Some 'Illegal Reasoning' of the First Year Undergraduate Students in Constructing Formal Proof

摘要

This paper describes the difficulties and type of illegal reasoning of novice students in formulating formal proof specially on the associative property of addition operation of rational numbers. Although the problem is not so hard but for beginner students is not the case. The participants are first year students at University of Muhammadiyah Malang on second semester. Subjects are chosen based on answers that show difficulty in establishing verification related to conceptual understanding, referential reasoning, and organization of proof-writing. The framework that was used to analyze students' proof comprehension and construction actions and contributions, particularly their completeness and type of reasoning, is described in the paper. The findings of the study resonate closely with those of researchers in the developed world. Students' difficulties with how to begin proof, understanding of the rules and nature of proof, conceptual understanding, and proof techniques and strategies. Related with illegal reasoning, a novice student indicated generic reasoning, unable to make generalization, circular reasoning, and non-referential reasoning.