Visual Thinking Profile of Mathematics Students in Graph Theory Problem Solving Process

摘要

Graph theory can be applied to a number of cases such as shortest path, travelling salesman problem, and minimum spanning tree. In Graph Theory course, visualization used as media to make problem solving easier. Visual thinking is an integral part of problem solving, as in using diagram or picture to explain, documenting, count, or demonstrate steps involved in finding a solution. This article comprises a visual thinking profile of mathematics students in solving graph theory cases. We use a descriptive-explorative method using a qualitative approach. The subject of this research is students of Mathematics Department students (I dan J offerings) that took the Graph Theory course in even semester, the year 2018-2019. Data were taken from the task-based interview, using a semi-structured format. The instruments of the research are taken from Polya's Problem Solving Techniques. Result of research are 1) Visual thinking profile in understanding (when visual input came into mind as well instructions of problem solving, then mental imagination is processed and represented as image/graph model); 2) Visual thinking profile in planning (when visual input of image/graph model came into mind, as well as of previous experience, then mental imagination developed ideas to determine steps/algorithms to solve the problem); 3) Visual thinking profile in implementing (when visual input of understanding and planning came into mind, then mental imagination is processed and used to solve graph theory cases); and 4) Visual thinking profile in crosschecking (when pictures or graph model came into mind, then the visual imagination is used as a basis of recalculation in order to find the final conclusion of the solution). In the graph theory course, implementation of visual thinking for students in the problem-solving process used Powtoon-based multimedia application.