| Summary: | 碩士 === 國立臺灣師範大學 === 教育心理與輔導學系 === 100 === In this study, three different prototypes of “common denominator”, “reciprocal multiplication” , and “integration” as the worked-out examples were applied to explore the learning effect on conceptual knowledge and procedural knowledge of fraction division, especially that on the students with low prior knowledge. The pilot study pre-examined 115 5th graders and 108 6th graders via the examination of prior knowledge and conceptual knowledge. The pilot study result shows lower difficulties in accordance with better discrimination in most of the items. The analysis of internal consistency reliability fitted the goodness; criterion-related validity was qualified for the significant correlation with the mathematics-achievement scores. Therefore, the study only revised minor part of the items. Other items were expected to be adopted in the formal examination. The valid samples in the formal examination were 148, including 5th graders sampling from elementary schools in Taipei and Taoyuan. The participants divided by classes as a unit were designed to three conditions with different worked-out-example teaching instruction. The examination of prior knowledge was proceeded before the instruction. The worked-out-example instruction was then proceeded in the second (integrated group) or third (the other groups). The students were divided into heterogeneous group and they could learn via discussing the examples as well as solving the questions. The examination of fraction division with procedural knowledge and conceptual knowledge were provided after the worked-out examples. The results exhibited the anticipated learning effects on the students with 80% and 90% correct rate via learning conceptual knowledge and procedural knowledge of fraction division respectively. The difference between three groups was not significant according to ANCOVA analysis since the performance of three groups were fine simultaneously. The effect resulting from different groups occurred in the students with low prior knowledge. The effects of learning conceptual knowledge in integrated group were better than those in the reciprocal multiplication group. The effects of learning procedural knowledge in integrate group or reciprocal multiplication group were better than those in the common denominator group. In conclusion, the prototype of worked-out examples in integrated group demonstrated the best efficiency and benefit for the students with low prior knowledge. Additionally, the acts of the students in class, the restriction of the research, and the advice of instruction were all described and discussed in this article.
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