Examining pre-service mathematics teachers’ reasoning errors, deficiencies and gaps in the proof process

Enes Demir 1, Tugba Ozturk 2 * , Bulent Guven 2
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1 Department of Mathematics Education, Siirt University, Siirt, Turkey
2 Department of Mathematics Education, Karadeniz Technical University, Trabzon, Turkey
* Corresponding Author
EUR J SCI MATH ED, Volume 6, Issue 2, pp. 44-61. https://doi.org/10.30935/scimath/9522
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ABSTRACT

Proving is a process that has important roles in terms of learning and teaching in almost all the areas of mathematics. Because the process of proof constructions an extensive process that includes skills as mathematical thinking, reasoning and making connections. Reasoning is one of the most important components of this process. However, most students have difficulty in making a good reasoning and they make various reasoning errors in the process. The purpose of the study is to investigate the reasoning errors that pre-service mathematics teachers exhibit during proof construction. This study was carried out with 80 university students from second, third, fourth and fifth grade levels. An open-ended exam based on abstract mathematics and algebra was used. To deeply examine reasoning errors in the proving process, clinical interviews were conducted with pre-service teachers. A scale was developed by considering the literature review and the expert opinions; this was used to analyse the data about the reasoning errors. The results illustrate that the reasoning errors mostly do not show differences for all grade levels. However, the percentages of reasoning errors according to the grade levels and to the upper classes these errors show resistance to decrease the deficiencies. It is important to design a learning environment enabling students to experience proof construction in order to reduce or eliminate the reasoning errors.
Keywords: Pre-Service Teachers, Proof, Proof Process, Reasoning Errors

CITATION

Demir, E., Ozturk, T., & Guven, B. (2018). Examining pre-service mathematics teachers’ reasoning errors, deficiencies and gaps in the proof process. European Journal of Science and Mathematics Education, 6(2), 44-61. https://doi.org/10.30935/scimath/9522

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