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外文摘要
引文資料
題名:
幾何證明分段作業的學習效率分析研究
書刊名:
教育與心理研究
作者:
左台益
/
呂鳳琳
作者(外文):
Tso, Tai-yih
/
Lu, Feng-lin
出版日期:
2014
卷期:
37:1
頁次:
頁62-94
主題關鍵詞:
幾何證明
;
學習效率
;
認知負荷理論
;
Geometry proof
;
Learning efficiency
;
Cognitive load theory
原始連結:
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相關次數:
被引用次數:期刊(0) 博士論文(0) 專書(0) 專書論文(0)
排除自我引用:0
共同引用:
12
點閱:25
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。
以文找文
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.
以文找文
期刊論文
1.
Ayres, Paul L.(2006)。Impact of reducing intrinsic cognitive load on learning in a mathematical domain。Applied Cognitive Psychology,20(3),287-298。
2.
Ayres, P. L.(2001)。Systematic mathematical errors and cognitive load。Contemporary Educational Psychology,26,227-248。
3.
Chandler, P.、Sweller, J.(1991)。Cognitive load theory and the format or instruction。Cognition and Instruction,8,293-332。
4.
Chen, S. Y.、Fan, J.-P.、Macredie, R. D.(2006)。Navigation in hypermedia learning systems: Experts vs novices。Computers in Human Behavior,22(2),251-266。
5.
Cuevas, H. M.、Fiore, S. M.、Oser, R. L.(2002)。Scaffolding cognitive and metacognitive processes in low verbal ability learners: Use of diagrams in computer-based training environments。Instructional Science,30,433-464。
6.
Hummel, H. G. K.、Paas, F.、Koper, E. J. R.(2004)。Cueing for transfer in multimedia programmes: Process worksheets vs. worked-out examples。Journal of Comvuter Assisted Learning,20,387-397。
7.
Fischbein, E.(1993)。The theory of figurai concepts。Educational Studies in Mathematics,24(2),139-162。
8.
Kuchemann, D.、Hoyles, C.(2006)。Influences on students’ mathematical reasoning and patterns in its development: Insights from a longitudinal study with particular reference to geometry。International Journal of Science and Mathematics Education,4(4),581-608。
9.
Kalyuga, S.、Chandler, P.、Sweller, J.(2004)。When redundant on-screen text in multimedia technical instruction can interfere with learning。Human Factors,46,567-581。
10.
Kester, L.、Kirschner, P. A.、van Merrienboer, J. J. G.(2005)。The management of cognitive load during complex cognitive skill acquisition by means of computer-simulated problem solving。The British Journal of Educational Psychology,75,71-85。
11.
Moreno, R.(2004)。Decreasing cognitive load for novice students: Effects of explanatory versus corrective feedback in discovery-based multimedia。Instructional Science,32(1/2),99-113。
12.
Lin, F. L.、Cheng, Y. H.、linfl team(2003)。The competence of geometric argument in Taiwan adolescents。International Conference on Science and Mathematics Learning,12,16-18。
13.
Paas, F. G. W. C.、van Merriënboer, J. J. G.(1993)。The efficiency of instructional conditions: An approach to combine mental effort and performance measures。Human Factors: The Journal of the Human Factors and Ergonomics Society,35(4),737-743。
14.
Raman, M.(2003)。Key ideas: What are they and how can they help us understand how people view proof?。Educational Studies in Mathematics,52,319-325。
15.
Yang, K. L.、Lin, F. L.(2008)。A model of reading comprehension of geometry proof。Educational Studies in Mathematics,67(1),59-76。
16.
Van Gerven, P. W. M.、Paas, F.、van Merrienboer, J.、Hendriks, M.、Schmidt, H. G.(2003)。The efficiency of multimedia learning into old age。The British Journal of educational Psychology,73(4),489-505。
17.
Weber, K.(2001)。Student difficulty in constructing proof: The need for strategic knowledge。Educational Studies in Mathematics,48,101-119。
18.
Van Merriënboer, Jeroen J. G.、Sweller, John(2005)。Cognitive Load Theory and Complex Learning: Recent Developments and Future Directions。Educational Psychology Review,17(2),147-177。
19.
