Responsiveness to students' mathematical thinking is a characteristic of classroom discourse that reflects the extent to which students' mathematical ideas are present, attended to, and taken up as the basis for instruction. Using the Mathematically Responsive Interaction (MRI) Framework and data from 11 middle-grades classrooms, we illustrate…

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…

We build on mathematicians' descriptions of their work and conceptualize mathematics as an aesthetic endeavor. Invoking the anthropological meaning of practice, we claim that mathematical aesthetic practices shape meanings of and appreciation (or distaste) for particular manifestations of mathematics. To see learners' spontaneous mathematical…

Caring for student affect when teaching social justice mathematics (SJM) is important because discussions of social inequities may elicit emotional responses from students. This article extends previous conceptualizations of SJM, which typically encompass dual goals of teaching dominant and critical mathematics, by theorizing a third set of…

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…

Teachers' noticing of classroom activity shapes who is invited to participate, who is valued, and whose forms of knowing are included in mathematics classrooms. We introduce a framework for multidimensional noticing for equity that captures the stretch and expanse of teachers' attention and sense making of the local, sociocultural, and historical…

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…

Teacher evaluation policies have been central to policy efforts to enhance teaching quality. At the same time, ambitious mathematics instruction has been emphasized by teacher education programs as well as by the Common Core State Standards. Drawing on observation and survey data from early-career teachers, this study examines how teachers'…

This article addresses why instructors choose to not use inquiry-oriented instructional practices (IO-IPs) even if they believe the practices are beneficial. A national sample of undergraduate mathematics instructors (N = 269) responded to questionnaires on their use of IO-IPs, beliefs on student learning, and recognition of professional…

This article investigates the implementation of inquiry-oriented instruction in 20 undergraduate mathematics classrooms. In contrast to conventional wisdom that active learning is good for all students, we found gendered performance differences between women and men in the inquiry classes that were not present in a noninquiry comparison sample.…

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…

Empirical evidence exists that enhancing students' language can promote the mathematics learning of multilingual students at risk, whereas other target groups (e.g., monolingual students, successful students, both with diverse academic language proficiency) have hardly been considered. This cluster-randomized controlled trial (N = 589)…

This article contributes to the larger narrative around what makes a mathematics professional development (PD) successful and in what ways. We share a research-based PD model that was implemented in elementary schools in an urban school district for 3 years. The model uses a pseudo lesson study approach and emphasizes standards-based instruction.…

The purpose of this commentary is to acknowledge, illuminate, and counter the noticeable silences in the investigations of mathematics education researchers who conduct equity research with Black communities and other marginalized groups. For far too long, these communities have experienced a lengthy and complicated history of structural barriers;…

In this article, we use a two-dimensional assessment to examine the experimental impacts of a mathematics learning trajectory-oriented formative assessment program on student strategies for problems involving multiplication and division. Working from the theory that the development of students' multiplicative reasoning involves improvements in…