An analysis of mathematics understanding of prospective student-teachers of mathematics

This quantitative-qualitative descriptive study aims to reveal the mathematics understanding of prospective student-teachers, describe the types of their mistakes in mathematics understanding, and recommend appropriate teaching of mathematics understanding. The subjects were 34 first-year students taking the Geometry course in the Mathematics Education Study Program, at a State University in Yogyakarta, Indonesia. The test instrument was consisting of four items, two of which were about the problems of procedural instrumental understanding and the other two were about the problems of relational understanding. The data were analyzed through the stages of reducing data, presenting data, and concluding data. The results show that students' mathematical understanding is categorized as good (87.75%). Students' procedural instrumental understanding (87.75%) is better than their relational understanding (77.52%) which is in good and sufficient categories, respectively. Some students made mistakes in representing theorems, performing mathematical procedural using appropriate concepts/theorems, and interpreting conclusions or proofs using appropriate notation and representation. It is recommended that mathematical learning should prioritize relational understanding by exploring a concept with other concepts and using various representations, situations, and contexts. Learning should focus more on relational understanding, namely discussing a concept and its relationship with other concepts with different representations, situations, and contexts.