This paper aims to reveal the potential of inferentialism, an emerging philosophy in mathematics education, to extend contemporary constructivist research regarding conceptual development. Going against the traditional view of a notion as the name of a corresponding concept and a constructivist way of naming second-order models, we provide a new…

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…

The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…

Outlines the approach of a study that aimed to observe young children as they constructed meanings for randomness in computer-based setting. Provides a snapshot of two children working with the tools made available in that setting. Uses this picture to begin the formulation of a theoretical framework for the construction of meaning in one…

Begins with the assumption that by practicing something one often learns something else. A discussion is presented on the historical and social development of knowledge, the cognitive development of students, the role of teachers, and the meaning of learning situations. (PK)