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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.

Mathematical thinking is an important aspect of mathematics education and, therefore, also needs to be understood by prospective teachers. Prospective teachers should have the ability to analyze and interpret students’ mathematical thinking. Comparing model is one of the interpretation models from Wilson, Lee, and Hollebrands. This article will describe the prospective teacher used the model of the building process in interpretation students' mathematical thinking. Subjects selected by considering them in following the students’ strategies in solving the Building Construction Problem. Comparing model is a model of interpretation in which a person interprets student thinking based on student work. There are two types comparing model building process prospective teacher use in interpreting students’ mathematical thinking ie. comparing work and comparing knowledge. In comparing works, prospective teachers use an external representation rubric. This is used to analyze student activities in order to provide an interpretation that is comparing the work of students with their own work. In comparing knowledge, prospective teachers use internal representation rubrics to provide interpretation by comparing the students' work with their knowledge or thought.

This qualitative study aimed at describing student verbal interaction verbally through cognitive activities consisting of procedural, disputational, and exploration in solving geometry problems. This research was in the form of students' verbal interaction activities in group discussion which decribe students' thinking process in detail, both the correct and incorrect thinking process, when conveying their ideas to their friends to solve a problem. The data were collected through a video recording and made in the form of dialogue transcriptions. The research results showed that the form of student verbal interaction on the procedural activity namely (1) students conveyed their ideas to their peers without arguing with each other; (2) discussion activities with planning as its nature; (3) students shared information used in problem-solving. The form of student verbal interaction on the disputational activities were (1) students responded to each other ideas, suggestions, or answers between individuals; (2) students defended each other's ideas or answers so that it triggered a group discussion; (3) the activities would end when all the group member have the appropriateness of the thinking process from the discussed problems.

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