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Students' mathematical reasoning can be seen from the way they prove a simple mathematical statement. This article discusses the reasoning approach of 32 teacher candidates in proving even numbers. This descriptive-exploratory research uses an interpretative analysis of the assignments given to prospective teacher students in the first semester courses. We discussed how participants develop generalizations from adding two odd numbers to an even number. The results pointed out that participants used inductive-deductive reasoning and deductive reasoning to convince their strategies. This reasoning approach will be categorized into characteristics that may become a general and regular pattern for proving this even number problem.

reasoning; proving; inductive reasoning; deductive reasoning