Students’ visual thinking ability in solving the integral problem

Abstract

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with technological tools, describing and communicating information and ideas, developing ideas, and understanding improvement. This research describes students’ visual thinking ability to solve integral problems. The approach used in this study was descriptive qualitative. The subjects in this study were three students from the Department of Mathematics Education at the State Islamic Institute of Tulungagung. The data were collected by using tests and interviews. The steps to analyze the data were categorization, reduction, exposure, interpretation, and conclusion. Based on the analysis of students’ visual thinking skills in solving integral problems, there were three levels of visual thinking: semi-local visual, local visual, and global visual. At the semi-local visual level, students could only understand algebraically, and they have not shown it graphically at all. Meanwhile, at the local visual level, they have already understood geometry as an alternative language and been able graphically represented problems or concepts, even though it was not perfectly done yet. While on a global visual level, they could perfectly visualize visual thinking indicators, understand algebra and geometry as alternative languages for problem-solving, extract specific information from diagrams, graph problems, and use them to solve problems perfectly.

Keywords

• visualization, visual thinking, definite integral.