• Communications of Mathematical Education
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• v.21 no.2 s.30
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• pp.125-152
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• 2007

When we teach mathematics in college, we find a lot of mistakes, fallacies and flaws in the solution of the students. In this paper, we presented a variety of examples of mistakes and fallacies, including wrong proofs, misinterpreted definitions and the mistaken use of theory. The examples, taken from different classes and subjects, are based on our own experience of teaching mathematics. As the previous research argued, such mistakes, fallacies and flaws should be considered as natural phenomena in the students' progress and should be analyzed systematically for the more effective education. By providing a wide-ranging examples of mistakes and fallacies, and detailed analyses of them, we emphasized the significance of the analysis of mistakes and fallacies and proposed that more careful attention should be paid on the collection and development of teaching materials in the area of mistake and fallacy analysis. We hope that this study would be a meaningful contribution to the teaching of mathematics in college.