Algebra Flash!

by David Hellam, teacher
and Szymon Rutkowski, student
from Kuwait English School

Introduction

It is difficult to decide whether this is a lesson on algebra that uses Flash or a lesson on Flash that uses algebra. It was the result of two lessons close to the end of the 1999-2000 school year. The aim was to illustrate the different ways that a web-based algebra lesson could be made interactive.

An Old Approach

It is possible to re-create the look and feel of a mathematics textbook very easily with HTML. One refinement, of course, is that you can add hyperlinks to worked solutions to any example questions you wish to include. This approach, however, provides very little interactivity.

Using javascript, it is possible to refine the process a little. You could add a multiple choice test, or a simple answer-checking routine, as depicted in our example.

With Flash, similar content can be made more visually stimulating, but it still suffers from the same limitations as before.

Equation Solving Tools

We quickly decided that a better use for Flash would be to provide a set of online tools to help students solve equations, rather than merely present information about equations.

During  two lessons, each lasting 70 minutes, we put together three tools for three different types of equation. These have since been tidied up a little over the last two weeks, but they remain substantially the same as our original work.

Simultaneous Equations

It may seem odd to start with these, but it is not too hard to demonstrate with a spreadsheet how a pair of simultaneous equations can be solved using matrices.

Once that had been done, it was fairly easy to translate our work into Flash. However, this only produced a tool that would solve a pair of simultaneous equations. This may be useful. But not as useful as a solution that would help a student to produce their own solution.

Linear Equations

We therefore created our second Flash interactivity with this in mind. This would be a tool that would enable a student to practise solving equations.

Our first version relied on a student typing their instructions correctly, and only helped them solve one type of linear equation. We re-worked this over the week to produce something more versatile. 

The second version could cope with three different levels of difficulty. Plus, a calculator-style display to make the entering of commands as simple as possible.

The solution is by no means final. It doesn't cope with fractions. It does not display which operation has been carried out on each line. Neither does it allow you to undo a stage or indicate what type of problem you are working on.

This sort of tool is not new. People who are familiar with Mathcad, Derive, Mathematica or any other general-purpose mathematical program may wonder why we have bothered doing this.

However, as a simple, stand-alone utility that can be used across a variety of platforms, it has potential. In this respect, it owes more to an  educational utility like Solve for the BBC computer than other more sophisticated tools.

Quadratic Equations

This one presented an interesting challenge to us. Flash does not include a square root as a built-in function! Creating an actionscript to use the Newton-Raphson method for finding the roots of an equation of the form y = x² - a seemed to be a logical approach.

 First of all, we did some experiments on a spreadsheet to determine how many iterations we typically needed to do before we could be sure we had a good approximation of the square root.

Another advantage of this method would be if we decided to extend the solution further to solve different types of approach. At this point, we decided this tool would be more useful to other students who wished to investigate how to use Flash to solve equations of their own.