國中生後設認知、動機信念與數學解題策略之關系研究

A Study of the Relationship between Junior High School Students' Metacognition, and Mathematics Problem-Solving Strategies

本文為國科會兩年研究計劃中第一年部分的研究報告“這部分研究的主要目的有三：1.編製國中生的後設認知、動機信念與數學解題策略之測量工具“2.探討國中生的後設認知、動機信念與數學解題策略間的關係。3.分析不同後設認知及不同動機信念的國中生，其數學解題策略上的差異情形。本研究的受試來自臺北縣漳和國中及臺北市天母國中一、二年級的學生，正式施測時的人數為二年級男生30名及女生30名。使用的工具包括：後設認知量表、動機信念量表、數學測驗卷及數學解題策略評量表。資料分析採用積差相關、典型相關及t考驗等統計法。結果發現：1.國中生後設認知、動機信念及數學解題策略間有相關存在。2.國中生透過後設認知及動機信念可解釋其數學解題策略總變異量的40%”。3.不同後設認知及不同動機信念的學生，其數學解題策略上的得分有差異存在。

The purposes of this study were: 1) to develop the measurement instruments of junior high school students' metacognition, motivational belief, and mathematics problem-solving strategies; 2) to investigate the relationship between junior high school students' metacognition, motivational belief, and mathematics problem-solving strategies; and 3) to compare the differences of mathematics problem-solving strategies between junior high school students with different metacognition and motivational belief. There were sixty subjects (male 30, female 30) drawn from two junior rhigh schools (Chang Ho and Tian-Mu) in Taipei area. All the subjects were administered by Metacognition Inventory, Motivational Belief Inventory, Mathematics Test, and Mathematics Problem-solving Process Inventory. The obtained data were analyzed with Pearson product-moment correlation, canonical correlation, and t-test. The main findings of this study were as follows: 1. There were relationships between junior high school students' metacognition, motivational belief, and mathematics problem-solving strategies. 2. Junior high school students' metacognition and motivational belief could account for 40% of the total variance in their mathematics problem-solving strategies. 3. There were significant differences in mathematics problem-solving strategies between the junior high school students with different metacognition and motivational belief.