In this paper, we draw on our recent research to inspect again some of the theoretical perspectives we have been using to analyze data and to characterize teaching-learning in university settings. We focus particularly, within a sociocultural perspective on Activity Theory and the construct the "Teaching Triad," seeking to embed the…

Over the last three decades, educational researchers and policymakers have increasingly promoted instructional strategies that centralize group work in mathematics. One difficulty teachers face in implementing group-based instruction in mathematics involves facilitating meaningful group interaction amongst students. In this paper, we explore…

The notion of multilingual students' first language has been advocated as a resource in mathematics learning for some time. However, few studies have investigated how implementing students' L1 in the teaching practice impacts multilingual students' mathematics learning opportunities. Based on a 9-month-long ethnographic study conducted in Iran, we…

Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These…

Definitions play an integral role in mathematics and mathematics classes. Yet, expectations for definitions and how they are intended to operate, i.e., mathematical norms for definitions, can remain hidden from students and conflict with other discursive norms, explaining differences in mathematicians' and students' understandings of the nature of…

Mathematical induction is a powerful method of proof, taught in most undergraduate programs involving mathematics and in secondary schools in some countries. It is also commonly known to be complex and difficult to comprehend. During the last five decades, mathematics education research has produced numerous studies on the learning and teaching of…

Gestures are one of the ways in which mathematical cognition is embodied and have been elevated as a potentially important semiotic device in the teaching of mathematics. As such, a better understanding of gestures used during mathematics instruction (including frequency of use, types of gestures, how they are used, and the possible relationship…

In this paper, we are interested in a dynamic vision of diagrams, focusing on their evocative power, their force in mathematical activity and their potential for interaction with mathematical objects. We are inspired by the work of C. S. Pierce to see diagrams as "inscriptions that organise space and articulate relations" and that of the…

This study investigates the characteristics of Japanese primary school mathematics lessons that adopt a problem-solving approach. We argue that these characteristics are reflected in three key aspects: collective teaching and learning, the lesson as a "drama" (i.e., its structured flow), and the focus on mathematical knowledge. In this…

This study proposes a model of several dimensions through which products of teachers' context-based mathematics problem posing (PP) can be modified. The dimensions are Correctness, Authenticity, Task Assortment (consisting of Mathematical Diversity, Multiple Data Representations, Question-Answer Format, Precision-Approximation, and…

We attend to the composition of even and odd functions, as featured in imagined dialogues between a teacher and students, composed by sixteen teachers in a professional development program. Data were analyzed as aimed at addressing students' intellectual needs, with particular attention to the need for causality and the need for certainty. The…

The importance of integrating history into mathematics education is widely recognised in the literature and advocated in curricula worldwide, including in China. However, under the influence of the long-standing centrally designed curricula, teachers in China are accustomed to content- and teacher-centred examination-driven teaching practices.…

The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

Within the commognitive perspective, ritual and explorative routines are used in a very particular way to distinguish students' routines according to whether they are driven by social reward or by generating a substantiated narrative. Explorative routines in this theorisation may refer not to inquiry-based activity but to the result of a student's…

To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…