Young children's understanding of place value : design and analysis of a computer game
This thesis involved the iterative design of a computer game to explore the process of young children's understanding of place value, from their early interpretations of written multi-digits to their knowledge that each digit may represent different values according to the position occupied in the number. Previous studies have explored this development using traditional paper-and-pencil settings, where children are asked to write and recognise multi-digit numbers. In general, this evidence has contributed to the description of children's typical achievements as a function of their ages. However, as previous inferences about change were, for the most part, made through the comparisons of children's performance before and after it had taken place, little is still known about the changes that occur during this process. The study involved 29 six year-old boys and girls from three London schools, who played a specially designed computer game centred on a coinordering activity, during five sessions within a two-week period. The ordering activity enabled children's simultaneous interaction with 16 categories of numberpairs classified in terms of their conceptual relevance, designed to clarify the complexity of relations found between multi-digits, and focus children's attention on the particular features of each relation. For example, comparisons such as 42-52, focused on the 'tens', whereas the comparison 15-19, focused on the 'units'. The quantitative analysis of the results suggested that children's interactions with the game enabled the description of four independent overall patterns. These included relating the numbers through perceptual clues, interpreting them as parts that may be manipulated, seeing them as wholes but part of the number-line or understanding them as wholes and as a composition of units. The evidence suggested that whereas children's initial strategies were typically determined by the same overall pattern, interactions with the game enabled them to connect strategies across different patterns. Analysis of case studies further suggested that the game opened a window into children's thinking about place value by describing their different ways of interpreting 2- and 3-digit numbers. Children's progress and their ability to interpret the 2-digits as a composition of units did not appear to be exclusively explained by their interactions with the number-categories, but also seemed to depend on their previous concepts about the structure of the numeration system. On the other hand, considering that knowledge of the numeration system was a necessary but not sufficient condition for their interpretation of 3-digits, much of children's ability to interpret these numbers as a composition of units, could be explained by their interactions with the number-categories incorporated in the game.