Layers of Mathematical Understanding and Folding Back of Prospective Teachers on Arithmetic Sequence and Series

Abstract

Mathematical understanding is one of the objectives of learning mathematics, so students need to master it. The success of the process of growing students' mathematical understanding is inseparable from the role of the teacher. Therefore, student teacher candidates must have a complete mathematical understanding structure. This is what prompted him to carry out research to describe the layers of mathematical understanding and folding back prospective teacher students on the material of arithmetic sequences and series. The researcher took 18 sixth-semester students of S1 Mathematics Education at the State University of Malang. A purposive sampling technique was used to determine the participants. So, one subject was chosen in each category of mathematical understanding. Researchers used a descriptive approach with three stages of research procedures including planning, implementing, and drawing conclusions. The instruments used consisted of test questions and interview guidelines. Based on analysis carried out using indicators for each layer of mathematical understanding, information was obtained that subjects with high abilities were able to achieve layering arrangement and perform effective folding back independently. Subjects with moderate abilities were able to reach the observation layer and fold back effectively but needed help. Meanwhile, subjects with low abilities were able to reach the formalization layer but had not been able to fold back effectively. It can be concluded that subjects with better mathematical understanding have a more complete layered structure of mathematical understanding and can fold back independently and effectively.