Investigating a mathematics teacher and his eighth-grade students' proof evaluations

Şimşek, Halil İbrahim
Proof and reasoning can be considered as an essential aspect of mathematics education that should be developed by students from an early age. However, it should be noted that an argument without appropriate reasoning cannot be considered valid proof. Past studies show that students and teachers have difficulty distinguishing between valid and invalid proofs (e.g., Stylianides et al., 2017). In order to understand this problem more deeply, a case study was conducted with a mathematics teacher and his 20 eighth-grade students, aiming to reveal the similarities and differences in the proof evaluation of the teachers and the students. The data were gathered through written questionnaires and interviews. The results showed that while the axiomatic and inductive (example-based) arguments were convincing for both the teachers and the students, the authoritarian arguments were not. In addition, while the transformational and perceptual arguments were convincing for the teacher, the students did not find them convincing. In terms of showing that the mathematical statement always works, while the students considered all inductive arguments valid, more than half of the students did not consider axiomatic arguments valid. On the other hand, the teacher considered all axiomatic arguments valid, but only one inductive argument was valid for him. Also, it was found that the teacher mostly focused on examples, validity for all cases, and using algebra to evaluate the convincingness and validity of the arguments and to score arguments like they were his students’ responses. The students mostly focused on examples and understandability of the argument to evaluate convincingness, validity, and teacher expectancy.
Citation Formats
H. İ. Şimşek, “Investigating a mathematics teacher and his eighth-grade students’ proof evaluations,” M.S. - Master of Science, Middle East Technical University, 2023.