We constructed and calibrated an instrument targeting conceptual and procedural fraction knowledge. We used this instrument in a quantitative study with 126 secondary students (7th and 9th graders), testing the hypothesis that there are individual differences in the way students combine the two types of knowledge. Cluster analysis revealed four…

The cognitive significance of the body has become one of the major topics in current psychology. However, it is our contention that claims about the embodied nature of thinking must come to terms with the problem of the relationship between the body as a locus for the constitution of students' subjective mathematical meanings and the historical…

This study investigated how integrating social justice issues, STEM practices, and mathematics may support equity in mathematics education. We analyzed video of four lessons focused on inverse trigonometry and disability rights from a STEM project-based geometry class. Using an established observation protocol, we identified themes related to…

This study shares two frameworks for analyzing teacher actions that support students in generalizing and examines how those frameworks align with teacher questioning. One classroom teaching episode focused on the mathematical activity of generalizing is shared to illustrate effective generalizing promoting practices. We found several patterns of…

Backward transfer is when learning about a new topic influences an individual's prior ways of reasoning about a topic they previously learned about. This study looked at how quadratic functions instruction differentially influenced students' prior ways of reasoning about linear functions. Specifically, we compared students at three levels of…

We present an analysis of three 9th grade integrated mathematics lessons in which a group of teachers and researchers redesigned a sequence of lessons with the goal of engaging a linguistically diverse group of students in productive and powerful discussions (Herbel-Eisenmann et al. 2013). The three lessons were part of a design experiment. Two…

This study reviews how slope is developed in expository materials across a seven-textbook series. Slope development is analyzed using a framework of five slope components to describe which components are used and connected, and by investigating accompanying levels of covariational reasoning. Findings suggest that the series describes slope from…

We describe results of a long-term design experiment focused on promoting mathematics learning among multilingual ninth graders classified as English Learners. The intervention at a linguistically diverse public high school in the US focused on a unit introducing concepts related to linear rates of change. We analyze results from a…

This study employed hierarchical linear modeling to investigate the student- and school-level factors associated with the secondary mathematics achievement of English language learners (ELLs) and non-ELL students among a nationally representative sample of ninth graders in the United States. While certain characteristics, such as socioeconomic…

Facilitating productive mathematical argumentation is challenging; it is critical to develop a specific guiding vision of practices to help teachers learn to teach argumentation. However, what counts as acceptable classroom-based mathematical argumentation remains an open question. In this study, building on Habermas' theory of communicative…

Current reform efforts challenge teachers to create more student-centered classrooms focused on high quality classroom discourse (NCTM, 2014). There are difficulties, however, teachers face in bringing this vision to fruition. Over the past three years, we have worked with a group of 7-12 teachers supporting their efforts to implement high quality…

Supporting students' in-the-moment perseverance is a vital objective in mathematics education because it promotes learning with understanding. Yet, little is written about if and how student perseverance can improve over time. I examine the specific ways in which secondary students improved their perseverance as they engaged with challenging…

To disrupt patterns of marginalization that play out through interactions in math classrooms, teachers need to identify and address inequities in student participation, both in terms of participation outcomes and processes. In this study, I take an expansive view of participation and examine how the "quiet" participation of one 9th grade…

This study investigated how the use of structured participation, specifically group presentation roles, supported more equitable participation in doing and learning mathematics. We analyzed videos of two lessons focused on radius, diameter, circumference, and area of circles in which students worked in small groups in a STEM project-based geometry…

Quantifying angularity is critical for the study of K-12 school mathematics and beyond; yet, quantifying angularity is challenging for individuals across these grade levels. Using data from a yearlong teaching experiment with ninth-grade students, I address the role of attentional motion in quantifying angularity and present four such motions…