Pre-Service Classroom Teachers' Proof Schemes in Geometry: A Case Study of Three Pre-service Teachers

Abstract

Problem Statement: Recent research and evaluation reports show that students are not learning geometry efficiently. One identifier of student understanding related to geometry is teachers' knowledge structures. Understanding what a proof is and writing proofs are essential for success in mathematics. Thus, school mathematics should include proving activities. Proofs are at the heart of mathematics, and proving is complex; teachers should help their students develop these processes in the early grades. The success of this process depends on teachers' views about the essence and forms of proofs. Hence, it is necessary to investigate the classroom teachers' perceptions related to proofs. Purpose of the Study:The purpose of this study is to determine the proof scheme of pre-service teachers when proving a geometry theorem. In this sense, the study is oriented by the research question: which proof schemes do pre-service teachers use when making proofs in geometry?Method: The current case study is a detailed examination of a particular subject. Firstly, an open ended question was asked, and then semistructured interviews were conducted. The three students investigated in this study were selected by considering their Basic Mathematics scores. Two girls having maximum and average scores and a boy having a

Proving geometry theorems: Student prospective teachers’ perseverance and mathematical reasoning

“…In proving the congruence of flat buildings, both subjects made assumptions that were too specific so that the resulting proof could not be generalized. This condition is in line with a case study conducted by Oflaz et al (2016) which shows one of the proof schemes carried out by prospective teachers is to use inductive proof where prospective teachers provide examples to help them at the beginning of the proof process to then complete the proof and make generalizations.…”

Pre-service mathematics teachers investigating the attributes of inscribed circles by technological and theoretical scaffolding

“…Whether due to a lack of appropriate knowledge or insufficient experience (Oflaz et al, 2016), mathematics students often have difficulty presenting proofs in geometry. However, the research process proposed herein, that is, the combination of technology and supporting scaffoldings, allowed them to explore, discover, and offer proofs for new and unfamiliar features in geometry in a comfortable and non-threatening environment.…”

“…Unfortunately, the school curriculum does not always foster the development of these skills. As a result, knowing how to properly write a proof in geometry often poses a challenge for both pre-service and in-service mathematics teachers (Noto et al, 2019;Oflaz et al, 2016) either due to their lack of sufficient mathematical knowledge or insufficient experience in the teaching process.…”

An Ontological Study on Proof: If and only If Propositions

“…So propositions become much more difficult to prove. It is known that undergraduates had difficulty making proof (Doruk, 2019;Oflaz, Bulut & Akcakin, 2016;Sema & Şenol, 2022). There has also been a lot of research on the views of mathematics teacher candidates and teachers towards making proofs Doruk, Özdemir & Kaplan, 2015;Knuth, 2002;Yopp, 2011).…”