後設認知理論在數學教法上之應用

The Application of Metacognitive Theory in Mathematics Teaching

陳靜儀(Ching-Yi Chen)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2015年)

https://doi.org/10.6840/cycu201500156

摘要

本研究旨在探討後設認知能力對於學生數學學習的影響，透過文獻的探討與分析，瞭解學生後設認知能力的高低與數學解題能力是否有所關連，並利用此特性提出適當的數學教學模式，以協助學生的數學學習，進而達到提升學生的學習動機、學習成效，並培養學生獨立思考解題的能力。
文獻探討與分析後獲致的結果如下：
一、後設認知能力與數學成就有相關，高後設認知能力者數學成就較佳。
二、後設認知能力與數學解題具有關聯性，高後設認知能力者解題成功的機率較高。
依據文獻探討分析的結果，結合數學解題技巧，研究者提出了「後設認知教學模式」，其教學階段化分如下：
一、教學前準備。
二、陳述性知識教學。
三、程序性知識教學。
四、學生實作與反覆練習。
五、討論與反思。
六、檢核。
其中程序性知識教學中的後設認知解題五步驟為：
一、讀題與分析。
二、擬定計畫。
三、計畫檢核。
四、執行計畫。
五、驗證。

關鍵字

數學解題 ； 後設認知

並列摘要

The purpose of this research is to understand the effect of metacognitive abilities to students' mathematics learning. Through discussion and analysis of the literatures to understand whether the level of students' metacognitive abilities are connected with mathematical problem solving abilities. And then use this feature to propose an appropriate mathematics teaching model, in order to help students learning mathematics, and thus to enhance students' motivation, learning effectiveness, and to develop independent thinking and problem-solving abilities of students.
The results of discussion and analysis of the literatures are as follows:
1. Metacognitive abilities and mathematics achievement are related, and the student of higher
metacognitive abilities is mathematics achievement better.
2. Metacognitive abilities and mathematics problem solving are related, and the probability of
higher metacognitive abilities by solving success is higher.
Based on the results of analysis of the literatures and combine mathematical problem-solving skills, researchers have proposed a "metacognitive teaching model". The teaching stages are as follows:
1. Teaching preparation.
2. Declarative knowledge teaching.
3. Procedural knowledge teaching.
4. Students implement and practice.
5. Discussion and thinking.
6. Examine.
In procedural knowledge teaching, metacognitive problem solving five steps are as follows:
1. Read and analysis the problem.
2. Make plan.
3. Examine plan.
4. Execution plan.
5. Verification.

並列關鍵字

mathematical problem solving ； metacognition

參考文獻

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