# Students’ thinking process in constructing mathematical proof using semantics strategy

Abdussakir, Abdussakir (2014) Students’ thinking process in constructing mathematical proof using semantics strategy. Doctoral thesis, Universitas Negeri Malang.

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## Abstract

In fact, students encounter many difficulty understanding and constructing a proof. We argue that the difficulty of students in constructing a proof cannot be determined only by viewing the proof constructed. Furthermore, the process they do in constructing a proof will give a better clue of difficulties they encounter. Several studies have been conducted to investigate the proving processes of students. However, those studies emphasize the proving procedures rather than the thinking process in proving.

This study is aimed to reveal the thinking process in proof construction performed by students with semantic strategy. The thinking process of students will be analyzed using theoretical framework of David Tall about the three worlds of mathematical thinking. This study describe the way the students constructing proofs, the reasons of students to think out of formal world, the thinking processes that occur outside of formal world, and the return processes to the formal world.

This study is one of descriptive-exploratory study and use qualitative approach. The sources of the research are fourth-year students that selected through think aloud process when completing the given tasks. The subjects of the research are students who used the semantic strategy and then performed a task-based interview to get more data and accuracy. The subjects are continuously selected until saturation of data obtained. For data presentation, at least two subjects selected for each of the following categories: (1) finding concept definitions, (2) reflecting, and (3) finding non-definition clues.

Based on the theoretical study and data analysis it can be concluded that there are three ways of thinking in semantic strategy, namely (1) started from formal world then move into the symbolic or embodied-symbolic world with possibility of more than once and ends within or outside of the formal world, (2) started from symbolic world or embodied-symbolic world then move to the formal world with possibility of more than once and ends within or outside of the formal world, and (3) all thinking processes performed outside of formal world that does not obtain formal proof.

Item Type: Thesis (Doctoral) proses berpikir; bukti matematis; menyusun bukti; strategi semantik; tiga dunia berpikir matematis 13 EDUCATION > 1301 Education Systems > 130103 Higher Education Faculty of Mathematics and Sciences > Department of Mathematics Abdussakir Abdussakir 03 Apr 2017 12:16