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SURVEY PAPER

The relationship between mathematical practice and mathematics pedagogy in mathematics education research Keith Weber1   · Paul Dawkins2 · Juan Pablo Mejía‑Ramos1 Accepted: 1 June 2020 © FIZ Karlsruhe 2020

Abstract 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. Keywords  Instructional design · Mathematics instruction · Mathematical practice · Methods

1 Introduction Many mathematics educators believe that mathematicians’ practice should inform the way that mathematics is taught to students. In particular, many mathematics educators maintain that classrooms should be organized so students participate in similar activities and engage in similar interactions to those that mathematicians do (e.g., Ball & Bass, 2000; Lampert, 1990; Harel & Sowder, 2007; Schoenfeld, 1992; Sfard, 1998; Weber, Inglis, & Mejía-Ramos, 2014; see Skovsmose, 2020, for a dissenting viewpoint). As such, some mathematics educators believe that understanding how mathematicians engage in mathematical practice has implications for how mathematics classrooms should be organized, and thus they believe that research into mathematicians’ practice is relevant for mathematics education. For a more comprehensive discussion, see Schoenfeld (1992).

* Keith Weber [email protected] 1



Graduate School of Education, Rutgers University, 10 Seminary Place, New Brunswick, NJ 08901, USA



Texas State University, San Marcos, TX, USA

2

Because some mathematics educators perceive a link between mathematicians’ practice and mathematics instruction, research into how mathematicians practice their discipline exists as a legitimate branch of mathematics education research, at least to the extent that articles investigating mathematical practice appear in leading mathematics education journals. In the last two decades, the journal Educational Studies in Mathematics has published inquiries into how mathematicians solve problems (Carlson & Bloom, 2