How do the Undergraduate Students Use an Example in Mathematical Proof Construction: A Study based on Argumentation and Proving Activity

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.