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…

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…

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…

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…

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…

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'…

This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. I defined the enactment of cognitively demanding tasks to involve task selection and maintenance of the cognitive demand of high-level tasks and examined those two…

This article introduces an interview-based instrument that was created for the purposes of characterizing the visions of high-quality mathematics instruction of teachers, principals, mathematics coaches, and district leaders and tracking changes in those visions over time. The instrument models trajectories of perceptions of high-quality…

Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…

The current era of common curriculum standards, increased accountability, and rapid expansion of technology within a complex and highly charged political context has influenced changes in assessment practices in mathematics classrooms. This research commentary situates high-stakes assessments in a historical context, discusses recent advances in…

Research in experimental and developmental psychology, cognitive science, and neuroscience suggests that tool fluency depends on the merging of perceptual and motor aspects of its use, an achievement the authors call "perceptuomotor integration." Just as expertise in playing a piano relies on the interanimation of finger movements and…

Amid debates about the continued salience of gender in mathematics, this report summarizes an IES-funded investigation of gender-related patterns in the Early Childhood Longitudinal Study-Kindergarten Class of 1998-99 (ECLS-K). Girls' and boys' mathematics achievement, confidence, and interest were examined, along with experiences at…

The authors examined curricular effectiveness in high schools that offered parallel paths in which students were free to study mathematics using 1 of 2 content organizational structures, an integrated approach or a (traditional) subject-specific approach. The study involved 3,258 high school students, enrolled in either Course 2 or Geometry, in 11…