The Level of Students' Reading Comprehension on Proof by Mathematical Induction

摘要

The proof is one of the centres in learning mathematics not only for students of mathematics programs but also for a mathematics education program. The benefits of studying mathematical proof in mathematics education are very important because it increases problem-solving skills, persuasive argumentation, reasoning, creativity and mathematical thinking. However, there are still many students who have difficulties in understanding mathematical proof, including proof by mathematical induction. This study aimed to identify the extent of the level achieved by students when reading proof by mathematical induction. The data were analyzed through data reduction, data presentation, and drawing conclusions. Three chosen participants from higher class, middle class and lower class participated in this study. The results showed that the level of reading comprehension achieved by students on proof by mathematical induction was 1) surface, 2) recognizing elements, and 3) chaining element. On the surface level in which there is a facet basic knowledge, all subjects passed this level well because none of the participants had difficulty in recognizing the symbols and terms in the proof provided. On the recognizing elements level, the higher class participant achieved good facet logical status because she was able to correctly recognize the premise and conclusion, but she was still not good at facet summarization. The middle-class participant achieved good facet logical status, while a participant from the lower class did not do well. Both of these participants were also not good at facet summarization. Whereas at the level of chaining element, only the higher class participant achieved facet generality and application quite well. She was able to apply the same idea from the given proof to other similar questions. The results suggest that lecturers should design different strategies or develop instruments to help students in comprehending mathematical proof using mathematical induct