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Effective mathematics teaching involves eliciting and interpreting student thinking, and then using students' current understandings as a basis for instruction. Research indicates these skills are not innate but can be acquired through structured experiences. In this article, we describe the development and implementation of an interview module aimed at supporting secondary preservice teachers' ability to elicit and use evidence of student thinking. Analysis of preservice teachers' noticing of student thinking across components of the interview module demonstrated positive benefits of the assignment. We share our design considerations and results, and offer potential adaptations to the module for other mathematics methods instructors interested in using the module to develop secondary preservice teachers' ability to notice student thinking.

This manuscript presents findings from a study about the knowledge for and planned teaching of standard deviation. We investigate how understanding variance as an unbiased (inferential) estimator -not just a descriptive statistic for the variation (spread) in data -is related to teachers' instruction regarding standard deviation, particularly around the issue of division by n-1. In this regard, the study contributes to our understanding about how knowledge of mathematics beyond the current instructional level, what we refer to as nonlocal mathematics, becomes important for teaching. The findings indicate that acquired knowledge of nonlocal mathematics can play a role in altering teachers' planned instructional approaches in terms of student activity and cognitive demand in their instruction.

Research-based guidelines for learning variation exist (e.g., Franklin et al., 2007; Garfield, delMas, & Chance, 2007), but little is known about how teachers plan to teach standard deviation, or how these plans align with recent recommendations. In this article, we survey lesson plans designed by in-service and preservice secondary mathematical teachers. We report on the accuracy, technology usage, and visual representations in the lesson plans. We consider how many elements are used, the level of conceptual development, and the mathematical nature. Findings support differences between preservice and master’s level students in education, as well as a tendency by in-service teachers to teach in alignment with prior learning experiences, despite professional development. Implications for teacher education and curricular development are offered. First published May 2018 at Statistics Education Research Journal Archives