Covariational Reasoning of Prospective Mathematics Teachers: How Do Dynamic Animations Affect?
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Abstract
Covariational reasoning is about the ability of coordinating the variation in two simultaneously and dynamically changing quantities and being able to see these quantities at the same time by forming a multiplicative unit. Covariational reasoning ability has been considered as necessary and foundational to the understanding of many mathematical concepts ranging from elementary to tertiary levels. In this study, covariational reasoning abilities of prospective elementary school mathematics teachers and the effects of dynamic animations created in computer-based environments on these abilities have been investigated. Case study was used as a research design one of which is a qualitative research methodology. The participants of the study were 19 prospective elementary school mathematics teachers attending to an elective Computer-Assisted Mathematics Education course and four of them were selected for semi-structured interviews. The results showed the weakness in prospective elementary school mathematics teachers’ covariational reasoning abilities and the potential of dynamic animations in supporting covariational reasoning. The animations in dynamic computer environments seem to have minimal effect on paper and pencil solutions in general. However, these animations, if they were used with their data collection and graph drawing properties, affected prospective teachers ways of reasoning in two ways: (i) forcing them to revise and rethink about the current ways of reasoning used during paper and pencil solutions, and (ii) lowering the cognitive load or removing the necessity of deep thinking on the situation. For the first case, the activities supported with the dynamic animations play a supportive role in developing covariational reasoning. For the second case, the dynamic animations did not contribute to prospective teachers’ covariational reasoning, rather they just played a mediating tool role that helps them to find a result.
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