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題名:以認知負荷理論探討數學問題設計與後設認知策略教學對國小高年級學生數學解題之影響
作者:郭秀緞
作者(外文):Hsiu-tuan Kuo
校院名稱:國立高雄師範大學
系所名稱:教育學系
指導教授:陳密桃
學位類別:博士
出版日期:2006
主題關鍵詞:認知負荷後設認知策略教學數學解題數學問題設計cognitive loadmetacognitive strategy instructionmathematic problem solvingmathematic problem design
原始連結:連回原系統網址new window
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本研究旨在探討數學方面的問題設計對不同數學專技程度的學生,其認知負荷以及解題表現的影響,並進一步根據認知負荷理論及相關實證研究,設計後設認知策略教學模式,以了解此教學模式,對學生監控自我認知負荷,以及解題表現的影響。為達上述研究目的,本研究共進行三個實驗。實驗一以236位五年級學生為樣本,探討內在要素互動性低的數學問題,其不同的問題設計對不同數學專技程度學生之認知負荷與解題表現的影響;實驗二以229位六年級學生為樣本,探討內在要素互動性高的數學問題,其不同的問題設計對不同數學專技程度學生之認知負荷與解題表現的影響;實驗三乃根據相關文獻,設計一套後設認知策略教學模式,並以兩個班級學生為研究對象,證驗此教學模式對學生監控認知負荷以及解題表現的影響。本研究的資料處理方面,各實驗皆包括量的研究與質的研究,以呈現研究結果。
本研究的研究結果可歸納如下:
1、解決內在要素互動性低的數學問題時,學生認知負荷的高低和數學解題表現的優劣,與數學問題設計方式的不同沒有關聯。
2、解決內在要素互動性高的數學問題時,學生認知負荷的高低和數學解題表現的優劣,與數學問題設計方式的不同有密切的關聯。
3、不論是解決內在要素互動性低的數學問題,或是解決內在要素互動性高的數學問題時,學生認知負荷的高低和數學解題表現的優劣,與其數學專技程度的高低有關聯。
4、不論是解決內在要素互動性低的數學問題,或是解決內在要素互動性高的數學問題時,學生所感受的認知負荷與其解題表現,有顯著的負相關。
5、「後設認知策略教學」有助於提昇學生監控其認知負荷的能力。
6、「後設認知策略教學」可增進學生的數學解題表現。
根據研究結果,本研究針對數學方面的教材呈現、教師的教學以及後續的研究等方面,分別提出建議,以供數學教學及後續研究的參考。
The aim of this research is to explore how the problem designs affect the students who have different level of expertise on mathematics, with particular reference to their cognitive load and problem-solving performance. Furthermore, according to the cognitive load theory and relative empirical researches, the mode of metacongitive strategy instruction is designed so as to understand its influences on both students’ monitor to their cognitive load and their problem-solving performance. For these purposes, three experiments are employed. Firstly, there are 236 fifth-grade students to be examples in the first experiment and they are asked several mathematic problems of low intrinsic element interactivity. That is for the sake of examining how do different problem designs affect the cognitive load and problem-solving performance of students who have different level of expertise on mathematics. Secondly, the examples are 229 sixth-grade students in the second experiment. The inquiry is the same. But, instead of low intrinsic element interactivity, the mathematic problems are changed to high intrinsic element interactivity. Thirdly, a mode of metacognitive strategy instruction is designed based on related research. Students in two classes are the objects of this experiment to verify its effects on students’ monitor to their cognitive load and their problem-solving performance. With regard to the data collection, each experiment includes both quantitative and qualitative data.
The results of this research are as follows:
1. Concerning resolving the mathematic problems of low intrinsic element interactivity, students’ cognitive load and problem-solving performance are not affected by the difference of mathematic problem designs.
2. Regarding resolving the mathematic problems of high intrinsic element interactivity, the difference of mathematic problem design has significant influence on both students’ cognitive load and problem-solving performance.
3. No matter resolving the mathematic problems of high or low intrinsic element interactivity, students’ cognitive load and problem-solving performance would be influenced significantly by their level of expertise.
4.No matter resolving the mathematic problems of high or low intrinsic element interactivity, there is significant negative correlation between students’ cognitive load and their problem-solving performance.
5.Metacongitive strategy instruction is benefit to improving students’ monitoring ability of their cognitive load.
6.Metacongitive strategy instruction has advantages for improving students’ problem-solving performance.
In the end, according to the results are mentioned above, this research provides some suggestions for the display of teaching materials, teaching, and follow-up studies. Hope they are useful for teaching on mathematics and relative research in the future.
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