The relationship between mathematical practice and mathematics pedagogy in mathematics education research

This paper introduces two central questions (1) what are available methodologies for making claims about mathematical practice and (2) when and how do claims about mathematical practice influence mathematics instruction. To motivate these questions, we critically analyze the relationship between research into mathematicians’ practice and the design of mathematics instruction in three ways. First, we describe three influential research programs in mathematics education and illustrate how each research program uses claims about mathematical practice to inform their instructional goals. Second, by examining these important works, we highlight intrinsic difficulties in investigating mathematical practice. Our conclusion is that every research methodology for investigating mathematical practice is fundamentally limited and we require triangulation from multiple methods and theoretical lenses to fully understand mathematical practice. Third, we highlight reasons for why mathematical practice sometimes should not inform mathematics instruction. We conclude this paper by discussing how the articles in this special issue address our two central questions.