ABSTRACT
Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. In this chapter, the authors describe the ways that traditional mathematics pedagogy reinforces these disciplinary misconceptions, and outline the relevant research on emerging signature pedagogies of mathematics. In the traditional pedagogy of first-year undergraduate mathematics during most of the twentieth century, instructors lectured on facts and theorems that they carefully wrote on the chalkboard, and then presented solutions to related practice items. A component of any signature pedagogy in mathematics must include instructional and assessment techniques that address conceptual knowledge and promote perseverance in problem-solving situations. Additionally, SoTL research is needed that replicates works cited in the chapter and extends the current research by looking for associations between changing beliefs and instructional strategies. Continued scholarly investigation of teaching and learning in mathematics depends on the interaction of mathematicians and mathematics educators.
