Argumentation in Covariational Reasoning: Middle School Student’s Solving Covariation Problem with Different Cognitive Style

The aim of this research is to describe the process of covariational reasoning and how to build argumentation in solving covariation problems for middle school students who had verbal and visual cognitive style. This qualitative descriptive research investigated the differences in covariational reasoning and how to build argumentation process for students with verbal and visual cognitive style, whether they have different covariational reasoning processes in solving covariation problem or not. The participants of this research are 2 students, one with verbal cognitive style and other with visual cognitive style. The participant selected from the result of the cognitive style test, the mathematics performance test and the teacher’s recommendation. Data were obtained using covariation problems and interviews. The result of this study pointed out that student with verbal cognitive style were able to construct images of function’s dependent variable changing in tandem with the imagined change of the independent variable, and in some situations, were able to construct images of rate of change and were able to construct images of rate of change for contiguous intervals of a function’s domain. Student with verbal cognitive style was constructing her argumentation of mental action deductively. While, student with visual cognitive style was able to exhibit mental action of initial coordination, direction of changes coordination and had some difficulties in doing mental action of amount of change coordination. The student with visual cognitive style was constructing her argumentation of mental action inductively. We discuss implications of these results for perspectives on argumentation in covariational reasoning, students’ understandings of graphs and discuss curricular treatments of function again with a covariational lens, and areas of future research