Background: Groupwork is a desirable activity in mathematics classrooms for the opportunity it creates for collaborative reasoning and interdependence. Correlations between group-level processes and outcomes have helped characterize the features of more successful groups, but group-level constructs can obscure how students negotiate ideas. This…

Background: Calculus instruction is underexamined as a source of racialized and gendered inequity in higher education, despite research that documents minoritized students' marginalizing experiences in undergraduate mathematics classes. This study fills this research gap by investigating mathematics faculty's perceptions of the significance of…

Background: Supporting students during collaborative learning in mathematics is challenging for teachers. We developed the Small-Group Scaffolding Tool (SGS-Tool) to assist teachers regarding how and when to offer support. The tool is based on three characteristics of scaffolding small groups at the group level: contingency to the…

Background: Educational video games are increasingly used in classrooms because they can offer meaningful contexts for problem solving. However, educational video games bring together two historically disparate activities: school mathematics and video games. How these two activities complement, compromise, or contradict each other influences how…

Background: This study considers the moment-bymoment mathematics discourse of teachers and students and the relationship of these discourses to student learning. I focus on the discursive constructs of responsiveness to students' mathematical thinking and the intellectual work in teacher and student discourse. Responsiveness to students'…

Background: We explore how school-based mathematical experiences shape out-of-school mathematical experiences, developing the idea that learners hybridize norms and practices around authority and evaluation across these two contexts. To situate our study, we build on constructs of participatory identity and framing. Methods: Drawing from a large…

Background: When mathematics teachers embrace the call for pedagogical change, instructional shifts are likely to unfold in complex ways. While we typically view teachers as leading this process, within a figured worlds framework, students play active roles in negotiating the identities, rights, and obligations of all members of a classroom in the…

Teaching students to reason with data is not a totally new enterprise. A small but insistent statistics education community has been studying the process for decades. This commentary provides an introduction to some major themes of that research, in order to provide common ground for conversations between learning sciences researchers and those…

Research suggests that troubleshooting activities that require students to reflect on teacher-crafted erroneous examples; i.e., erroneous solutions to problems that correspond to widespread naïve ideas, are beneficial to learning. One possible explanation to these beneficial effects is that troubleshooting activities encourage students to test the…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

Conceptualizing numbers as discursive constructs generated in, and for the sake of, communication, we investigated the development of the numerical discourse of Milo, a boy who was 2 years and 8 months old when we first met him and whom we then followed for 18 months. Our analyses of the child's evolving responses to the question "Where is…

We present the analysis of an episode of mathematical problem solving in a group, where data came from multiple advanced recorders, including multiple video cameras, Smartpen recorders, and mobile eye tracking glasses. Analysis focused on a particular group that was ineffective in their problem-solving process. Relying on the commognitive theory…

This study examined whether learning with heuristic worked examples can improve students' competency in solving reality-based tasks in mathematics (mathematical modeling competency). We randomly assigned 134 students in Grade 5 and 180 students in Grade 7 to one of three conditions: control condition (students worked on reality-based tasks),…

Presenting novices with examples and problems is an effective and efficient way to acquire new problem-solving skills. Nowadays, examples and problems are increasingly presented in computer-based learning environments, in which learners often have to self-regulate their learning (i.e., choose what type of task to work on and when). Yet, it is…

Teacher learning is a huge challenge in instructional change, but relatively little work has carefully examined the mechanisms by which teachers learn, in contrast to the extensive work on programs that help teachers learn and the high-leverage instructional practices that are strong predictors of student learning. Specifically, relatively little…