In the past year, we have used this space to tackle a chronic and important concern in mathematics education: how to increase the impact of research on practice. Because of the unique nature of this issue of JRME, we pause to address the critical idea of replication in educational research. In later issues, we will continue our primary theme and consider how the ideas raised in this editorial can further our understanding of the relationships between research and practice.
Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats noticing as a complex phenomenon that is distributed across individual cognition, social interactions, material resources, and normed practices. Specifically, this research demonstrates that different centers of focus emerged in two middle grades mathematics classes addressing the same content goals, which, in turn, were related conceptually to differences in student reasoning on subsequent interview tasks. Furthermore, differences in the discourse practices, features of the mathematical tasks, and the nature of the mathematical activity in the two classrooms were related to the different mathematical features that students appeared to notice.
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