The controversial mathematical reasoning process of prospective teachers when solving mathematical problems

An important aspect of the learning process is reasoning. One of the studied reasonings is controversial reasoning. Controversial reasoning can be used to determine the understanding of prospective teachers. The purpose of this study is to explain the controversial reasoning of prospective teachers when solving problems. This research is descriptive qualitative. The instruments used are tests and interviews. There are 50 prospective teachers who are given a problem, then their work is analyzed to find out their reasoning. Data analysis in this study is a) reviewing tests and interviews, b) determining the data used, c) analyzing test and interview results, d) making patterns, and e) presenting data. The conclusion of this study is the controversial reasoning process of prospective teachers, namely a) logically concluding, b) explaining the model, facts, and concept relationships, c) determining the conjecture, and d) using the conjecture to analyze the situation and make an analogy with the given problem. Suggestions for other researchers are to develop appropriate instruments for generating controversial reasoning for prospective teachers. In addition, after prospective teachers solve controversial problems, they can explore their critical and creative thinking processes.