| Popis: |
This thesis reports an investigation of individual differences in children's learning of a concept in mathematics, involving rates of change on linear graphs. Evidence in the literature suggests both that high levels of strategy variability are associated with conceptual change in mathematics and that there are individual differences in strategy variability. Therefore it is argued that differences in strategy variability can offer useful insight into children's learning of mathematics. A series of experiments are reported that each aimed to explore individual and group differences in strategy variability amongst secondary school mathematics students. Methods used for data collection progressed from whole-class testing of students, to individual testing, to individual interviews employing think-aloud protocols, as the need grew for increasingly detailed data on children's strategies for solving problems. Early studies showed a gender difference in strategy variability, so later studies were designed to elaborate on and clarify this relationship. In combination, the results of the studies reported here suggest that there are robust differences in strategy variability between boys and girls and that this effect interacts with the context in which the problems are solved. The use of think-aloud protocols produced a complete reversal of the gender effect on strategy variability. The implications of these findings are discussed, both in terms of learning theory and in terms of their potential impact on the mathematics classroom. The main contribution of this investigation to the literature is in helping to establish strategy variability as a key to understanding cognitive development and as an indicator of children's specific needs for intervention and support in the classroom. |
