The Layer Profile of the Students’ Understanding of Image Making and Image Having in Completing Mathematical Problems

Abstract

Mathematical understanding is an important aspect in learning mathematics. Pirie and Kieren's theory classified that eight layers of mathematical understanding, including image making and image having. In solving the problems, these layers can show the students such a way of solving problems. The purpose of this study is to describe the layers of understanding of the image making and image having for junior high school students with three dimensional material. The participants of this study were two students with equivalent mathematical abilities at Public Junior High School 3 Tulungagung. The results of the study show that the layers of understanding of image making and image having of those 2 students are almost the same with equal abilities. The findings show that both students can show an initial picture of solving the problem and the reason for thinking about the idea. There are no significant difficulties from the two subjects. However, for the second subject, there was a little difficulty in describing the completion step when she was given two different shapes. Keywords— Mathematical Understanding, Pirie and Kieren's Theory, Image making and image having layers.