幾何證明分段作業的學習效率分析研究

Abstract

本研究引進認知負荷理論並以「平行線截比例線段」的證明為例，探討專家和生手理解幾何證明與認知負荷感受的關係，並進一步分析其學習效率。依據數學結構與Duval（1998）的幾何推理訊息組織三層次之構念進行切割分段，形成分段與未分段兩種學習版本。根據49位專家和66位生手在不同學習版本的理解表現與認知負荷感受，以Paas與van Merriënboer（1993）所提出的學習效率公式分析專家和生手在不同學習版本下的學習效率。研究結果顯示：一、專家的理解表現與認知負荷感受無關，但生手的理解表現與閱讀意願及信心指數呈正相關；二、信心指數可做為學生理解幾何證明的一個參考指標；三、降低作業複雜度能提升專家在各理解層次的學習效率與生手在局部層次的學習效率。

In this study, we adopt cognitive load theory and take Thales’ theorem as an example to investigate how expert and novice’s understanding on geometric proof interacts with perception of cognitive load and further investigate their learning efficiency. We follow mathematics structure and the construct of reasoning with three levels of organization (Duval, 1998) to process segmentation, which forms two learning versions, the segmented version and the non-segmented one. According to 79 experts’ and 66 novices’ performance of comprehension and perception of cognitive load, we utilize measurement of learning efficiency provided Paas and van Merriënboer (1993) to analyze experts’ and novices’ learning efficiency under different learning versions. The results are as follows: Firstly, experts’ performance of comprehension is irrelevant with their perception of cognitive load. However, novices’ performance of comprehension is positively correlates with their willingness to read and confidentiality. Secondly, confidence can be considered to be a reference to examine students’ comprehension on geometric proof. Thirdly, lowering the complexity of tasks will promote experts’ learning efficiency under each level and novices’ learning efficiency under local level.