Maple V

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Mathematical Ulterior Motives

- the mother of all ulterior sites -

Do you have problems with factorisation? Do the sides of your equations not see eye to eye? Are your graphs worth less than a thousand words? Do you end up somewhere in between when you try to maximise?

If you have any of these problems you should start to jump up and down! Are you jumping?

For less than US$100 you can solve all of these problems. Let me show you how!

To factorise a third degree polynomial is easy:

> factor(8*x^3-36*x^2+54*x-27);

To factorise a number is easy:

> ifactor(11111);

Equations can be given names, and are displayed beautifully:

> eq:= 5*x/3-14=3-7*x/9;

To solve an equation is easy:

> solve(eq);

To solve second degree equations does not break a sweat:

> solve(-3*x^2-2*x+17=0);

> solve(11*x^2+8*x+14=0);

If you wonder why the last equation only gave complex roots (I is the complex unit), you should plot it:

> plot(11*x^2+8*x+14,x=-5..5);

A farmer has a rectangular field next to the river. The field's fence is 40m. How should he choose the length and width to maximise the field's area. Translated: What is the maximum value of x*y when 2*x+y=40?

We can do the substitution in our head:

> area(x):=x*(40-2*x):

But may need some help for the graph:

> plot(area(x), x=0...20);

When the slope of the tangent is 0 we have a maximum:

> solve(diff(area(x),x));

And the maximum is (% stands for the result of the previous operation):

> area(%);

This was just a taste. A taste written by someone who has less than three hours of practice flying Maple V. I did not show examples of how you can program in Maple, run animations, etc.

(Note: The examples above were written in Maple and exported as html into this page.)

Using Maple V in the classroom

The technology is here. Users of mathematics outside the classroom use Maple V (or similar programs like Matematica, Derive, MathCad or symbolic calculators capable of much of the same). What about your students?

Maple V can be used as a tool

to discuss and develop concepts and skills with the teacher playing a central role
for the student whenever she sees fit

When my father went to school he was taught an algorithm for extracting square roots, when I went to school we used square root tables, but were taught several factorising algorithms. My sons use a calculator for the square root, are lean on factorisation, but still has to do manually the tasks Maple V did in a blink of an eye above.

To use Maple V is not easy. Students who survived their math classes performing algorithms with little or no understanding, have a harder time if they have to use Maple. Tools give a profit, but only if you invest in understanding how to use them and succeed.

What is the aim for learning mathematics? Why do we teach students to factorise? Solve equations? What is the big picture? Where does a program like Maple V fit into that picture?

Using Maple V could make the learning of mathematics so much harder! If 90% of what students normally do can be done by pressing a button (more or less), then what should the students do in the time freed? Should they be discovering problems, translating the problems into Maple tasks and interpreting the results? Think and ponder over concepts and patterns? Discuss and argue with each other, tolerant and curious towards other viewpoints?

In short, should they be trained, not to be monkeys on a circus expected to respond to certain stimuli in a prescribed way, but to be human beings, struggling with making judgements, evaluating options, analysing results, creating solutions?

The technology is here, the tool is here. Why do we ignore it?

References:

Here you find many Maple links:

Mathematics Archives, Maple, archives.math.utk.edu/maple.html.
Indiana University, Maple, www.indiana.edu/~statmath/math/maple/index.html.
Maple's site, www.maplesoft.com.

Maple V can be purchased from www.amazon.com.

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