The concept concept in mathematics education: A concept analysis

Abstract

The notion concept is used in different ways within the field of mathematics education. The aim of this study is to carry out a concept analysis of the notion concept, within some frequently used frameworks describing conceptual understanding. Building on a philosophical literature review resulting in distinctions that can be used for interpreting views on concept, the study addresses the question: Which views on concept may be found in texts using the chosen frameworks, from the perspective of the distinctions mental versus non-mental, intersubjective versus subjective and molecular versus holistic? The design involves a literature review in mathematics education, resulting in a selection of texts. Views on concept, and to some extent on concept image, conception, and schema, are then interpreted with the help of indicators, and represented in 3D matrices. There are two categories of views on concept within the texts: a mental and intersubjective category, and a non-mental and intersubjective category. One difference between the views is whether conceptual structures have molecular or holistic features. Concerning the notions concept image, conception, and schema, there are generally three different views: an individual view and two culturally dependent views. The different views are sometimes combined. One result is findings regarding how language is used within the texts, where non-mental and mental arenas, and terms and meanings of terms, are not always distinguished. The main contribution of the study is to deepen the understanding of views on the notion concept and how terminology is used in mathematics education. This opens the way for a discussion of how the terminology mentioned above may be used coherently within the field of mathematics education.