This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students' mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students' mathematical potential, quality…

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 book is about promising research advancements that sparked directly or indirectly from intellectual contributions by distinguished internationally recognized mathematics educator and researcher, Edward A. Silver. The features of this book include: (1) A focus on the research areas that have benefited from Dr. Silver's intellectual…

In this chapter, I propose a stance on learning fractions as multiplicative relations through reorganizing knowledge of whole numbers as a viable alternative to the Natural Number Bias (NNB) stance. Such an alternative, rooted in the constructivist theory of knowing and learning, provides a way forward in thinking about and carrying out…

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…

In this chapter, we focus on the difficulties children face when learning place value and how current psychological theories of relational learning may be leveraged by teachers. We discuss two major psychological mechanisms known to support relational learning--statistical learning and structure mapping--and review the evidence showing how these…

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…

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…

This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and…

Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…

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 unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

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…