We investigate teacher beliefs about discourses for equation solving and the challenges these beliefs might pose for the implementation of instructional practices that promote deductive reasoning in algebra. To uncover these beliefs, we recorded three video explanations of solutions to the same linear equation with distinct discursive…

This study focused on issues of equity related to small-group participation in a distance learning calculus class. Equity is defined as the fair distribution of opportunities for students to participate and learn. I examined how opportunities for mathematical and social participation were constructed through acts of positioning for four students.…

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…

The development of proofs and argumentation is one of the major standards for mathematical practices in K-12 education that researchers and practitioners alike are continuing to improve. Further, the use of discourse is considered essential in the learning of mathematical concepts at these levels. However, K-12 educators continue to confound how…

In this paper we frame our observations in enactivism, specifically problem posing, to propose the notion of problem drift as a method to analyze the curriculum generating actions of small group learning systems in relation to teacher interventions intended to trigger specific content goals. Teacher attentiveness to problem drift is suggested to…

In this case study, we examine the usage of language -- how teachers used and regulated their language when teaching English language learners (ELLs) with learning disabilities (LD) how to solve mathematics multiplication problems. We focus on types of scaffolds used by teachers to identify how scaffolding helps ELLs with LD build better…

In this study, we explore four, second graders' performances on integer addition problems before and after analyzing contrasting cases involving integers. The students, as part of a larger study, participated in a pretest, small group sessions, one short whole-class lesson on integer addition, and a posttest. Based on their integer mental models…

This paper explores the nature of students' quantitative reasoning and conceptions of functions supporting their ability to symbolize quadratic function rules, and the meanings students make of these rules. We analyzed middle school students' problem solving activity during a small group teaching experiment (n = 6) emphasizing quadratic growth…

In a developmental research approach, from a sociocultural position, we address the meanings students make of mathematics in teaching sessions and how this relates to the intentions of the teacher and approaches to teaching. Analyses of data come from small group tutorials of one tutor with first year university mathematics students (n=5). We…

The aim of this paper is to report early findings from university mathematics teaching in the tutorial setting. The study addresses characteristics of the teaching of an experienced research mathematician and through interviews, her underlying considerations. An analysis of a teaching episode illuminates her use of generic examples to reveal…

This paper uses a socio-political practice perspective of mathematics to investigate the action of first year university students as they work in small groups to explain the meaning of mathematical objects in "practical terms". Written transcripts representing video recordings of the action were analysed using critical discourse analysis…

This research reports on data and analysis investigating the sharing of ideas and strategies from the level of a small group to the level of the whole class (and vice versa) in a fourth grade mathematics classroom utilizing digital technology. This research takes a sociocultural perspective positioning meaning and learning as shaped by mediational…

Small group interactions can provide rich conceptual mathematical understandings. This paper reports on the mathematical talk of Maori and Pasifika students as they participated in small group activity. The findings illustrate that when the students were scaffolded to work collaboratively the talk shifted between focusing on mathematics…

Enacting tasks at high levels of cognitive demand helps preservice teachers make sense of mathematical ideas and serves as a model for instruction. Small group discussions can be useful pedagogical tools for maintaining a task's cognitive demands. In this article, we contrast two small group discussions within a preservice elementary classroom to…