This paper conceptualizes children’s mathematical thinking from a materialist perspective on language and mathematics. This perspective considers human and non-human bodies as ontologically equivalent; that is, as both being agentive, vibrant, and animated, thus resisting static representations. This conceptualization is an alternative to the interactionist and language-based models that have dominated research in language and mathematics. This conceptual approach informs the paper’s non-hierarchical analysis of a bilingual classroom studying the concept of equivalent fractions. The non-hierarchical nature of this analysis permits a dynamic shift of focus from learners to materials to mathematical concepts. This non-traditional analysis informs the paper’s final discussion regarding the nature of children’s mathematical thinking. The discussion highlights how working outside language-based interactionist models provides an alternative view of children and artefacts as equal partners working within and as part of the vibrant boundaries between matter and meaning.

本文从对语言和数学的唯物主义角度概念化了儿童的数学思维。这种观点认为人体和非人体在本体论上是等效的。也就是说，既具有代理性，活力又充满活力，因此可以抵抗静态表示。这种概念化是主导语言和数学研究的交互论和基于语言的模型的替代。这种概念性方法为本文对研究等效分数概念的双语教室的非层次分析提供了参考。这种分析的非分层性质允许动态地将焦点从学习者转移到材料再到数学概念。这种非传统的分析使本文对儿童数学思维的本质进行了最后的讨论。