Mathematics

The language involved in de-contextualized integer comparisons poses challenges, as students may interpret “most” based on absolute values rather than on order. Using the context of temperature, we explored how students’ integer value comparisons differed based on question phrasing (which temperature is hottest, most hot, least hot, coldest, most cold, least cold) and on numbers presented (positive, negative, mixed). Participants included 88 second graders and 70 fourth graders from a rural school district in the Midwestern USA, and each student solved 36 integer comparisons.

This study investigated relationships between changes in certain types of coaching knowledge and practices among mathematics classroom coaches and how these explain changes in the attitudes, knowledge, and practice of the teachers they coach. Participants in this study were 51 school-based mathematics classroom coaches in the USA and 180 of the teachers whom they coached between 2009 and 2014. The participating coaches were recruited from schools that hired their own coaches independently from this research project.

Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations—their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations.

Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations—their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations.

Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations—their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations.

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data from a cycle of design-based research about building students’ understanding of covariation.

Case studies from the FAACT project.

Understand students’ fraction concepts through interview tasks.  Includes tasks and guide to record student thinking.