Meaningful collaborative interactions in asynchronous online mathematics teacher professional development (PD) may provide teachers with valuable opportunities to learn. We studied collaborative interactions in online teacher PD activities that involved embedded videos, prompts, discussions, and multiple online tools. Analysis of teacher responses…

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…

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…

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…

This article shows that enabling teachers to integrate comparing solution strategies into their teaching fosters student flexibility in algebra. We designed two professional development (PD) programs that either focused exclusively on comparing solution strategies, or additionally introduced the accountable talk approach to guiding productive…

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…

This article presents the results of a design-based research study related to slope that took place in a high school algebra 1 classroom. In the study, students explored situations related to making predictions. As students engaged with these situations, they reinvented and made meaningful multiple subconstructs of slope. I present the findings in…

Our field has generally reached a consensus that active-learning approaches improve student success; however, there is a need to explore the ways that particular instructional approaches affect various student groups. We examined the relationship between gender and student learning outcomes in one context: inquiry-oriented abstract algebra. Using…

Research has demonstrated that textbooks exert a considerable influence on students' learning opportunities and that technology has the potential to transform mathematics instruction. This brief report provides a systematic analysis of how technology tasks are integrated into secondary mathematics curricula by analyzing a sample of 20 textbooks.…

Precalculus and calculus are considered gatekeeper courses because of their academic challenge and status as requirements for STEM (science, technology, engineering, and mathematics) and non-STEM majors alike. Despite college mathematics often being seen as a neutral space, the field has identified ways that expectations, interactions, and…

We compared students' learning gains in authentic seventh-grade classrooms (N = 144) in 4 different interventions that incorporated a computer game that aims to teach players to solve linear equations. Significantly higher learning gains were measured in the implementations that were specifically designed to mediate the attribution of algebraic…

Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the…

This research focuses on the retention of students' algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3-5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly…

One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion,…

In this Research Commentary, the author explores what is meant by "teaching for understanding" and delves into these questions: How does teaching for understanding interact with the backgrounds of the students who experience it or the attributes of the contexts in which they learn? Which empirical findings are context dependent, and…