Taking a socio-cultural perspective, in this study we explored the challenges toddlers might face as they practice 1-1 correspondence in the playful context of setting a table, and how different individuals may participate in this playful activity. Findings indicated that toddlers' competence in carrying out one-to-one correspondence may be…

How students build mathematics knowledge together in classrooms is of central concern in research focused on the role of language in learning and doing mathematics. This paper explores how students compose mathematics knowledge together in relation to the social construction of influence. Drawing on the influence framework (Engle et al. in J Learn…

We present exploratory analyses of three cases in which groups of four (quartets) worked with video recordings of choreographed performances from the opening ceremony of the 2016 Rio Olympic Games. We asked quartets to view the recordings, explain what performers were doing by reenacting what they noticed in the video, and create their own…

This paper illustrates how the academic literacy in mathematics framework (Moschkovich, J Math Behav 40:43-62, 2015) can be used to uncover the multiple layers of work bilingual learners accomplish during mathematical discussions. Using this framework allows researchers to examine students' joint mathematical activity in terms of mathematical…

This paper aims to investigate the following question: How do students use mathematics in modeling activities? With this purpose, the paper reports on mathematization and use of mathematics, and deals with empirical data with focus on modeling activities performed by students in the first year and in the fourth year of a degree in mathematics.…

In this paper, we offer a theoretical account of the emotion-cognition dialectic (i.e. the unit of feeling and cognition in thought) in identity formation (or identification), focusing on early childhood and mathematics. We consider how contradictory (emotional-cognitive) experiences which arise in different forms of mathematical activity (a…

This paper is centred around a framework for studying teaching--Mediating Primary Mathematics (MPM)--developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the…

We articulate a student perspective on task design in mathematics education, foregrounding a dynamic relationship between intentions of task designers, teachers, and students. First, we characterize a student perspective on task design. Second, we provide theoretical perspectives that we use as tools to account for different facets of task design…

The way in which mathematics is communicated and represented in schools (including the written language, symbols and diagrams of mathematics textbooks and the verbal/spoken classroom interaction itself) constructs particular views of the nature of mathematics and expectations about students' participation in mathematical activity. In a previous…

In an ethnomathematics-based program there exists the need for teachers to identify pedagogical actions in the form of teaching-learning practices. In this theoretical paper we outline a curriculum proposal based on D'Ambrosio's "Trivium," composed of "literacy," "matheracy," and "technoracy." The Trivium…

In this paper, we emphasize the methodological challenges of analyzing data with/in an enactivist framework in which (1) all knowing is doing is being, while focusing on, (2) how an entry by the observer transforms usual ways of analyzing data. In this sense, the association of knowing with doing suggests a shift in attention away from what…

Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

Contemporary theories of expertise development highlight the crucial role of deliberate practice in the development of high level performance. Deliberate practice is practice that intentionally aims at improving one's skills and competencies. It is not a mechanical or repetitive process of making performance more fluid. Instead, it involves a…

The design research programme learning by imitative and creative reasoning (LICR) studies whether, how and why tasks and teaching that enhance creative reasoning lead to a more productive struggle and more efficient learning than the common but inefficient task designs based on imitating given solution procedures. The purpose of this paper is to…

Contemporary curriculum demands the development of both problem solving skills and negotiative skills required for collaborative group work. Tasks are required that create the best possible conditions for students to develop both of these skill sets. Open-ended tasks have been shown to provide these conditions, but they also require the teacher to…