Investigating a teacher-perspective on pedagogical mathematical practices: possibilities for using mathematical practice to develop pedagogy in mathematical coursework.

One of the challenges of university mathematics courses in secondary teacher preparation is incorporating pedagogical discussions. The focus in a mathematics course is—and should be—on mathematics. But research also suggests that without addressing pedagogical implications these content courses are not meaningful to secondary teachers' future classroom practice. The thrust of this paper is exploring ideas for how to leverage mathematical practice in university mathematics courses—and, in particular, what have been described as Pedagogical Mathematical Practices (PMPs). The paper reports on a study of (n = 10) pre- and in-service mathematics teachers that explored the viability of the PMP construct, with the intent of specifying particular PMPs. Drawing on interviews with teacher participants who had recent experiences in an inquiry-oriented discrete mathematics course, the study reports on the ways in which they identified a set of mathematical practices as being productive pedagogically. The study contributes a teacher-perspective on the construct of PMPs, including the identification of four PMPs from the study data: explicit visualization; multiple approaches; concrete exemplification; and informal justification. Implications for their potential use in university mathematics courses with regard to teacher education are discussed. [ABSTRACT FROM AUTHOR]