Elementary

Bostic, J., Matney, G., Sondergeld, T., & Stone, G. (2018, November). Content validity evidence for new problem-solving measures (PSM3, PSM4, and PSM5). In T. Hodges, G. Roy, & A. Tyminski (Eds.), Proceedings for the 40h Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1641). Greenville, SC.

In this study we investigate the teaching of the associative property in a natural classroom setting through observation of classroom video of several elementary math classes in a large urban school district. Findings indicate that the associative property was often conflated with the commutative property during teaching. The role of the associative property in many computational tasks remained fully implicit, even after the property had been formally introduced.

This study explores how preservice teachers (PSTs) transfer the intended specialized content knowledge (SCK) to elementary classrooms. Focusing on the case of the associative property of multiplication, we compared three PSTs’SCK during enacted lessons in fourth grade classrooms with their own learning in professional development (PD) settings. Findings revealed the PSTs’ successes and challenges in unpacking an example task, especially in areas of making connections between concrete and abstract representations and asking deep questions that target quantitative interactions.

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.

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.