Abstract
The emerging of formal mathematical proof is an essential component in advanced undergraduate mathematics courses. Several colleges have transformed mathematics courses by facilitating undergraduate students to understand formal mathematical language and axiomatic structure. Nevertheless, college students face difficulties when they transition to proof construction in mathematics courses. Therefore, this descriptive-explorative study explores prospective teachers' mathematical proof in the second semester of their studies. There were 240 pre-service mathematics teachers at a state university in Surabaya, Indonesia, determined using the conventional method. Their responses were analyzed using a combination of Miyazaki and Moore methods. This method classified reasoning types (i.e., deductive and inductive) and types of difficulties experienced during the proving. The results conveyed that 62.5% of prospective teachers tended to prefer deductive reasoning, while the rest used inductive reasoning. Only 15.83% of the responses were identified as correct answers, while the other answers included errors on a proof construction. Another result portrayed that most prospective teachers (27.5%) experienced difficulties in using definitions for constructing proofs. This study suggested that the analytical framework of the Miyazaki-Moore method can be employed as a tool to help teachers identify students' proof reasoning types and difficulties in constructing the mathematical proof.
Highlights
Abstrak Memunculnya bukti matematika formal merupakan komponen penting dalam mata kuliah matematika tingkat lanjut
The construction of formal mathematical proof is an important component of advanced mathematics courses for undergraduate degree (Shaker & Berger, 2016)
0.42% of the total prospective teachers experienced such proving errors
Summary
Abstrak Memunculnya bukti matematika formal merupakan komponen penting dalam mata kuliah matematika tingkat lanjut. Kerangka kerja analitik metode Miyazaki-Moore dapat digunakan sebagai alat yang bermanfaat bagi guru untuk mengidentifikasi tipe-tipe tipe bukti penalaran siswa dan kesulitan dalam membangun bukti matematika. Blanton, Stylianou, and David, (2003) agreed that college students need to develop required proving skills to construct a proof In this case, teachers’ knowledge about proof must be given to students because that can help the students strengthen the concept and skill of proof (Carrillo, et al, 2018; Stylianides, 2007). The math teachers’ rationales beyond teaching proof and proving in schools are due to the fact that students have experienced similar reasoning to the mathematicians, such as learning a body of mathematical knowledge and gaining insight about why assertions are true. Edwards and Ward (2004) said that the students could not use mathematical definitions or construct the relation between every day and mathematical languages
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