Abstract
Various studies have been conducted regarding the use of examples in a mathematical proof. This study aims to describe how the students use the example in the proof analyzed by argumentation and proving activity. Qualitative methods are used to explain the phenomena that arise in the use of examples on mathematical proof. The data collected is the result of student work, think aloud, field notes and interview results. The results show that the example is used as an exploratory tool, an example as an investigative tool for justification and an example as a conviction tool. In Toulmin’s view, examples as explorers serve as data, examples as an instrument of investigation for justification serve as warrant and backing while the example as a conviction tool serves as a qualifier to convince them of the resulting claim. An example as an investigative tool for justification produces two types of argumentation structures: argument structures consisting of one cycle and two cycles. An example of an exploratory tool serves as a data form of simple argumentation. Examples play an important role in mathematical proof although the example is not deductive proof. Examples can be used with various functions depending on the student’s needs.
Highlights
The vital role of students in learning for example has always received attention (Iannone et al, 2012)
This research is a qualitative research with phenomenological design that aims to explain the phenomenon use of examples that occur in the mathematical proving process viewed from Toulmin’s argumentation and proving activities
When the problem of proof is considered the student is too abstract, the example is used to understand all the information contained in the problem
Summary
The vital role of students in learning for example has always received attention (Iannone et al, 2012). Mathematicians say that the experimental process for example is an important aspect of proving development (Epstein & Levy, 1995). Use of examples on student proving (Cañadas, Castro, & Castro, 2009; Ellis et al, 2012; Reid, 2002); by prospective and teacher (Nardi, Biza, & Watson, 2014; Nardi, Biza, & Zachariades, 2012) and by mathematicians (Alcock & Inglis, 2008; Inglis, Mejia-ramos, & Simpson, 2007; Inglis & Mejia-Ramos, 2010). Epstein and Levy (1995) argue that “many mathematicians spend a great deal of time thinking and analyzing specific examples” and have the most significant effect, all beginning with experimentation based on examples. There are several types of mathematical proofs. Balacheff (1988) presents four types of examples used by students in proof: (1) Naive empiricism, which is to confirm the truth of the statement after verifying some
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