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.…

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…

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 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…

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)

Presents and investigates a theoretical perspective on the development of understandings of mathematical operations with a particular focus on addition. Presents a case study on the development of a young boy and concludes that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking. Contains 46…

Task performance experiments concerning properties of mathematical groups with 10 and 11 year-old children are discussed including transfer effects, effects of structural relations, individual differences, and memory (both short and long term). (JG)

An analysis of a 10-minute episode in which 7-year-old students (n=3) engage in collaborative small group activity is presented to explore the relationship between individual learning and group development. Students learned as they interactively constituted situations for justification or validation, yielding an institutionalized solution method.…