| Summary: | 碩士 === 國立臺中教育大學 === 教育測驗統計研究所 === 102 === The study aims to discuss the interactions of the multiple problem-solving strategies, the concepts and the error patterns. Try to figure out the relations between the strategies and the math performance of the sixth grade students in “direct proportion” unit. The researcher used the self-developed “The Direct Proportion of Mathematical Concept Test” composed of the constructed-response items. It can provide abundant information to realize the situation of the students’ inner concepts and fixed misconception through the constructed-response items. Based on the results, the major findings of the study were summarized as follows：
A、There are four strategies to solve the proportion problems by examining the process of the students’ response. They are ratio(A)、B(multiple)、C(math formula) and D(unit). Furthermore, The researcher divided the students in three groups：one is using B(multiple) consistently, another is using C(math formula) consistently and the last one is using M (mixed strategy).
B、The study shows that there is a significant correlation between habitual strategies and the math performance. The students using C (math formula) consistently have better performance than those who use B (multiple) habitually and M (mixed-strategies).
C、The students used the certain strategy represent that they possess these concepts of the strategy. Therefore, teachers can reteach these concepts when students fail to solve the problems by the single habitual strategy.
D、The students using mixed strategy have more error patterns due to their incomplete concepts. Moreover, the students who used B strategy habitually tend to equip the certain error pattern. It means that students have troubles to decide multiplication or division when they wants to figure out the unknown quantity. According to this, teachers can correct this error pattern directly to save more time.
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