Children’s daily lives are filled with examples of intensive quantities (e.g. speed, cost). However, over 30 years of research shows that the intensive quantity concept is difficult for children to grasp. This thesis examines the factors that contribute to children’s difficulties with relational thinking about intensive quantities. To achieve this, a series of studies were conducted in which children’s performance on intensive quantity problems is compared with performance on comparable extensive quantity problems. The first study (N=228) provided a general examination of the performance of children aged 4-9 years on different intensive quantity problems (direct relations, inverse relations, proportional equivalence and sampling). Its main contribution was to establish the sequence in the development of different aspects of children’s relational thinking about intensive quantities. It also examined whether relational thinking success was sensitive to variations in problem presentation. Three types of problem presentation were used (Physical Demonstrations, Computer Diagrams, and Manipulatives) and little variation in children’s performance was observed. Studies 2-4, earned out on 7 to 9 year olds, examined how extensive and intensive quantity settings contribute to success with direct and inverse relations problems. Study 2 (N=l 13) and Study 3 (N=244) approached this question with a comparison methodology. In both studies problems were easier for children in extensive quantity settings. Study 3 also compared two forms of problem presentation. Children receiving problems with relational language (more, less, the same) performed significantly better than children receiving quantitative descriptions on inverse relations problems. Study 4 (N-121) extended the comparison of extensive and intensive relational thinking problems to computational problems. This comparison produced no significant differences in perfonnance between extensive and intensive quantities. Sufficient evidence was found with non-computational problems to argue that understanding intensive quantities as a quantity expressed as a ratio presents children with a unique challenge, which cannot be explained solely by the need to work with inverse relations. The educational implications of these findings and future directions for research are discussed.
Permanent link to this resource: https://doi.org/10.24384/5h9c-r134
Bell, David Daniel
Supervisors: Nunes, Terezinha
Faculty of Health and Life Sciences
Year: 2008
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