Representation and Structure
Representations and structures ‘stand for’ the mathematical object (cf. Duval, 2006; Golding and Shteingold, 2001) and make visible different aspects and characteristics of it. Hence, in order to see different facts of the corresponding mathematical objects and to develop and appropriate concept image, usually several of such representations have to be integrated (Ainsworth, Bibby, and Wood, 1998; Duval, 2006; Even, 990; Goldin and Shtenigold, 2001; Janvier, 1987; Tall, 1988).
– Cited in Dreher and Kuntze 2014
When introducing and developing the understanding of a concept, children need to experience multiple representations in order to build an understanding of what it is, what it isn’t and how it connects to other aspects of mathematics. With each new representation that children experience, careful thought needs to be put into how it is introduced, what mathematics will be highlighted and how it will be interpreted within the class. Links need to be made explicit in order for children to notice.