In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…

Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

In this writing, I report on how two 12-year old children used fraction strips to add 1/2 and 2/5. In their interaction with the tool, I look for the emergence of the tool-mediated Zone of Proximal Development to analyse the knowing that become available to the children. In thinking about this interaction, I ask what is the role of the more…

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

As members of a research group taking initial steps for creating mathematics curriculum in an Indigenous language (Yakama Ichishkíin), we engaged with an unanticipated outcome: the ways Indigenous identities and homelands are fractionated, as part of ongoing colonizing harm. Our work centers on how mathematics instruction can help heal, by…

Discusses formalizing in mathematics and provides anecdotal illustrations of formalizing in a constructivist environment, using students aged 12 and 8 involved in fraction work. (Contains 19 references.) (MKR)

Analyzes two transcripts of children's mathematical behavior to observe the nature of recursive levels and interrelationships among them. Describes several levels of the recursions. (YP)

Discusses the concept of symmetrisation--the mental process in which individuals are not able to distinguish separate entities--in relation to students freezing before a mathematics problem. Examines whether the development of the concepts of fraction and equation in two mathematics textbooks addresses the problem of symmetrisation. (MDH)

Presents activities developed for teacher training courses for the middle school level that integrate mathematics history with the selected topics of number systems, fractions, and geometry. The activities seek to give relevance to history and to motivate and deepen students' understanding of the evolution of mathematical concepts. (MDH)