Exploring the combinatorial reasoning of high school students with reflective and impulsive cognitive style in solving problems

Combinatorial reasoning was a basic competence that every student must have for solving mathematical problems, as it highly related to providing argumentation or strategy in solving mathematical problems. It was the process of creating complex constructs out of a set of given elements that satisfy the conditions explicitly given or inferred from the situation. Considering this issue, this study aimed to explore the combinatorial reasoning of high school students with cognitive-reflective and -impulsive styles in solving problems. More specifically, It correlated combinatorial reasoning with tempo cognitive style, since it applied time-based problem solving in which the speed of responding and the frequency of either correct or wrong answer might affect students’ mental action in solving problems. This study was a qualitative research. It used High school students in eleventh grade as the research subject through matching familiar figure test. The researchers distributed a task containing several problems that had similar concept for each and then organized an interview to explore the students’ combinatorial reasoning in solving the given problems. Cognitive-reflective subject decided to use two strategies –formula and filling slot- for the sake of her affirmation, while cognitive-impulsive subject decided to only use one strategy –formula. The cognitive-reflective subject tended to be more accurate and careful in solving the problems. Otherwise, the cognitive-impulsive ones tended to be careless and less accurate, given that the subject decided to do spontaneous mental action. The result of this study found some similarities and differences on the combinatorial reasoning of both reflective and impulsive students. The similarities referred to their ways in explaining the notation in the formula they used and generalizing their strategies. The differences referred to the process of investigating various factors, considering any probabilities that might reveal, and evaluation.