Abstract
This paper synthesises research from three separate studies, analysing how different representations of a mathematical concept may affect young children’s engagement with mathematical activities. Children between five and seven years old engaged in counting objects, identifying triangles and completing repeating patterns. The implementation of three counting principles were investigated: the one-to-one principle, the stable-order principle and the cardinal principal. Children’s reasoning when identifying triangles was analysed in terms of visual, critical and non-critical attribute reasoning. With regard to repeating patterns, we analyse children’s references to the minimal unit of repeat of the pattern. Results are discussed in terms of three functions of multiple external representations: to complement, to constrain and to construct.
Highlights
Young children begin to learn mathematics by examining their environment
In this paper we review studies of young children engaging with concrete, figural and tablet representations of three mathematical concepts: counting objects, identifying triangles and completing repeating patterns
When the caps were presented in a circle, two of the children said “I don’t know”, without even attempting to count the items. This points to children who may not have experience counting objects that are not arranged in a set order
Summary
Young children begin to learn mathematics by examining their environment. How many cookies has mom placed on their plate? What shapes are the cookies? Does the plate have some kind of pattern around its edge? From these interactions, children begin to form concept images. How many cookies has mom placed on their plate? According to Vinner and Hershkowitz (1980), visual representations, impressions and experiences make up the initial concept image, while formal mathematical definitions are usually added at a later stage. The introduction of touch-screen tablets has added representations that combine the visual and the manipulative; the need to take into consideration the coordination of eye and hand movements (Sinclair & de Freitas, 2014). Sinclair and de Freitas (2014) describe a child who sees “seven-ness”, which the simultaneous touch on the screen has made possible. Add to this scenario sound, such as one click each time one dot appears on the screen, and there is an interplay between three senses: seeing, hearing, and touch
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