Exploration of students' representation in solving pythagorean theorem problems based on cognitive style

Abstract

This study aims to explore the students' representations in solving Pythagorean theorem problems. Participants of this study consisted of a female student with reflectiv estyle and a female student with impulsive cognitive style. They had an equivalent mathematical ability. This study used the qualitative method. The researcher decides on the methods of data collection based on mathematical problem-solving tasks and task-based interviews. To obtain valid data, the researcher performs the time triangulation. The findings of the study showed that: (1) the mathematical representations of reflective student were (a)recognizingand presenting known and unknown information visually by sketching the car's path, (b) revealing then formulating problem-solving strategy using visual representation, (c) revealing mathematical model manipulation involve Pythagorean theorem, and (d) looking back the solution by using verbal representation;(2) the mathematical representations of impulsive student were (a)recognizing then presenting known and unknown information verbally, (b) revealing then formulating a problem-solving strategy using visual representation, (c) revealing mathematical model manipulation by saying that the distance between point A and B can be determined using the Pythagorean theorem, and (d) looking back the solutions by using verbal representations.