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…

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…

Slow faculty uptake of research-based, student-centered teaching and learning approaches limits the advancement of U.S. undergraduate mathematics education. A study of inquiry-based learning (IBL) as implemented in over 100 course sections at 4 universities provides an example of such multicourse, multi-institution uptake. Despite variation in how…

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students'…

In many STEM-related fields, graduating doctoral students are often expected to assume a postdoctoral position as a prerequisite to a faculty position, yet there is no such expectation in mathematics education. This phenomenon is likely due in large part to an abundance of faculty positions; however, it may also result from the field's…

This study examined the relationship between high school mathematics curricula and student achievement and course-taking patterns over 4 years of college course taking for a sample of over 10,000 students from 32 postsecondary 4-year institutions. Three types of curricula were studied: National Science Foundation (NSF) funded curricula, the…

How issues of power and identity play out in mathematical practices are described by Na'ilah Suad Nasir and Maxine McKinney de Royston. Their article offers a perspective on how to better understand the sociopolitical nature of teaching and learning mathematics. They present data from studies of mathematics teaching and learning in…

This article describes teachers' collective work aimed at learning to teach mathematics for social justice. Teacher interviews, discussions, lessons, and written reflections were analyzed using grounded theory methodology, and teachers' conversations were examined concerning the relationship between mathematical goals and social justice…

This study investigated the processes used by prospective mathematics teachers as they examined middle-school students' work solving statistical problems using a computer software program. Ways in which the model may be used by other researchers and implications for the design of pedagogical tasks for prospective teachers are discussed. (Contains…

This study investigates 3 preservice secondary mathematics teachers' understandings of limits of sequences and their changing conceptions of limit during and after instruction involving interactive, dynamic sketches embodying the formal definition of the limit of a sequence. Manipulating a coherent visual representation of the formal definition in…

This study investigated introductory calculus students' spontaneous reasoning about limit concepts guided by an interactionist theory of metaphorical reasoning developed by Max Black. In this perspective, strong metaphors are ontologically creative by virtue of their emphasis (commitment by the producer) and resonance (support for high degrees of…

Sets of mathematics problems are generally arranged in 1 of 2 ways. With "blocked practice," all problems are drawn from the preceding lesson. With "mixed review," students encounter a mixture of problems drawn from different lessons. Mixed review has 2 features that distinguish it from blocked practice: Practice problems on the same topic are…