by David Hellam, teacher
and Szymon Rutkowski, student
from Kuwait English School
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
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.
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.
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.
We therefore created our second Flash interactivity with this in
mind. This would be a tool that would enable a student to practise
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
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
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
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.