葉明達、柳賢(20070900)。建立判讀理解層級:高中生進行數學論證判讀活動困難之探討。教育與心理研究,30(3),79-109。
延伸查詢
20.
Larkin, J. H.、McDermott, J.、Simon, D. P.、Simon, H. A.(1980)。Expert and novice performance in solving physics problems。Science,208,1335-1342。
21.
Paas, Fred G. W. C.、van Merriënboer, Jeroen J. G.(1994)。Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach。Journal of Educational Psychology,86(1),122-133。
22.
Selden, A.、Selden, J.(2003)。Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?。Journal for research in mathematics education,34(1),4-36。
23.
Sweller, John(2010)。Element interactivity and intrinsic, extraneous, and germane cognitive load。Educational Psychology Review,22(2),123-138。
24.
左台益、呂鳳琳、曾世綺、吳慧敏、陳明璋、譚寧君(20111100)。以分段方式降低任務複雜度對專家與生手閱讀幾何證明的影響。教育心理學報,43(專刊),291-314。
延伸查詢
25.
Sweller, John、van Merrienboer, Jeroen J. G.、Paas, Fred G. W. C.(1998)。Cognitive architecture and instructional design。Educational Psychology Review,10(3),251-296。
26.
Mayer, Richard E.、Moreno, Roxana(2003)。Nine Ways to Reduce Cognitive Load in Multimedia Learning。Educational Psychologist,38(1),43-52。
27.
Hanna, Gila(2000)。Proof, Explanation and Exploration: An Overview。Educational Studies in Mathematics,44(1-3),5-23。
28.
Inglis, M.、Alcock, L.(2012)。Expert and novice approaches to reading mathematical proofs。Journal for Research in Mathematics Education,43(4),358-390。
29.
Weber, Keith、Mejia-Ramos, Juan Pablo(2011)。Why and how mathematicians read proofs: An exploratory study。Educational Studies in Mathematics,76(3),329-344。
研究報告
1.
張俊彥(2008)。TIMSS 2007國際數學與科學教育成就趨勢調查國家報告。
延伸查詢
圖書
1.
Hanna, G.、de Villiers, M.(2012)。Proof and proving in mathematics education。New York, NY:Springer。
2.
Reigeluth, C. M.(1983)。Instructional-design theories and models: An overview of their current status。Lawrence Erlbaum Associates。
3.
Sweller, John、Ayres, Paul、Kalyuga, Slava(2011)。Cognitive load theory。Springer Verlag。
其他
1.
Niss, M.(2002)。Mathematical competencies and the learning of mathematics: The Danish KOM project,http://www7.nationalacademies.orgmseb/mathematicalcompetencies_and_the_leaming_of_mathematics.pdf, 2004/10/15。
圖書論文
1.
Duval, R.(1998)。Geometry from a cognitive point a view。Perspectives on the teaching of geometry for the 21st century。Dordrecht:Kluwer Academic。
2.
Hanna, G.、Jahnke, H. N.(1996)。Proof and proving。International handbook of mathematics education。Dordrecht:Kluwer Academic Publishers。
3.
Longo, G.(2012)。Theorems as constructive visions。Proof and proving in mathematics education。New York, NY:Springer。
4.
Seiden, A.(2012)。Transitions and proof and proving at tertiary level。Proof and proving in mathematics education。New York, NY:Springer。
5.
Zaslavsky, O.、Nickerson, S. D.、Stylianides, J.、Kidron, I.、Winicki-Landman, G.(2012)。The need for proof and proving: Mathematical and pedagogical perspectives。Proof and proving in mathematics education。New York, NY:Springer。
6.
Duval, R.(1995)。Geometrical pictures: Kinds of representation and specific processing。Exploiting mental imagery with computers in mathematics education。New York, NY:Berlin:Springer-Verlag Berlin Heidelberg。
7.
Keller, J. M.、Suzuki, K.(1988)。Use of the ARCS motivation model in courseware design。Instructional designs for microcomputer courseware。Lawrence Erlbaum Associates。
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