Natural language is known to play a crucial and specific role for children's learning in school mathematics. Not only does it carry special vocabulary, but subtle differences between natural languages may lead to surprising challenges, for instance, for learners who are not taught mathematics in their mother tongue. In this paper, the…

Students' proficiency in the language of instruction is essential for their mathematical learning. Accordingly, language-responsive instruction, which includes adapting teaching material to students' language needs, is thought to promote mathematical learning, particularly for students with lower levels of proficiency in the language of…

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…

This study investigated how 46 pre-service teachers (PSTs) planned for differentiation of instruction in mathematics. Content analysis was utilized to explore the differentiation strategies included and student characteristics considered in PST plans and how PSTs used differentiation strategies and student characteristics to differentiate lesson…

Definitions play an important role in mathematics by stipulating objects of interest to mathematicians in order to facilitate theory building. Nevertheless, limited research has examined how mathematicians approach writing definitions or the values of the mathematical community that are upheld through norms related to definition use and writing.…

This paper introduces the term "explorative mathematical argumentation" (EMA), signifying a concept for describing and analysing learners' mathematical argumentation processes. Despite multiple recent empirical evidence for argumentation promoting learning in science education, still little is known about the development of early…

In this contribution, we address the gap that has appeared in mathematics education research and practice with the emergence of dynamic geometry environments and build on the opportunities these environments offer to school geometry. In our qualitative empirical study, we investigate how to elaborate on the general model of conceptual knowledge to…

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…

Instructors manage several tensions as they engage students in defining, conjecturing, and proving, including building on students' contributions while maintaining the integrity of certain mathematical norms. This paper presents a case study of a teacher-researcher who was particularly skilled in balancing these tensions in a laboratory setting.…

The notion of definition is a central building block of mathematics. In addition to specific definitions, it is desirable that students learn about meta-mathematical aspects of definitions such as their role of classification, and about characteristics of definitions such as arbitrariness. We investigated how such meta-mathematical aspects emerge…