Considerable research has been conducted on the critical role of gesture and action in children's mathematical thinking. However, teacher professional development (PD) has not tended to include specific supports for attending to nonverbal student thinking. In this Brief Report, we argue for including supports for multimodal teacher noticing in…

Changes in U.S. textbooks indicate that U.S. first-grade students in the Common Core era were exposed to a wider variety of word problem types than students in previous generations were. We compared the performance of U.S. first graders in the Common Core era with that of previous generations in solving 11 types of additive word problems to…

We conduct a critical review to explore how research on mathematics classroom assessment has positioned students (127 studies, 2015-2020). Our analysis shows how research has positioned students as passive recipients of assessment by portraying assessment through discourses of measurement and cognition. Conversely, students are positioned as…

A follow-up of a cluster-randomized trial evaluated the long-term impacts of a scale-up model composed of 10 research-based guidelines grounded in learning trajectories. Two treatment groups received the intervention during the prekindergarten year, and one of these groups received follow-through support in kindergarten and first grade.…

Emergent graphical shape thinking (EGST) involves interpreting or constructing a graph as dynamically generated, which is useful across science, technology, engineering, and mathematics fields. Although evidence suggests that students as young as middle school can engage in EGST with support, other research indicates most college students and U.S.…

Algebra has been identified as a gatekeeper to careers in STEM, but little research exists on how algebra appears for practitioners in the workplace. Surveys and interviews were conducted with 77 STEM practitioners from a variety of fields, examining how they reported using algebraic functions in their work. Survey and interview reports suggest…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

This study examined the prevalence of teacher tracking in a population of 1,822 mathematics teachers in 184 high schools in a single state. Results showed that 70% of teachers were tracked by course level, course track, or both. Three fourths of high schools tracked at least 58% of their mathematics teachers. We also found significant differences…

This exploratory study investigated the behaviors and content of onscreen calculator usage by a nationally representative sample of eighth-grade students who responded to items from the 2017 National Assessment of Educational Progress mathematics assessment. Meaningful features were generated from the process data to infer whether students…

Many mathematics educators believe a goal of instruction is for students to obtain conviction and certainty in mathematical statements using the same types of evidence that mathematicians do. However, few empirical studies have examined how mathematicians use proofs to obtain conviction and certainty. We report on a study in which 16 advanced…

Generalizing is a critical aspect of mathematics learning, with researchers and policy documents highlighting generalizing as a core mathematical practice. It can also be challenging to foster in class settings, and teachers need access to better resources to teach generalizing, including an understanding of effective forms of instruction. This…

Multiply minoritized learners face racialized, gendered, and ableist hierarchies of mathematical ability that shape the organization of schools and classrooms and can significantly challenge access to identities as mathematical learners and practitioners as well as to fundamental human dignity. Classrooms and everyday interactions can perpetuate…

This article presents a philosophical and pragmatic critique of critical mathematics (CM) and current vocational mathematics (VM) in the United States. I argue that, despite differences, CM and VM advocates share the view that the inauthentic contextualization of secondary mathematics does particular harm to students from historically marginalized…

We investigated how the time elementary preservice teachers (PSTs) spent studying certain mathematics topics during teacher education coursework was related to performance on teaching-related tasks administered after graduation. In two studies, participants completed tasks assessing their specialized content knowledge (SCK) for teaching 12…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…