Statistics education has begun to mature as a discipline distinct from mathematics education, creating new perspectives on the teaching and learning of statistics. This commentary emphasizes the importance of coordinating perspectives from statistics education and mathematics education through boundary interactions between the two communities of…

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to…

In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for…

The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. The authors conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical…

The NCTM Research Committee invited Richard Lesh, instrumental in the founding of the NCTM Research Presession, to join the members of the current Research Committee in reflecting on its formation, the hopes he and others had in mind when they started it, and the current state and future of research in the field.

This commentary articulates the need to investigate problems of mathematics instruction at community colleges. The authors briefly describe some features of this often-ignored institution and the current status of research. They also make an argument for how investigations of instruction in this setting can both advance understanding of this…

Although policy documents promote teaching students multiple strategies for solving mathematics problems, some practitioners and researchers argue that struggling learners will be confused and overwhelmed by this instructional practice. In the current exploratory study, we explore how 6 struggling students viewed the practice of learning multiple…

We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for learners while they extend their numeric domains from whole numbers to include negative integers. In particular, we highlight 2 key subsets of integer reasoning: understanding or…

In this article we report 3 experiments demonstrating that a simple booklet containing self-explanation training, designed to focus students' attention on logical relationships within a mathematical proof, can significantly improve their proof comprehension. Experiment 1 demonstrated that students who received the training generated higher…

A growing body of literature has identified quantitative and covariational reasoning as critical for secondary and undergraduate student learning, particularly for topics that require students to make sense of relationships between quantities. The present study extends this body of literature by characterizing an undergraduate precalculus…

This study of early-career teachers identified a significant relationship between upper-elementary teachers' mathematical content knowledge and their students' mathematics achievement, after controlling for student- and teacher-level characteristics. Findings provide evidence of the relevance of teacher knowledge and perceptions for…

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…

This article describes how teachers in a professional development course responded to what they noticed about children's participation in elementary mathematics classrooms and how what they noticed was connected to the teachers' positionality toward equitable mathematics pedagogy. Findings suggest that a lens of participation supported…

This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…

Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack.…