• The Mathematical Education
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• v.54 no.1
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• pp.83-98
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• 2015

By analysing the examination papers for geometry, we classified the errors occured in the proofs for geometric problems into 5 main types - logical invalidity, lack of inferential ability or knowledge, ambiguity on communication, incorrect description, and misunderstanding the question - and each types were classified into 2 or 5 subtypes. Based on the types of errors, answers of each problem was analysed in detail. The errors were classified, causes were described, and teaching plans to prevent the error were suggested case by case. To improve the students' ability to express the proof of geometric problems, followings are needed on school education. First, proof learning should be customized for each types of errors in school mathematics. Second, logical thinking process must be emphasized in the class of mathematics. Third, to prevent and correct the errors found in the proofs for geometric problems, further research on the types of such errors are needed.