Triangle is a mathematical concept which has been studied since preschool until high school. Even prospective elementary school teachers study the triangle until the level of college. However, the results of the analysis towards performance of prospective elementary school teacher found that there was an imperfection understanding of triangle concept. Therefore, this study aimed to trace the understanding of prospective primary teachers towards the concept of triangle. Furthermore, an investigation on the learning experience of mathematics that affected the formation of its concept was conducted. Thus, a description of epistemological mathematics belief would be obtained, especially the learning process that was the causes of concept’s formation itself.

This research was a qualitative descriptive design in the form of case study. The subjects of the study were two prospective elementary school teachers. Instruments used in the form of problem-solving tasks and interview guides. Problem-Solving Task (PST) was non-routine. Furthermore, interviews were conducted to delve deeper into the understanding of the triangle concept and to explore the causes of imperfect concept understanding.

The results of data analysis showed that the concepts which were not understood by subjects, for instance: base, altitude, area, and the variety of triangles. The base of triangle was understood as one of the horizontal sides of the triangle located at the bottom. The altitude of the triangle was understood as the upright side of the triangle or the perpendicular distance from the base to the opposite vertex. The result showed that the subject did not understand the base and altitude concepts. Conceptual understanding was due to the triangle images that given in elementary school untill college were right-angled triangles, equilateral triangles, and isosceles triangles. Triangle images such as PST were never found in either the examples given by the teacher or those contained in textbooks. The subject determine the area of ​​triangle only use the formula. During this time the area of ​​triangle was presented by showing directly the size of the base and the altitude of the triangle. Problem solving could only be done by using triangle spacious formulas.

The imperfection triangle concept’s understanding was due to less varied presentation examples or problems. The examples given continuously formed the perception as it often appeared. The learning process shaped the mathematical epistemological beliefs of the concept. Conceptualization imperfections would affect the problem-solving process, especially non-routine issues.