Covariational Reasoning of Prospective Mathematics Teachers: How Do Dynamic Animations Affect?

Mahmut Kerti̇l

doi:10.16949/turkbilmat.652481

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.

Highlights

Change, variation, and covariation of quantities are foundational for many of the mathematical concepts (Confrey & Smith, 1994; Thompson, 1994)
The purpose of this study is to investigate the covariational reasoning of elementary school prospective mathematics teachers in a series of modeling activities, and the potential effects of computer-based dynamic animations on their reasoning
The unit of analysis focused on during the study was prospective mathematics teachers’ covariational reasoning abilities that they demonstrated in their written solutions and the effects of dynamic animations while solving the modeling activities involving simultaneously and dynamically changing quantities

Summary

Introduction

Variation, and covariation of quantities are foundational for many of the mathematical concepts (Confrey & Smith, 1994; Thompson, 1994). According to Carlson et al (2002), covariational reasoning involves the mental actions used in the process of coordinating the variation in simultaneously changing quantities. These mental actions were developmentally classified at different levels from person to person. Thompson and Carlson (2017), on the other hand, described the high level of covariational reasoning as the ability to construct a multiplicative object as a result of uniting. Covariational reasoning of prospective mathematics teachers: How do dynamic animations affect? Turkish Journal of Computer and Mathematics Education, 11(2), 312-342

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