A Comparative Research on Proving: The Case of Prospective Mathematics Teachers

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.

A Case Study on How Primary-School in-Service Teachers Conjecture and Prove: An Approach From the Mathematical Community

“…For this reason, we agree with Ubuz and Yayan (2010) when stating that "an important step to improving subject matter knowledge should be better subject matter preparation for primary teachers" (p. 799). We also believe that addressing difficulties in the content knowledge of primary-school teachers (see, for instance, Oflaz, Polat, Altaylı Özgül, Alcaide, & Carrillo, 2019) would shed light on where to focus so that teachers to acquire essential content knowledge to teach in the various mathematical domains (regarding proving as mathematical content, see, for instance, Siswono, Hartono, & Kohar, 2020;van Dormolen, 1977). In this way, studying teachers' activities when they strive either to prove mathematical assertions or to formulate conjectures constitutes the first step and exploring the reasons behind the difficulties found when conjecturing and proving would be an interesting topic for further research.…”

Tracing proof schemes: some patterns and new perspectives

“…Regardless of whether the participants are mathematics students, from different disciplines, or pre-service teachers, it is seen that their proving skills in different learning areas (AN, GEO, ENT, MIX) are either on average or they are not at a sufficient level or so on (e.g., Cusi & Malara, 2007;Nagel et al, 2018;Oflaz et al, 2019;Pala & Narlı, 2018;Sen & Guler, 2015;Sevgi & Orman, 2020;Sevimli, 2018;Tossavainen, 2009). It is seen that students in terms of verifying a mathematical result (e.g., Aydoğdu Iskenderoğlu, 2003), and pre-service teachers in terms of how the validity of proofs are evaluated (e.g., Uygan et al, 2014) generally have reasoning close to the empirical proof scheme in the ALG-GEO and GEO, respectively.…”