Pemahaman konsep pecahan dalam kalangan tiga kelompok pelajar secara keratan lintang

Abstract

The main objective of this study is to investigate the understanding of fraction concepts across three groups of learners. The subjects of the study are 66 primary school students, 67 Form Four students and 57 second-year students of a higher learning institution. The study focuses on learners’ understanding of basic concepts of fraction and the four operations involving fractions. Quantitative data, gauged via 22 open-ended test items, were analyzed descriptively to determine the test scores, obtained by the subjects of each group, measuring their understanding of aspects of fraction concepts. The findings revealed that learners at the tertiary level scored better than learners at the primary and secondary levels, and learners at the secondary level performed better than those at primary level. There is no significant difference between the scores of subjects at tertiary and secondary levels, with respect to their understanding of quotient and mixed number. It was also discovered that learners at all three levels found it difficult to grasp the concepts of fractions as numbers and equivalent fractions. Although there is no significant difference among the groups in their scores on subtraction, multiplication and mixed operations, their mean scores in these operations were low. Thus, more in-depth investigations are required to determine learners’ understanding of the concept of the four operations involving fractions, the concept of fractions as numbers and equivalent fractions. Semi-structured interviews conducted on 21 subjects from each group revealed that primary school learners have yet to understand the concept of fraction as number. Although these subjects were able to draw images but the decisions they made did not reflect the images they possessed. These learners were also unable to see the significance of the relationship between parts and wholes that depict fractions. Learners in secondary schools and higher learning institutions had employed inaccurate strategies when making decisions, and it would be difficult to make them unlearn these strategies which they had memorized. These learners had also failed to make connections between the rules and strategies employed with the decisions they made. They have knowledge on basic concepts of fraction but failed to use this knowledge to make decisions. Learners at all three levels were found to possess a procedural understanding of operational aspects involving fractions, thus the ability to execute calculations successfully, but had however, failed to explain why an action was taken