In this presentation, the intention is to make a contribution to the existing research on algebra learning by presenting a new theoretical approach, variation theory. From a variation theory perspective (Marton & Tsui, 2004), learning is seen as a function of how the learner’s attention is selectively drawn to critical aspects of the object of learning. A critical aspect is the capability to discern aspects presented, for example in algebraic structures by experiencing them. To experience a rational expression is to experience both its meaning, its structure (composition) and how these two mutually con¬stitute each other. So neither structure nor meaning can be said to precede or succeed the other. If these aspects are not focused on in a teaching situation or in textbooks, they remain critical in the students' learning. The chosen theory will be exemplified by presenting results from a case study (included in a longitudinal study) concerning the simplification of rational expressions.

The research questions in this article are: (1) What aspects are discerned by the students when simplifying rational expressions?; (2) Does classroom instruction using the variation theoretic approach have any positive impact on students’ learning of factorising rational expressions? If so, what is the magnitude of the impact?; (3) How does classroom instruction using this approach impact students’ learning of factorising rational expressions?; (4) What actually happens inside the classroom when the variation theory approach is used?

The presentation is based on data collected, during a 3-year period, in a development project. The analysis is grounded in 30 exercises and 12 written reports which refer to simplifying rational expressions. Initial analysis entailed coding student responses for types of discerned aspects and the teachers report for types of focused aspects.

The findings suggest that developing an understanding of the students’ critical aspects can be a productive basis in helping teachers make fundamental changes to their instructions and improve the mathematical communication in the classroom.

The communication in the classroom succeeds or not depending on the opportunities offered in the classroom to work out the meaning of the whole by knowing the meaning of the simple parts, the semantic significance of a finite number of syntactic modes of composition, and recognizes how the whole is built up out of simple parts.