In this theoretical article, we explore the possibility that instead of a mathematical connection arising "in-between" two (or more) pre-existing ideas or objects, which have presumably been known or understood, that connection is itself the motor of understanding. The standard view of connection, in which two existing ideas or concepts…

This paper reports on a teaching experiment on mathematical modelling in an upper secondary school class that investigates how the constructs of "model eliciting" and "emergent modelling" may be brought together to inform teaching and learning. A prominent role is covered by the process of task design, seen as a complex process…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

This paper presents the "Mathematics Teacher's Specialised Knowledge" (MTSK) model. It acknowledges earlier contributions to understanding and structuring teachers' knowledge, in particular, the special debt owed to Shulman's notion of "pedagogical content knowledge" and to Ball and collaborators' "Mathematical Knowledge…

This paper makes an important and original contribution to the updating of methodological approaches to research syntheses. We analysed all 813 Proceedings of the British Society for Research into Learning Mathematics from 2003 to 2018, first using a quantitative corpus-survey and qualitative thematic coding and, again, independently, using topic…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…

Children in a first-grade class who were taking their first steps in formal mathematical knowledge were given a sequence of five modelling tasks during their regular mathematics lessons. These tasks were different in nature from the problems they encountered in their textbooks. They are more complex and challenging, requiring analysis of the…

International comparisons of languages have shown how mathematical concepts can be expressed and conceptualised in different languages. For multilingual students, these findings raise the question of how the interplay of languages and conceptualisations shape multilingual learning processes. This paper presents an investigation of case studies of…

Vygotsky's work on the individual/social relation provides theoretical tools for interpreting the origins of thinking and learning. Drawing on Vygotsky's ideas and data from one classroom, categories of practice relating to teaching and learning were developed in order to identify themes for an exploration of mathematical development within the…

This article focuses on "the unexpected" in relation to teacher change. We take an enactivist approach to charting the parallel development of one teacher (Hannah) as she learnt to value and plan for unexpected events in her mathematics classroom, and one of her students as he learnt to notice and trust mathematical patterns. Shifts are…