A Diagnostic Study on Subtracting Fractions for Sixth Graders Based on Ordering Theory and LFT-extended

• Main Authors: CHEN, CHIEN-HSIUNG, 陳健雄
• Other Authors: SHEU, TIAN-WEI
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/96432202529741690786

碩士 === 國立臺中教育大學 === 教育測驗統計研究所 === 95 === The purpose of this study was to apply the Ordering Theory (OT) and LFT-extended analysis to diagnose sixth graders’ concept structures of subtracting fractions. The researcher tested 133 six graders in one of the elementary schools in suburban Taichung, and obtained the examinees’ graphs of concept structures both on “Subtracting fractions with the same denominator” and “Subtracting fractions with different denominators” by using Ordering Theory (OT). Then, by the help of LFT-extended programs, the researcher integrated the experts’ graphs of concept structures on subtracting fractions as the referenced standard. Finally, the researcher made a contrast between the examinees’ graphs of the test and those of the experts’, and calculated the examinees’ reach ability measure and the discrepancy index to understand the similarity of concept structures graphs among different classes so that to provide them the suitable remedial instructions. Through the procedures of the analysis, the following conclusions were found. 1. The graphs among classes varied based on different abilities. In “Subtracting fractions with the same denominators”, class A approached to the experts’ graphs; however, in “Subtracting fractions with the different denominator”, it was class D that approached to the experts’ graphs. 2. For remedial instruction in “Subtracting fractions with the same denominator”, three different classes needed help in concept connections (concept 5 to concept 6) while the other class needed help in connecting concept 2 to concept 5 and concept 4 to concept 5. 3. For remedial instruction in “Subtracting fractions with different denominator”, two classes needed help in the same concept connections (concept 8 to concept 11), and the other two classes needed help in concept 7 to concept 8 and concept 11 to concept 12 respectively. In the end, some recommendations and suggestions for future research are provided.