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There is a diversity in the field of mathematics education regarding how the term “concept” is used. In this study, a concept analysis is carried out, analyzing the use of the notion concept in some frequently used frameworks within mathematics education. The study takes an analytic philosophic approach, using an analyzing instrument based on a philosophical literature review resulting in two distinctions used for interpreting views on concept. It was found that intersubjective positions are more common than subjective ones. Furthermore, a main diversity concerns whether concepts are mental representations that have reached a certain level of development, or non-mental abstract objects. When mental and non-mental positions are combined, it becomes difficult to consistently describe the nature of concepts. This leads to unclear theoretical frameworks, and in the long run scientific results become less useful to interpret and compare.

A mathematical problem that involves conceptual challenges, may offer students opportunities to show and develop their conceptual understanding. However, to meet specific conceptual learning goals, a deliberate design of the problem is important. In the study, a single problem is used in different versions to investigate what conceptual understanding of the concept perimeter is visualized in students’ solutions. The result shows that the chosen problem offers reasonable conceptual challenges and thus is suitable for visualizing and possibly developing students’ conceptions. Three conceptual aspects are identified and suggested to be used to support further discussions on task design: properties and definitions of concepts, the use of non-typical examples, and the relations between processes and concepts.

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.

The word ‘concept’ is used with several meanings in mathematics education. In order to obtain a coherent theoretical framework, a concept analysis of the notion concept is performed for some current frameworks in the field. The taken approach includes creating a tool for analysing views on concept, based on a literature review in philosophy. This tool uses three distinctions of views on concept: mental versus abstract, subjective versus intersubjective, and molecular versus holistic. Examples from texts in mathematics education are given, where the three distinctions are present. Further, the taken approach offers a perspective on concept that simplifies comparisons between frameworks.

There are examples of conceptual incoherencies within the field of mathematics education. In this paper, a concept analysis of the notion concept in Tall’s framework of Three worlds of mathematics is conducted. In the first phase of the study, an analysing tool is constructed from a literature review in philosophy and cognitive science. This tool makes two distinctions. One distinction is between views considering concepts as abstract and views considering concepts as mental. The other distinction is between views considering concepts as intersubjective and views considering concepts as subjective. Preliminary results show that different views on concept are mixed in the framework of Three worlds of mathematics.