Day by Day: Investigating Variation in Elementary Mathematics Instruction That Supports the Common Core

The Common Core State Standards for Mathematics (CCSS-M) aim to engage students in complex mathematical practices, including modeling, reasoning, and argumentation. Currently, little is known about how teachers’ daily instruction supports these practices. This study draws upon data from daily logs completed by third-, fourth-, and fifth-grade mathematics teachers from 39 states to learn about students’ engagement in standards-aligned mathematical practices. We find that there are both substantial fluctuations in students’ engagement in these practices and reported cognitive demand from day to day, as well as large differences across teachers. Practices in which students engage are related to teachers’ perceptions of student ability. These findings offer a broad perspective on how CCSS-M–based instruction unfolds across a range of states and policy environments.

Developing Teacher Candidates' Formative Assessment Practices

This chapter describes an initiative to better prepare teacher candidates to use formative assessment practices in their elementary mathematics instruction. Specifically, the initiative involved a curriculum and pedagogical redesign of an elementary mathematics methods course sequence. During the redesign implementation, the instructors intentionally modeled formative assessment practices for teacher candidates and had teacher candidates complete scaffolded field-based assignments in their elementary field placement classrooms in order to practice formative assessment strategies. Throughout the chapter, there are illustrative examples of how the instructors implemented this initiative as well as how teacher candidates carried out the formative assessment practices in their settings. The chapter concludes with a discussion about teacher candidate growth and challenges when learning about and implementing formative assessment practices in mathematics.

Leadership Development Through Design and Experimentation: Learning in a Research–Practice Partnership

A core function of district leadership is providing instructional vision and support for school leaders and teachers. In this article, a Research–Practice Partnership focused on the improvement of elementary mathematics teaching and learning provides the context to study leadership development. We examine the process of one design team within the Research–Practice Partnership consisting of district leaders and university researchers using organizational learning. We found that as the team iteratively negotiated the design and implementation of a practical measure aimed at assessing and improving elementary mathematics instruction system-wide, the team’s learning transformed the tools and routines of its work.