Abstract
How can we understand the structure of mathematics in the context of school mathematics? It appears that there are challenges in teaching and learning mathematics that relate to its structure. This paper examines the structure of mathematics in the context of school mathematics and the need to explore and understand the structure of mathematics in relation to the school subject. The three dichotomies of inductive/deductive, defining/proving and arbitrary/necessary are used to elaborate on the structure of mathematics in the context of teaching and learning in school. Here I will explain these dichotomies while referring to the new school curriculum in mathematics in Norway and to the nature of mathematical argumentation in general. This will show that there is a bias towards the deductive side of mathematics, while the aspects that are inductive and arbitrary are overlooked. The analysis in this study points out the importance of the potential in developing mathematics teaching that nurtures the student’s feeling for mathematics and mathematical reasoning, while taking into account the entanglement of these three dichotomies that we witness in school mathematics.
