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…

Encouraging students to develop multiple solutions for given problems is an important way to improve mathematical knowledge. However, the influence of this teaching element on students' interest-related motivational orientations is an open question. In this article, we report the results of an experimental study (N = 145) that was carried out…

This study is a longitudinal look at the different mathematics placement profiles of Black students and White students from late elementary school through 8th grade. Results revealed that Black students had reduced odds of being placed in algebra by the time they entered 8th grade even after controlling for performance in mathematics. An important…

This study investigates relationships between teacher characteristics and teachers' beliefs about mathematics teaching and learning and the extent to which teachers claim awareness of their students' mathematical dispositions. Regression analyses revealed statistically significant relationships between teachers' beliefs and…

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…

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 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…

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…

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…

Identity is an important tool for understanding students' participation in mathematics lessons. Researchers usually examine identity at a macro-scale: across typical classroom activity and in students' self-reports. However, learning occurs on a micro-scale: in moments during a lesson. To capture identity in these moments, I used…

The release of the Common Core State Standards for Mathematics and their adoption across the United States calls for careful attention to the alignment between mathematics standards and assessments. This study investigates 2 models that measure alignment between standards and assessments, the Surveys of Enacted Curriculum (SEC) and the Webb…

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…

This study examined the effect of 2 types of mathematics content organization on high school students' mathematics learning while taking account of curriculum implementation and student prior achievement. Hierarchical linear modeling with 3 levels showed that students who studied from the integrated curriculum were significantly advantaged…

This study investigated the development of length measurement ideas in students from prekindergarten through 2nd grade. The main purpose was to evaluate and elaborate the developmental progression, or levels of thinking, of a hypothesized learning trajectory for length measurement to ensure that the sequence of levels of thinking is consistent…