The purposes of this study were (a) to test the efficacy of whole-class equal-sign instruction, (b) to contrast the effects of symbolic and nonsymbolic instructional representation, (c) to determine whether visual representation compensated for language deficits, and (d) to evaluate maintenance of intervention. We randomly assigned 195 children…

Using restricted-use data from the 2011 National Assessment of Educational Progress mathematics assessment, the current study examined the relationship between the presence of elementary mathematics coaches and specialists (MCSs) and the mathematics achievement of more than 190,000 fourth-grade students in more than 7,400 schools nationwide. In…

Students with disabilities (SWDs) perform below their peers in math on national and state assessments. The quality of teachers who provide these students with math instruction is an unexamined variable that could influence this low achievement. We used data from more than 1 million students to compare the quality of teachers assigned to teach math…

Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., "add," "more," "triangle"). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary…

The purpose of this longitudinal study was to investigate the relationships between mathematics teacher preparation and graduates' analyses of classroom teaching. Fifty-three graduates from an elementary teacher preparation program completed 4 video-based, analysis-of-teaching tasks in the semester before graduation and then in each of the 3…

The nature of mathematical activity and discourse that teachers foster in classrooms is likely influenced by their explanations of sources of students' difficulty. Several small-scale qualitative studies suggest that how teachers make sense of student difficulty matters for whether they engage all of their students in rigorous mathematical…

The goal of this study was to describe fraction-calculation errors among fourth-grade students and to determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low-, average-, or high-achieving). We…

This article illustrates an argument-based approach to presenting validity evidence for assessment items intended to measure a complex construct. Our focus is developing a measure of teachers' ability to analyze and respond to students' mathematical thinking for the purpose of program evaluation. Our validity argument consists of claims addressing…

We investigated the alignment between a teacher survey self-report measure and classroom observation measure of ambitious mathematics instructional practice among teachers in two urban school districts using two different standards-based mathematics curricula. Survey reports suggested mild differences in teachers' instructional practices between…

Central to ambitious teaching is a constellation of practices we have come to call "leveraging student thinking." In leveraging, teachers position students' understanding and reasoning as a central means to drive learning forward. While leveraging typically is described as a feature of mature practice, in this article we examine…

As videos of teaching become increasingly available and used as tools for analyzing classroom practice, it is important for researchers and practitioners to reflect on the nature and purposes of video representations of teaching. Too often classroom videos are made and viewed in ways that narrow interpretations about the nature and quality of…

An intervention experiment served to evaluate the efficacy of highly guided discovery learning of relations underlying add-1 and doubles combination families and to compare the impact of such instruction with minimally guided instruction. After a pretest, 78 first graders were randomly assigned to one of three intervention conditions: highly…

This study used ECLS-K 1998-1999 data to evaluate whether specific kindergarten teaching practices predicted school-year learning gains differently, depending on children's ethnicity, SES, and fall test scores. Exploratory factor analyses guided the creation of four literacy and five math instruction composites from teachers' reports of their…

Many districts are using content-focused coaching as a strategy to provide job-embedded support to teachers. However, the current coaching literature provides little guidance on what coaches need to know and be able to do to engage teachers in activities that will support their development of ambitious instructional practices. Furthermore, little…

Mathematics standards expect students to communicate about mathematics using oral and written methods, and some high-stakes assessments ask students to answer mathematics questions by writing. Assumptions about mathematics communication via writing include (a) students possess writing skill, (b) students can transfer this writing skill to…