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Miyazaki, Mikio

doi:10.1023/a:1003956532587

Cited by 22 publications

(11 citation statements)

References 5 publications

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“…Even though Moore's (1994) research used interview to see errors in mathematical proof, the present study tended to examine more on deductive and inductive proof without employing interview like what Miyazaki (2000) did. The data were collected using a simple task of constructing one mathematical proof "Prove that the sum of two odd numbers is an even number".…”

Section: Methodsmentioning

confidence: 99%

“…The data of participants' responses about proof correctness were analyzed by using Miyazaki's (2000) classification for types of reasoning in mathematical proof and Moore's (1994) classification for types of errors in a mathematical proof. Table 1 and Table 2 show the scheme of proof analysis used to analyze prospective teachers' proof.…”

Section: D7mentioning

confidence: 99%

“…In connection with examining student's mathematical proof, Miyazaki and Moore methods might have inspired many researchers for analyzing student's proof with particular objectives. For example, Kögce, Aydin and Yildiz (2010) adopted Miyazaki's (2000) classification of proof to investigate high school students' level of proof based on types of reasoning. Furthermore, Ozdemir and Ovez (2012) looked for the relationship between prospective teachers' perception proof types proposed by Almeida (2000) and their proving processes related to the experienced types of difficulties (Moore, 1994).…”

mentioning

confidence: 99%

“…There are two universally recognized proving methods namely deduction and induction (Kögce et al, 2010;Miyazaki, 2000). Deduction method of proof involves several methods encompassing direct proof, proof by contraposition, and proof by contradiction (Baki, 2008;Moralı et al, 2006).…”

mentioning

confidence: 99%

“…Deduction method in mathematics begins with a general statement or hypothesis and examines the possibilities to reach a specific logical conclusion (Morris, 2002). Induction method is generally used by 8 th grade students or secondary school students because they have already learned to prove numerical or geometrical proposition (Miyazaki, 2000). These two methods are based on the types of reasoning used by someone in carrying out a proving process, of which each respectively refers to deductive reasoning and inductive reasoning.…”

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confidence: 99%

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Deductive or Inductive? Prospective Teachers’ Preference of Proof Method on an Intermediate Proof Task

2020

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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.

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Section: Methodsmentioning

confidence: 99%

Section: D7mentioning

confidence: 99%