Rina Hershkowitz

Arguably, all educational research is conducted with the goal of improving teaching and learning. However, research may not explicitly suggest implications for practice. Furthermore, teachers may not be convinced by findings based on academic theories and methods of analysis that are foreign to them. This suggests that findings of such research may have a low level of implementability. We posit that replication of research by teachers can lead them to findings that are more implementable for them. In this article we elaborate the notion of implementability of educational research findings, make a theoretical case for teachers’ qualitative replication of basic research, and offer the notion of pedagogical sensemaking as the activity by which research findings may become implementable for teachers. We investigate this practice based on empirical data gathered in a graduate course for practicing teachers, who were required to replicate a well-known piece of basic research in mathematics education. The impact sheet to this article can be accessed at 10.6084/m9.figshare.27151317.

This chapter focuses on how the interplay between the practices of researching and teaching can help to foster development of knowledge about and for mathematics teaching. It will treat researching and teaching, researcher and teacher, simply as convenient typifications, recognizing the possibility that institutions and individuals may participate in both practices and take on both roles. Moreover, as the previous sentence illustrates, this chapter will reserve practice for use in the sense of social practice; it will employ the more direct terms teacher and teaching to refer to what some sources speak of as practitioner and practice. Building on the view widely held amongst mathematics educators that any communal knowledge base for mathematics teaching should draw both on craft knowledge created within the practice of teaching and on scholarly knowledge created within the practice of researching, the particular focus of this chapter will be on synergy between these practices, and on knowledge conversion between them.

Artifacts both mediate our interaction with the world and are objects in the world that we reflect on. As computer-based artifacts are generally intermingled with multiple praxes, studying their use in praxis uncovers processes in which individuals, the community, and tools are involved. In this article, we examine a now common computer-based artifact in mathematics classrooms, the representative. This artifact is often in continual transformation in the course of action during school activities. We document how several praxes with representatives mediate the construction of meaning. We show that the ambiguity of computer representatives regarding the examples and concepts they are meant to represent boost this construction. The construction of meaning of mathematical functions is described as a process that occurs through social interaction and the interweaving of the ambiguous computer-based artifacts. We show that this construction depends heavily on intentional design of activities by the teacher, lea...