Yeo, Amelia

2023, Meng, Rui, Yeo, Amelia, Ding, Meixia, Alibali, Martha W.

Mathematics instruction often involves multiple representations of concepts. Understanding connections among representations is a hallmark of conceptual understanding. In this research, we examine how teachers connect representations in elementary mathematics lessons about equality. We focused on three first-grade mathematics lessons from China, because students in China generally demonstrate a relational conception of the equal sign (i.e., interpreting it as indicating “sameness” or the idea that two expressions have the same quantity). We sought to understand how teachers in China support students’ acquisition of this conceptual understanding. Teachers used a wide variety of different representations in lessons about equality, including counters, picture equations, number words, and symbolic equations. Teachers expressed links between representations repeatedly and in multiple ways, and they frequently engaged their students in co-constructing links. Teachers expressed most links multi-modally, frequently using gestures, actions, and drawing to indicate the linked representations and to highlight correspondences between them. The sequence of linking episodes within each lesson tended to follow principles of “concreteness fading”, starting with more concrete representations and progressing to more abstract ones. The findings suggest new directions for the analysis of mathematics instruction, both within and across cultures.