An analysis of concepts in mathematics
Concepts are a core feature of mathematics and mathematics education. But a new thesis shows that within mathematics education there are differing views on what a concept is and how it should be defined.
Concepts are often described as the building blocks of mathematics. School mathematics courses contain a whole host of concepts, such as addition, triangles and derivatives. Students are also expected to develop their conceptual understanding, such that they are able to describe, use and understand the links between concepts. But what is a concept? In her thesis, Lotta Wedman has analysed how key scientific texts in the field of mathematics education define and use the word ‘concept’.
“There are two main views on what a concept is. The first view is that concepts are mental representations or images that students develop as they experience the world. More broadly, shared images – for example of what a triangle is – are created within society. The second view takes concepts to be abstract objects that can be used as building blocks in mathematics, for instance. In this second view, concepts can be described with the help of definitions,” says Lotta Wedman.
In the scientific texts on mathematics education that were analysed in the theses, the two views are sometimes mixed, so that one sentence in which concepts are mental representations might be followed by one in which concepts are abstract objects. This makes the texts difficult to understand.
Lotta Wedman hopes that her thesis can help to create a clearer definition of concepts and conceptual understanding within the field of mathematics education research. This may in turn lead to a clearer picture of what we want students to learn in mathematics lessons. One question raised by the differing views is how concepts are structured, in other words what the relationships between different concepts look like:
“There are currently differing views on how concepts link up with each other and what relationships are important for solving mathematical problems. When studying the concept of a rectangle, for example, one might ask whether it is enough to know about the relationship to other quadrilateral shapes such as the square and the parallelogram, or whether relationships to concepts such as perimeter, area and multiplication have a role to play. The matter of how students form conceptual structures is something that could merit further investigation,” says Lotta Wedman.
Lotta Wedman, tel: + 46 76318021, email: firstname.lastname@example.org
Lotta Wedman is defending her dissertation The concept concept in mathematics education: A concept analysis at the Department of Pedagogical, Curricular and Professional Studies on Friday 11 September.