There is a need for a more robust conceptualization of engagement in mathematics education research. Investigating how teachers describe engagement can provide insight into relationships between purposes of engagement and dimensions of engagement. In this exploratory study, we examined how 28 secondary mathematics teachers in two states in the USA talked about their students' engagement. During interviews, we asked teachers to provide their definitions for engagement, describe their teaching strategies for engaging students, and describe their observations of engagement during a video clip from their own classroom. We interpreted teachers' talk to identify how they described the nature of mathematics engagement (dimensions such as behavioral, cognitive, affective, and/or social engagement) and purposes of engagement (engagement in learning or in schooling [Harris, 2011]). When teachers described the purpose of engagement as engagement in learning, they also tended to describe the nature of engagement with cognitive and social dimensions and with multiple dimensions of engagement.

We examined the relationships between different aspects of mathematics engagement for 285 students in their first year of high school in the United States. Path Analyses were used to trace the relationships between students’ self-reported prior motivation and appraisals of control and value of mathematics, perceptions of teacher support and peer support. These variables and observed teacher and peer support as coded from video by researchers, were examined as potentially impacting students’ self-reported in-the moment affect and task-level control and value appraisals Our results showed three key contributions. First, significant paths corresponded to relationships predicted by Control Value Theory (CVT) across a particularly robust set of variables and over the course of their first semester in high school. Second, results added further nuance by considering the objects that students’ in-the-moment emotions were directed toward, showing distinctions between positive and negative emotions directed at the mathematics task, students’ teachers and peers, and selves. Third, results more closely considered the impact of both observed and perceived aspect of support from peers and teachers in the classroom, in both its academic and social forms. Implications are discussed for theory and practice. © 2022, The Author(s).

We investigated what high school mathematics teachers and their students noticed about students' mathematical engagement to develop a framework for teachers' and students' noticing of mathematical engagement. This framework offers clarity about the complexity of engagement, and it includes three elements: evaluations of the valence of engagement (whether students were engaged or disengaged), descriptions of dimensions of engagement (affective, behavioral, cognitive, instrumental, social, or relatedness), and features of engagement (interpretations of what took place in the classroom to support or constrain students' engagement). We interviewed 30 sets of high school mathematics teachers and focus groups of their students and asked them to reflect on students' engagement during a videotaped lesson from their classrooms. Results illustrate cases of how noticing of engagement between teachers and students can be shared (or not), from strongly shared (agreement on all three elements in the framework), partially shared (agreement on two elements), and minimally shared (agreement on one element). Cases of partially and minimally shared noticing of engagement suggest opportunities for teachers to learn about their students' perspectives or how to communicate with students about their intentions for engaging them.

When Katrina Lindo taught Integrated Mathematics 1 to ninth- and tenth-grade students, she encountered some students who appeared initially resistant to doing mathematics. Lindo wanted her students to see themselves as capable of making sense of mathematics. Lindo said that being a mathematician is "the process of taking what you know and using what you know to make sense of what you don't know, so we're all mathematicians." The authors had the opportunity to spend time in Lindo's classroom to discuss with her the classroom discourse that was observed. In this article, the authors illustrate discourse moves that Lindo used to engage students with mathematics. These moves are shared together with Lindo's reflections so that readers can consider ways to offer students' opportunities to develop productive dispositions and identities.

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

Spontaneous problem posing (SPP) is presented as a phenomenon central to mathematical thinking, wherein learners generate problems without formal prompting, and where posed problems originate from the learner’s motivation to improve their knowledge. Because of this, they may serve as important markers of productive mathematical engagement—in particular, affective engagement—both for problem posers and their classroom communities (D’Mello & Graesser in Learning and Instruction, 22(2), 145–157, 2012). We report on a study which utilized mixed methods to examine SPP and associated affective engagement of students in four early high school mathematics classrooms in two geographic regions of the USA. For each classroom, we used observational and experience sampling methods to examine the patterns of affect problem posers and their peers experienced at individual and group levels, respectively, on a day with at least one instance of SPP observed compared with a day with no observed instances of SPP. Results show evidence of positive affect among problem posers, while their peers reported fewer negative emotions about mathematics tasks on days with SPP than on days without SPP. Moreover, a detailed analysis of two spontaneous problem posers revealed that they showed a desire to extend their own mathematical thinking, expressed dissatisfaction with their current knowledge, and directed their problems primarily towards the teacher. Results are discussed regarding the need to support students’ confidence in their original mathematical ideas in class, and for reducing negative emotional responses to mathematics tasks. © 2020, Springer Nature B.V.