Using Rasch Analysis to Examine the Effects of Year 5 Students' Understanding of Whole Numbers Multiplication

摘要

This study aims to examine the effect of an intervention with line array representation on student's understanding of whole number multiplication. This was done by comparing the scores of pre- and post-tests in multiplication. The tests were administered to 32 Year 5 students; aged 10-11 years old, in an intact classroom of an urban primary school in the district of Kota Kinabalu, Sabah, Malaysia. A test of multiplication was developed and used in this study as a pre-test and a post-test. This test, which was aligned with Year 5 Standards in the Malaysia Primary Mathematics Curriculum, was developed by one of the researchers. Aimed at examining student's computational knowledge in manipulating numerical symbols, the test contained 33 multiple-choice items of 18 single digit and 15 multi-digit multiplication in whole numbers that were divided into nine categories. Students' responses for both pre- and post-test were obtained and analysed using Bond and Fox Steps using pre-test item difficulties as anchors. The analyses were focused on person measures and Wright maps. The increase in mean person ability from +0.82 logit in the pre-test to +1.15 logits in the post-test showed that students' understanding in multiplication had improved after the intervention. Results showed that students of high ability were likely to have gained more in this intervention than were the children of average or low ability. This study has shown that the Wright map is helpful for determining which ability group of students has acquired the competencies in each category. High ability students who were likely to answer correctly in all categories, especially in the distributive strategy that involved higher order thinking skills items and have shown higher relational understanding in multiplication. Average and low ability students were likely answer correctly most of the lower order thinking skills items demonstrating only instrumental understanding. This study suggests other possible areas for developing tests of multiplication should include different visual representations and multiplicative situations or tasks.