Identifying students' error in proving the congruency theorem of a triangle with the think aload method

Abstract

Students of the Mathematics Education study program need to know and understand how to prove theorems based on previously acquired knowledge in the form of undefined understanding, postulates, definitions, constructs, and selected theorems to prove the next theorem. In relation to proving this theorem, lecturers need to know how far the steps that have been taken by students, including mistakes made in proving the theorem. One way that can be used is to provide several theorems for students to prove, then the steps they go through in proving these theorems can be known by using the think aloud method. If the method is applied and recorded, it will be seen clearly and can be identified errors and difficulties experienced by students in proving the theorems assigned to prove them. To obtain research data, it is done by giving the task of proving several theorems about congruence. Then students write down the results followed by voicing what they think. The students' voices were then described and analyzed descriptively to find out the results. From the results of the analysis, it is finally known that several errors occurred when proving the theorem, among others: (1) Students are still influenced by past experiences of learning geometry and have been recorded in their minds which do not match the geometric structure being studied. Students assume that the definition used in proving the theorem is the same as the definition they have known so far. (2) Students are still confused in relating the meaning of the base (undefined), postulates, definitions, constructions and theorems, so they are still not systematically used. Students tend to use conceptual thinking, which is a way of thinking that is concerned with understanding concepts and the relationships between them and their use in proving theorems. (3) Students lack the correct frame of mind in proving theorems. Students misunderstood the definition or did not write the definition in the structure made; This error is not due to inaccuracy or negligence, but because the role of definition in preparing the steps of proof is not fully understood. Students find it difficult to use all known information (concepts) to be realized in sketches (pictures) and then the sketches (pictures) that are made are used to build a concept. Here it appears that there are two problems that arise, namely the problem of model construction and concept application. Model construction can be matched with modeling in problem solving, while concept application is an activity using sketches (models) to derive more specific and general properties (rules). (4) Students are less creative in proving theorems, so there are no ideas for proving theorems in the next step. The flexibility of students' thinking that is consistent and coherent in one geometric structure with other geometric structures has not been seen; the accommodation process in students' internal thinking has not been running. Students do not write down theorems, but write explanations to get pictures as proof; this error is more on the technical aspect.