Abstract
It is of critical importance, in particular, for mathematics teachers who will teach future generations to understand and do mathematical proofs. It is important to determine future teachers' beliefs about and difficulties with proofs because their knowledge of this issue affects their teaching. This study aims to determine and compare the proof schemes of prospective mathematics teachers from two state universities, one in Turkey and the other in Spain. The case study was conducted within this study. The participants were 51 prospective teachers at their second year from the department of teaching mathematics education at Huelva University in Spain and 45 prospective teachers from the department of teaching mathematics education at Cumhuriyet University in Turkey. The Proof Test consisted of four questions about proofs for parallelograms. Semi-structured interviews were subsequently conducted to investigate the prospective teachers’ responses in-depth. The findings suggest that prospective teachers from Turkey and Spain indicated affinity in proving. The majority of the prospective mathematics teachers were either unable to complete the proof or completed the proof in an inaccurate way.
Highlights
Proof is a keystone of mathematical thinking
3.2.1 Results of the Detailed Analysis of the Works of Three Prospective Teachers Who Were Selected from Spain Sample 3.2.1.1 Daniel’s Proof Schemes Daniel said that he got average marks in Maths in Secondary Education, he claims that he used to show no interest in Maths
Monica does not manifest an inductive proof scheme and based on his reasoning it can be said that she has the ritual and perceptual proof scheme (Figure 17). Regarding her opinion about the teaching of the notions of proof in the mathematics classes, Monica considers that this knowledge constitutes only one of the parts of mathematics and that should not receive more attention than other areas that she considers more relevant, such as arithmetic or algebra. 3.2.1.3 Marta’s Proof Schemes we show the case of Marta, a prospective teacher, who expresses being "enchanted with mathematics" and having obtained excellent marks throughout her academic training
Summary
Being competent at proving is of critical importance for mathematics teachers who will teach future generations to understand and do mathematical proofs (VanSpronsen, 2008). A vast majority of university mathematics students have problems understanding and doing proofs (Coe & Ruthven, 1994; Martin & Harel, 1989; Oflaz, Bulut & Akçakın, 2016). The fact that students do not understand what proofs are or their function underlies these problems. It is important to determine future teachers' beliefs about and difficulties with proofs because their knowledge of this issue affects their teaching. This study aims to determine and compare the proof schemes of prospective mathematics teachers from two state universities, one in Turkey and the other in Spain. The interactivity and variety of mathematics education studies enable international comparison studies (Xsenofontos, 2010)
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