The author has been influenced throughout his time in mathematics education by the work of Caleb Gattegno. Gattegno made extensive use of the word awareness whereas much educational literature from a psychological perspective talks about memory (for example, Justicia-Galiano, MartÌn-Puga, Linares & Pelegrina, 2017). This has, amongst other…

Earlier approaches to sense-making in mathematics have looked at the ways students comprehend a mathematical concept. Recent research suggests that some students make sense not only of mathematical objects that have a being, but also of objects that have yet to become. In such cases, learning mathematics is not just an act of comprehending a given…

This comment on Gascón & Nicolás (2017) explores relationships between mathematics education research and conceptualizations of time. Using Fabian's critique of temporal perspectives in anthropological research (1983) and Lemke's framework of timescales (2000), we consider ways in which implicit attitudes towards time in research can position…

In this paper, we provide an elaboration of the notion of mathematical structure -- a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and…

Multiplication can be presented to students through different models, each one with its pros and cons. In this contribution we focus on the repeated sum and the array model to investigate the relations between the two models and those between them and multiplication properties. Formal counterparts are presented. Taking both a mathematical and…

In this theoretical paper, I examine the similarities and incommensurabilties between studies using the term "beliefs", and discursive frameworks studying "identity". I start by reviewing critiques against beliefs research voiced from discourse and socio-culturally oriented researchers in the field of mathematics education. I…

Modern conceptions of critique express preoccupations with obtaining certainty and truth, with establishing foundations, and with linking knowledge and rationality. Modern conceptions of critique have been challenged, and critique has taken new formats. In particular critique has developed without demands of providing foundations for knowledge and…

How are we to understand the power of certain literary metaphors? The author argues that the apprehension of good metaphors is importantly similar to the apprehension of fruitful mathematical analogies: both involve a structural realignment of vision. The author then explores consequences of this claim, drawing conceptually significant parallels…

This article describes aspects of classroom discourse, illustrated through vignettes, that reveal the complex relationship between the forms in which mathematical objects exist and their ostensive representations. We illustrate various aspects of the process through which students come to consider the reality of mathematical objects that are…

This communication supports an argument that preservice elementary teachers ought to study number language as part of their mathematics content courses, just as they study relationships between numeration and quantity. In particular, the paper spells out some ways in which number language can be seen as problematic by carefully detailing various…