Abstract
We introduced instrumental realism as an epistemological approach aimed at analysing changes in the language of mathematics. According to this approach, we can distinguish changes of language of four different kinds.
From the perspective of instrumental realism, the task of mathematics education is to induce changes of all four kinds in the learner's cognitive system. Different approaches to mathematics education (constructivism, realistic mathematics, hermeneutic approach, genetic method) differ in the didactic importance they attach to each kind of these changes.
The quality of an approach can thus be judged by how successfully it induces each of these kinds of change in the learner's mind. We assume that the cognitive changes that a teacher induces in the mind of a pupil when teaching mathematics are analogous to the cognitive changes that occurred in the minds of the mathematicians who discovered the concepts, procedures, and knowledge that we teach pupils today.
If this assumption is correct, a knowledge of history enables us to realize the complexity of the changes that the teacher seeks to induce in the mind of the pupil. The aim of this article is to attempt an analysis of genetic constructivism from the perspective of instrumental realism.
We want to show that genetic constructivism contains the didactic means to induce authentic cognitive changes of all four kinds in the pupil's mind. Our analysis is a kind of epistemological reconstruction, focusing on the conceptual structure of genetic constructivism.
It is therefore not indicative of the empirical content of the theory under investigation, but we believe that refining our understanding of the conceptual structure of genetic constructivism will allow developing a clearer picture of the parameters that will need to be taken into account in its empirical scrutiny.