Chapter 13: Needs Versus Demands: Some Ideas on What It Means to Know Mathematics in Society

Why do we have to learn the division of two fractions? This is a simple question from students, nevertheless causing trouble to mathematics teachers all over the world. But, do they really have to be prepared for answering specific questions like this about any mathematical concept, formula and method? As an educator, I find it important that future mathematics teachers know about the justification problem and are prepared to discuss the global problem: Why teach—and learn—mathematic at all. I see this as a prerequisite for going into a dialogue with pupils about local problems like: Why learn to divide fractions in lower secondary school in Sweden? Any answer to the global problem providing reasons for teaching mathematics may be economic, cultural, technological, political, ideological, historical etc. (Jensen, Niss, & Wedege, 1998). Thus, any answer is value based and, furthermore, any reason given is based on an idea of the content in mathematics education. It is not possible to reflect upon the question why without engaging with the question what and vice versa. “Why” is tangled with “what” in mathematics education and, in any discussion about reasons for teaching and learning mathematics, the issue of content is present, explicitly or implicitly. Thus, the philosophical issue behind any justification debate in mathematics education is about the nature of mathematics and on knowing mathematics. That is the reason why the teacher students in Malmö read Paul Ernest’s article, Relevance versus Utility: Some ideas on what it means to know mathematics (Ernest, 2004).