAS.

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Teaching tip: These examples should be divided over different “fun” sheets where the level of difficulty is increased according to the level of the students.

Factoring:

Students arrive at the rules for factoring by investigating patterns, e.g., difference of two perfect squares. Again, have students test conjectures by giving different examples to do “by hand” and test their results using CAS.

Teaching tip: Have students attempt to factor the sum of two perfect squares, e.g., x²+4, and discuss the output on the calculator.

Extension work: The following can be linked to some statistics work.

Factoring quadratics using random polynomial generator: Have students determine how many quadratics are factorable from, for example, 100 tries.

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The many uses of CAS help to create a veritable mathematics laboratory in the classroom particularly in performing investigations. The following examples illustrate some of its many uses in enriching the classroom environment by having students discover through pattern recognition some of the basic rules and algorithms of algebraic manipulation. The screen shots are from the TI-Voyage 200.

Combining algebraic expressions

Factoring

Rational Algebraic Expressions

Pascal’s Triangle and Binomial Expansion

Partial Fractions

Derivative

INVESTIGATION OF PATTERNS – Making Conjectures

PEDAGOGICAL CAS OR Pecas

Rational Algebraic Expressions:

From these examples

make a conjecture as to how to

divide algebraic polynomial

expressions and test conjecture.

Teaching tip: Have the students test

their conjecture by investigating how

the calculator would treat the rational

expression shown in the screenshot.

Teaching tip: Generate rules for simplifying rational polynomial expressions based on the investigations attempted above.

Teaching tip: To test understanding of rational expressions, have the students explain in words the meaning of the expression

and rewrite it in at least 3 different equivalent ways. How would you check the equivalency of your expressions with the initial expression using CAS.

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