Symbolic Use Of Quantitative Representations In Young Children

MARTÍ, EDUARDO; SCHEUER, NORA; DE LA CRUZ, MONTSERRAT

“Show me what you know” Exploring representations across STEM disciplines

Teachers College Press

Lugar: Nueva York; Año: 2013; p. 7 - 21

We present a study designed to explore the emergence of children’s use of symbolic figurative representation of quantity (dots). How and when they begin to use very simple quantitative information in a representational way? We have chosen a very simple (i) symbolic means, (ii) numerical interval and (ii) symbolic task. i) Since research has shown that establishing one to one correspondences between symbols and reality seems to be a primitive basis to represent quantitative information, we use an iterative system based on identical dots as quantitative symbols. (ii) Since previous studies have shown that preverbal children can establish distinctions among collections of 1, 2 and 3, we have restricted the quantities we present to that number. (iii) We have adopted a pragmatic sense of representations: representations as instructions for regulating activity. Therefore, we ask: at which age children can interpret and use this kind of numerical representations? In our study children between age 2;11 years- and 4;1 years were invited to play a game where a horse goes forward along a path, as many steps as dots are on the upper face of a specially designed die (with one blank face, one face with a single dot, two with two dots and two with three dots). At first, the interviewer throws the die and asks the child to move the horse forward as many steps as dots appear on the die (none, 1, 2 or 3). These “die – steps” tasks are combined with “steps – die” ones, where children are asked to indicate the face of the die corresponding to the number of steps the horse should move in order to arrive at a milestone (his watering through). We present a pilot study with 17 children distributed among three main age groups (2; 11 to 3;1 / 3;5 to 3;7 / 3;11 to 4;1). All children were interviewed individually in the Kindergarten class at public schools at Bariloche, Argentina, during aprroximately 15 minutes. Results show a clearcut progress from the youngest to the oldest age groups: only some of the oldest children were just beginning to flesh out the game in both directions (die to steps and steps to die). However, in general terms, following the quantitative instruction (die to step) was easier than selecting it (step to die). Response patterns included the inability to regulate the number of steps according to the dots on the die; the categorical distinction between presence and absence of dots (that is, no steps are given when the blank face appears, one or more steps are given when at least 1 dot is visible); the distinction between no dots, 1 dot or more than 1 dot (no step is given, 1 step is given, several steps are given); a numerical and additive regulation of the steps. We discuss these results in the frame of models of symbolic and numerical development.