Obstacles in Constructing Geometrical Proofs of Mathematics-Teacher-Students Based on Boero’s Proving Model

Abstract

Abstract This study aimed at identifying the obstacles of mathematics-teacher-students based on Boero’s proving model. This study was conducted using a mix method by applying sequential explanatory strategy. The stages of the research were carried out by taking the quantitative data and revealing the qualitative data using semi-structured interviews. In the result of this study, it was found that most of mathematics-teacher-students had difficulties in constructing geometrical proofs of each Boero’s proving model. Even in the phase of writing formal proof, there were only 6.67% of students could write fully in the cases of indirect proving. There were 13.33% of students in the cases of direct proving. This study concluded several obstacles which students faced in constructing the geometrical proofs formally in each phase of Boero’ proving model. The obstacles included: the difficulty in making a diagrammatic sketch of conjecture which was completely made with the correct geometrical notation; the difficulty in knowing of cause-effect of geometrical problems to be proved, if it involved some conditional sentences; inability to write a conjecture made in the form of geometrical symbols, formulas and axiomatic deduction; the difficulty in selecting a valid statement of the conjecture made and the difficulty in writing formal proof.