An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments

  • Esra Demiray
  • Mine Işıksal Bostan


The purposes of this study are to investigate Turkish pre-service middle school mathematics teachers’ ability in conducting valid proofs for statements regarding numbers and algebra in terms of their year of enrollment in a teacher education program, to determine the proof methods used in their valid proofs, and to examine the reasons for their invalid arguments. A proof questionnaire containing three proof statements was administered to 115 pre-service middle school mathematics teachers in a large state university in Ankara, Turkey. The results showed that more than half of the pre-service teachers were able to conduct valid proofs for the given statements. In terms of year levels, it was seen that the seniors were the least successful group in conducting valid proofs for each statement. When pre-service teachers’ valid proofs were analyzed, it was concluded that mathematical induction and direct proof were the mostly used methods for the given statements. When pre-service teachers’ invalid arguments were analyzed, it was seen that “inserting numbers to verify the given statement” and “rewriting the givens in the statement” were the common reasons for stating invalid arguments.


Mathematical proof Pre-service middle school mathematics teachers Proof methods 


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Copyright information

© Ministry of Science and Technology, Taiwan 2015

Authors and Affiliations

  1. 1.Hacettepe UniversityAnkaraTurkey
  2. 2.Middle East Technical UniversityAnkaraTurkey

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