Student challenges related to topological concepts

This research; among the fundamental topological concepts "internal, external, boundary, closing and stacking points, open and closed clusters and neighborhood and neighborhood family" concepts experienced by students in the concepts, easy to understand the concept, easy to issue. In order to identify the reasons for their understanding and to facilitate understanding of the topological concepts described in the course. The study group consisted of 88 teacher candidates who studied in the second class of the primary mathematics Education Department of a university in 2017-2018 academic year and who had learned the topology course. The research was conducted with 15 teachers who were chosen by means of sampling method for the purpose of 88 teacher candidates. Within the scope of the study, the teacher candidates were given a total of 14 hours of topological training for 7 consecutive weeks (excluding visa week). Research data were collected through document review. Students were asked to write daily in the context of the difficulties they experienced in the course and the reasons of these difficulties, easy understanding, reasons for the easy understanding of the subject and suggestions that will make learning more lasting and understandable. For this purpose, the journals written by the students to answer the above questions at the end of each course were collected by e-mail and subjected to content and descriptive analysis. As a result of the analyses, the journals written by the students about the concepts they have learned during the course of seven weeks have been examined in detail, categories have been created and frequency of these are given. As a result of the research, it was observed that the difficulties students experienced in topology were due to the abstract and complex nature of the course, symbolism and lack of proof skills of the students. It was seen that the most easily understood topic in the topology course was the axiom of gaps. One of the reasons why students understand the subject is that the teacher can solve many examples of the subject. Therefore, the students suggested that the subject should be reinforced with sample solving and the subjects should be expressed on the shape or model.