The Understanding And Application Of The First Year Students In The Senior High School About Several Forms Of Proofs

Mathematical proof is one of the defining features of mathematics and as such it should be a major part of the secondary and the senior mathematics curriculum.This study uses both quantitative and qualitative research methods. Two survey instruments were used to collect data and information.The first instrument consists of the presentation of proofs in several forms across two curriculum areas (algebra and geometry). In these sections, students chose which proof they would construct their own and which proof they thought their teacher would think was the best. These examined the students' understanding about several forms of proofs. Then this instrument also explored their abilities in proof construction and how their understanding impact on this ability.The second instrument is interviews. To support our conclusions, we drew from a corpus of interviews with four students.The following is the summary of this study.Firstly, this study confirms that the students have a generally positive view of the role of proof in the curriculum.Secondly, form is important when judging a proof's validity. A proof is judged more valid if it is of a familiar form. General arguments that explain are considered more valid than examples that don't explain.Thirdly, students are not proficient in proving. Students' views on the form that a proof must have can lead them to do erroneous and nonsensical symbolic manipulations.The results of this study provide mathematics educators with further insight into how to improve our students' views of and competencies with proof.