國中生代數應用題教學策略效果之評估

A Study of the Effects of Teaching Strategies on Junior High School Students' Learning Outcomes in Mathematics Word Problems

本研究的主要目的有二：1．針對國中生在學習代數應用題時所可能發生的錯誤概念，設計出一套符合內化理論的數學教學策略方案。2．以實徵研究的方法考驗這一套內化理論的數學教學策略對國中生代數學習時的學習效果。本研究以臺北市螢橋國中二年級85位學生進行質的研究；另以天母國中二年級學生45位進行實驗教學的研究。使用的工具包括後設認知量表、動機信念量表、數學測驗卷以及兩個訓練課程（後設認知與動機信念訓練課程、代數應用題解題策略訓練課程）等。所得的資料採用質的分析以及單因子多變項變異數分析和混合設計二因子變異數分析等統計法來加以分析。結果發現：1．學生在代數應用題的學習上有系統性的錯誤概念產生。2．學生在進行「後設認知與動機信念訓練課程」後，對其動機信念未能產生立即的影響，但對其後設認知有立即的影響產生。3．學生在進行「代數應用題解題策略訓練課程」後，其數學解題能力有所進步。4．接受兩項訓練課程的實驗組一的學生在追蹤研究時的代數應用題上的表現最好。這些結果顯示：經由瞭解學生的錯誤概念，可以幫助教師設計良好的教學策略；同時，後設認知與動機信念對學生的學習會產生持續努力的效果。

The purposes of this study were: 1) to design, according to the internalization theory, a mathematics teaching strategy program to deal with junior high students' misconceptions in mathematics word problems; 2)to examine the effect of this teaching strategy program on junior high students' learning outcomes in mathematics word problems. Eighty five subjects were drawn from Ying-Chyau Junior High School for qualitative analysis, and 45 subjects were drawn from Tien-Mu Junior High School for the study of experimental teaching. The instruments used were ”metacognition Inventory”, ”Motivational Belief Inventory”, and ”Mathematics Test”. The subjects of the Experimental Group Ⅰ received both ”Metacognition and Motivational Belief Training Course” and ”Mathematics Word Problem Solving Strategy Training Course”, but the subjects in Experimental Group Ⅱ received the latter course only. The data thus collected were analyzed by qualitative analysis, one-way multivariate analysis of variance, and two-way ANOVA with mixed design. The findings were as follows: 1) The students had systematical misconceptions in mathematics word problems learning. 2) ”Metacognition and Motivational Belief Training Course” could not affect the subjects' motivational belief immediately, however, it could affect immediately their metacognition. 3) The students' abilities in solving mathematics word problems were enhanced after they had accepted ”Mathematics Word Problerm Solving Strategy Training Course”. 4) The subjects who accepted both the two training courses performed best in the follow-up stage. These results showed that understanding students' misconceptions could help teahcers to design good teaching strategies, and that metacognition and motivational belief could promote students to study hard continuously.