for the learning of mathematics

an international journal of mathematics education

Yusuke Uegatani ,  Hiroki Otani - Vol. 43 Num. 3 (2023)
 An inferentialist view of notions and concepts


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 view of the process of conceptual learning: Notions appear first, followed by concepts, which generate the next sentence. Arguing that learning is not an input—but rather an output—in a social environment, we, like constructivists, place value on learners’ creativity and potential to go beyond socially regulated knowledge.