The latest international research studies suggest that there is substantial room for improvement in the algebraic proficiency of a large proportion of students. Particular difficulty is found with the manipulation of expressions and the use of equations to solve problems. Many students never seem to appreciate that algebra is a tool rather than some arcane ritual.

EQUATION is a Windows program that introduces, in the form of a game, the basic principles of solving and formulating simple linear equations. It is based on the results of research carried out at Oxford University into children's experiences of learning algebra.

There are four particular aspects that make this program unique:

• promotion of simplification;
• the unthreatening introduction of symbolic notation;
• interactive feedback on solution processes;
• modelling word problems.

## Promotion of simplification

EQUATION starts as a game, with the balance puzzles commonly found in school textbooks. These puzzles are initially accessible to informal methods, but as the puzzles increase in difficulty, a simplification strategy becomes more attractive. Children enjoy the challenge of the game immensely.

## The unthreatening introduction of symbolic notation

Algebra is gradually introduced as a convenient abbreviation for playing the game, leaving until later the notions that algebra can generalise arithmetic.

This allows the jump from pictures to symbols to be perfectly natural. And once the balancing context has been left behind, negative signs and negative solutions become possible.

## Interactive Feedback on solution processes

EQUATION offers a major advantage over paper-based exercises. The student chooses the operation to perform; but the computer executes it. This means that attention can be devoted to strategic simplification decisions, without worrying about arithmetic. And students see the effect of an operation instantly, which prevents pages of error-strewn workings:

Suppose the student decides here to try to subtract an unknown (a typical error)

The student now sees:

It is now clear that subtracting an unknown was not a useful strategy. It is necessary to add.

The student now sees:

By getting feedback, students of algebra aged from fifteen to fifty have succeeded in correcting for themselves long-standing erroneous strategies.

## Modelling word problems

EQUATION presents students with graduated word problems that can be modelled by equations.

Once an equation has been successfully entered, it can be solved by telling the computer the operations to perform. Children using the program see algebra as a tool they can use confidently rather than some arcane ritual.