Penalaran Siswa SMA dalam Pembuktian Matematika pada Materi Trigonometri Ditinjau dari Kemampuan Matematika

Abstract

Reasoning in mathematical proof is a thinking process to draw conclusions based on logical ideas by rebuilding previous knowledge and connecting it with current knowledge in order to demonstrate the truth of a mathematical statement supported by logical arguments. To be able to know students' reasoning in mathematical proving is associated with problem solving because problem solving and reasoning have a close relationship. Differences in students' mathematical abilities allow for differences related to reasoning in mathematical proof. The purpose of this study is to describe the reasoning of high school students with high, medium and low mathematical abilities in proving mathematics on trigonometry material.
 This study used a qualitative approach with a descriptive research type. The research subjects consisted of 3 students from class X, namely students with high, medium and low mathematical abilities. The research data were obtained from the results of mathematical ability tests, mathematical proving tests, and interviews. Mathematical ability tests were used for the selection of research subjects, mathematical proof tests were used to find out how students reasoned in proving mathematics on trigonometry material and interviews were conducted to find out more clearly about the explanation of the reasoning process written by the subjects on the mathematical proof test.
 The results showed that the three students understood the problem by identifying information that was known and that was not known to students with high mathematical ability and logical reasons, but students with moderate and low mathematical ability, there were statements that were not accompanied by logical reasons. In planning the completion, students with high mathematical ability are accompanied by logical reasons but students with moderate and low mathematical ability have statements that are not accompanied by logical reasons. In carrying out the completion plan students with high mathematical ability can solve problems according to plan accompanied by logical reasons, for students with moderate mathematical ability can solve problems according to plan, even though there are statements that are not accompanied by logical reasons, but students with low mathematical ability they cannot solve problems and did not succeed in carrying out according to the plan because they were confused about proceeding with problem solving. In re-examining the process and results, students with high ability get conclusions from their completion and examine the process from the start, starting from reading the problem, planning, implementing plans and conclusions with logical reasons, for students with moderate mathematical ability getting conclusions from their completion and checking their calculations with logical reasons. However, students with low mathematical ability did not get a conclusion from the solution because they could not solve the problem and did not re-examine the process.