A given algebraic expression can be considered from two points of view:

- as a computation programme: it indicates the sequence of computations to do in order to obtain the number sent by the programme when numerical values are assigned to letters involved in the expressions (procedural aspect);

- as an object whose form can be described and with which operations, such as simplifying, factoring, substituting into another expression, etc., can be done (structural aspect).

Considering the structural aspect of algebraic expressions is required for instance when determining of the equivalence of two expressions is at stake. However, in the teaching of algebra at the secondary level of French school system, the structural aspect of algebraic expressions is less “visible” for the students and is often suppressed by the procedural aspect.

A description of an algebraic expression in natural language leads to considering its structural aspect: for example the expression (2x + 1) (x - 4) is described as a product of a sum and a difference, a sum of the product of 2 by x and 1, and the difference of x and 4. The first word of the sentence gives the form of the expression. A tree representation of an algebraic expression presents a certain “proximity” to the natural language representation. It allows highlighting the form of an algebraic expression, which is given by the highest level assembler. In this scenario, the activities are designed to allow the students to explore the structure of algebraic expressions using first the natural language and the tree representation of algebraic expressions. These two representation systems will then be linked to the usual symbolic language representation.

The innovative aspect of this scenario lies in the use of Aplusix educational software, which provides a microworld where students can use both tree and symbolic language representations of algebraic expressions.