Some thoughts on using Wolfram Alpha in teaching math

My main work at our institute is to find ways on how to integrate technologyparticularly free software and Web 2.0 applications in teaching mathematics. Recently, I have been thinking of integrating Wolfram Alpha in teacher trainings, but I can’t yet  justify to myself why (I don’t want to read the work of others yet).

Don’t get me wrong. Wolfram Alpha is a great tool — the first of its kind. You type your query and voila, all the related information pop up — graphs, numbers, tables, maps,  and almost all the things that you need. Fantastic, but if a lesson ends in generating information from Wolfram Alpha, then it’s no different from using Google or Wikipedia — well a little different probably because of the presentation.  I don’t want to let students use Wolfram Alpha just to get information; I want it to be a tool that would elicit thinking. » Read more

Demystifying Triangle Inequality

This is the first part of  the Triangle Inequality Series.


Given three segments, how are we sure that they will form a triangle?

Will the segments with lengths 3, 4, and 8 units form a triangle? What about 3, 5, and 8?

What conditions with respect to segment lengths must be satisfied, so that three segments form a triangle?

Shown below are the segments with lengths 3, 4 and 8 units. In the following illustrations, squares are used to clearly indicate the segments’ lengths.  Each square has side 1 unit.  As we can see, we cannot form a triangle if the sum of the lengths of the two sides is less than the third side.

Figure 1

Let us now examine a triangle with side lengths 3, 5, and 8 units. Referring to Figure 2, the sides will only be coinciding and will never meet when rotated outward as shown. » Read more