Abstract
Formal proof is a deductive process beginning from some explicitly quantified definitions and other mathematical properties to get a conclusion. Characteristics of student formal-proof construction are required to identify the appropriate treatment can be determined. The purpose of this study was to describe the characteristics of the construction of formal-proof based overview of the proof structure and conceptual understanding that the student possessed. The data used in this article were obtained from the 3-step processes: students are asked to write down the proof of proving-question, they are asked about the knowledge required in constructing proof using questionnaire, and then they are interviewed. The results showed that formal-proof construction could be modeled by the Quadrant-Model. First Quadrant describes correct construction of formal-proof, Second Quadrant describes insufficiencies concept in construction formal-proof, Third Quadrant indicates insufficiencies concept and proof-structure in construction formal-proof and Fourth Quadrant describes incorrect proof-structure in construction of formal-proof. This model could give consideration on how to help students who are in Quadrant II, III, and IV to be able to construct a formal proof like Quadrant I.
Highlights
Proof and proving in mathematics education are an important part of mathematics, as a pillar of the mathematics building
Mathematics education especially in mathematics learning in university emphasizes the constructing of mathematical proof
Of the 58 students who were given the task of mathematical proofs, there were five students who have written correct proof
Summary
Proof and proving in mathematics education are an important part of mathematics, as a pillar of the mathematics building. Mathematics education especially in mathematics learning in university emphasizes the constructing of mathematical proof. Students who enter college level should develop a formal mathematical knowledge. Mathematical proof of students needs to be trained so that they can understand the formal mathematical structure. Students are introduced to formal proof in the study of mathematics at university. Formal proof as a process begins from explicit quantified definitions and deduces that other properties hold as a consequence [2]. Learning how to construct formal proof is given to make sense a formal definition that can be used in building the basis of deduction theorem
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