This paper substantiates the notion of inclusive materialism by illustrating the role of signs and micro-perception in the learning process of multiplication. Inclusive materialism, offered by de Freitas and Sinclair, considers mathematical learning a process of becoming a learning assemblage, which embodies various materials in a Deleuzian sense.…

This study is part of the international survey studies on teachers' beliefs concerning the integration of children's literature in mathematics teaching and learning, and this paper reports the findings of the thematic analysis of open-ended survey responses elicited from 287 primary school teachers and teacher trainees in Taiwan. Using the seminal…

What are the effects of teaching the dominant mathematics on the wholeness and integrity of the cultural, social and linguistic resources of diverse communities? In this text, I seek to capture the risks associated with utilising non-Western resources in the teaching of the dominant mathematics in order to elucidate possible types of harms that…

Mathematics educators have shown increasing interest in theorizing knowing and learning as something alive or as something that comes alive through the involvement of the body. Almost all current efforts attempt doing so by focusing on the body in which the otherwise invisible living being exhibits itself, thereby failing to consider everything…

In this paper, we draw on the contemporary perspective of inclusive materialism offered by de Freitas and Sinclair to contribute to current discussions on the role of the body in the learning of mathematics. Using the notions of "distributed agency" and "assemblage," we illustrate the way in which three students engage with a…

The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical…

There is ample evidence that reasoning about stochastic phenomena is often subject to systematic bias even after instruction. Few studies have examined the detailed learning processes involved in learning probability. This paper examines a case study drawn from a large corpus of data collected as part of a research project that dealt with the…

A deep understanding of students' learning processes is one of the core challenges of research in mathematics education. To achieve this, different theoretical lenses are available. The question is how these different lenses compare and contrast, and how they can be coordinated and combined to provide a more comprehensive view on the topic of…

We argue that dialogic theory, inspired by the Russian scholar Mikhail Bakhtin, has a distinct contribution to the analysis of the genesis of understanding in the mathematics classroom. We begin by contrasting dialogic theory to other leading theoretical approaches to understanding conceptual development in mathematics influenced by Jean Piaget…

This paper investigates the nature of the interaction between the teacher and students as they worked on different mathematics activities in a single classroom over a 10-month period. Sociocultural theories and the Vygotskian zone of proximal development provide the main framework for examining the teaching and learning processes and explaining…

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through…

This article is written from our perspective as both researchers and mathematics teacher educators, and describes how our knowledge has grown as we engage concurrently in both teaching and research. Reflection-on-action is a means for us of approaching the relationship between theory and practice that comes out of the development of our work as…

The relationship between mathematical education (ME) and critical education (CE) is considered. Three alternatives in ME are discussed: structuralism, pragmatism, and process-orientation. These are related to key terms of CE to show the extent to which ME and CE contradict each other: there is no integration between the two. (MNS)

This paper addresses one approach to reconciling theory, research, and practice, namely, a multitiered teaching experiment involving a models and modelling approach to learning. The four-tiered teaching experiment explored in this paper involves participants at different levels of development who work interdependently towards the common goal of…

Different types of hierarchies in the learning of mathematics and criteria by which they might be judged are examined. Current works on mathematical learning hierarchies are illustrated and in particular the work of the mathematics team of the research project "Concepts in Secondary School Mathematics and Science" is examined. (MP)