COMPUTER ALGEBRA SYSTEMS - TECHNOLOGY IN MATHEMATICS EDUCATION

Mathematical Modelling

For students as well as for teachers the shift from problem solving (one correct answer) to mathematical modelling (multi-solution paths leading to approximate answers each with possible limitations or potential for extension) requires a new set of teaching and learning skills – symbolizing data, cleverly translating the task into the language of mathematics, i.e., into a mathematical model, the internal treatment of this problem in the field of mathematics right up to its solution(s) possibly with the aide of technology, and finally, a deliberate interpretation and critical examination of the results obtained. “Has our original question really been answered? How accurate and how reliable is the result?” “How applicable are my results to other (new) situations?” Thus using carefully selected examples, the typical process of mathematical modelling may become a central theme in the classroom.

This diagram shows the important steps in the process of creating a mathematical model:

CAS and Problem-Solving

Optimize the area of the rectangle that can circumscribe a rectangle of length L and width W.

One possible solution:

Create a geometric model of the given problem.

From the model one can see that the Area of the circumscribed rectangle will be:

A = (L cos (a)+W sin (a)) (L sin (a) + W cos (a)).

Using CAS:

Teaching tip:

Have the students actually get the derivative of f(a) (either manually or using CAS) and then

solve mentally for f (a) = 0.

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Before technology, the solution of the mathematical problem was probably the most time consuming part of such activities. With technology, however, we can place this part in its proper order of importance by allowing technology to do the number/analytical “crunching”.

For the younger student, the process involved above can be introduced through such activities as “picture mathematics”.

The student then needs to interpret the answers and evaluate f (a) accordingly.

White Box/Black Box Model

CAS as a “white box”

CAS as a “black box”

- Mathematical Modeling

- Picture mathematics