Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we…

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…

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…

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…

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.…

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…

We assessed the efficacy of two spatial learning programs grounded in early years learning pedagogical theory to improve numeracy performance in preschool. Engagement with a play-based spatial program led to better overall spatial reasoning and transferred to better numeracy compared with a business-as-usual control, underscoring the importance of…

Current reforms in geometry seek to challenge prevailing ideas about "what it means to do mathematics" (p. 139) by engaging learners in "the grasping of space" (p. 241). This study takes up this challenge by investigating problematizing activity as an embodied phenomenon among 21 eighth-grade learners who engaged with spatial…

Counting is fundamental to early mathematics. Most studies of teaching counting focus on teachers observing children count. The present study compares mathematical ideas that 12 PK, transitional kindergarten (TK), and kindergarten teachers noticed from observing their own students count during a classroom session of Counting Collections with ideas…

What does it mean to be "good-at-math," and how is it determined? Cobb et al. (2009) defined the normative identity of mathematics classrooms as the obligations that students must meet to be considered good-at-math. Obligations are negotiated between teachers and students through series of bids. Normative identities reveal distributions…

We present the evolving fraction conceptions of two elementary school children with mathematics learning disabilities (MLD). We use qualitative analyses to capture the mathematical knowledge and experiences of each child and show how teaching was used to support advancement of their fractional reasoning. Results illustrate two viable pathways of…

Images of mathematics and mathematicians are often negative and stereotyped. These portrayals may work to construct our impressions of mathematics and influence students' identity with and future participation in the subject. This study examined young adult fiction as a context in which school mathematics is portrayed and constructed. I used…

Recent international studies have found that teachers' attitudes, biased against historically marginalized groups, predict lower student achievement in mathematics (e.g., van den Bergh et al., 2010). It is not clear, however, if or how teachers' racial attitudes affect their evaluation of students' mathematical thinking to produce these effects.…

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…

The belief that mathematics ability is a fixed trait is particularly common and may be a key reason for many students' disinterest and underperformance in mathematics. This study investigates how mathematics teaching practices might contribute to students' beliefs about mathematics ability being a fixed or malleable trait (mindset). Through a…