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引文資料
題名:
The Effects of Proof Features and Question Probing on Understanding Geometry Proof
書刊名:
當代教育研究
作者:
楊凱琳
/
林福來
/
王繹婷
作者(外文):
Yang, Kai-lin
/
Lin, Fou-lai
/
Wang, Yi-ting
出版日期:
2008
卷期:
16:2
頁次:
頁77-100
主題關鍵詞:
幾何證明
;
文本
;
理解
;
Geometry proof
;
Text
;
Understanding
原始連結:
連回原系統網址
相關次數:
被引用次數:期刊(
1
) 博士論文(0) 專書(0) 專書論文(0)
排除自我引用:
1
共同引用:0
點閱:116
本研究主要探討的問題是:不同寫法、不同複雜度和不同種類的理解問題對學生理解幾何證明有何影響?在理論上,採用Duval的組織敘述之3種層次做為不同種類的理解,依此設計工具測驗153位國三學生對幾何證明的理解。研究結果顯示:1.不同寫法、不同複雜度和不同種類的理解問題之間沒有交互作用;2.局部理解是最容易的;3.不同複雜度會影響學生在局部理解和整體理解問題的表現。以上結果的一般性仍受限在沒有給命題的證明文本之測驗情境。在安排閱讀幾何證明的學習序列時,編輯者應該要考慮混合證明步驟數和命題熟悉度的複雜度因子。最後,本文將會提出進一步的研究議題。
以文找文
This study aims to investigate how the written formats, complexity of proofs and the types of understanding questions affect students’ understanding of geometry proof. Theoretically, Duval’s three levels of organizing statements - micro, local and global, are applied to assess 153 ninth graders’ understanding of geometry proof. The results show (a) there was no interaction among written formats, complexity of proofs, and types of understanding questions in terms of students’ understanding of geometry proof; (b) local understanding is the easiest for students; (c) the effects of the complexity of proofs on local and global understanding were statistically significant. It is noted that the generalizability of the results is limited by the task of proof texts without their corresponding propositions. The factor mixing proof steps and familiarity of propositions should be taken into account while arranging learning sequence of reading proofs. Afterward, further research is proposed in this paper.
以文找文
期刊論文
1.
Yang, K. L.、Lin, F. L.(2008)。A model of reading comprehension of geometry proof。Educational Studies in Mathematics,67(1),59-76。
2.
Lee, J. F.(1986)。Background knowledge and L2 reading。Modern language journal,70(4),350-354。
3.
Lin, F. L.、Yang, K. L.(2007)。The Reading Comprehension of Geometric Proofs: The Contribution of Knowledge and Reasoning。International Journal of Science and Mathematics Education,5(4),729-754。
4.
Dee-Lucas, D.、Larkin, J. H.(1990)。Organization and Comprehensibility in Scientific Proofs, or "Consider a Particle"。Journal of Educational Psychology,82(4),701-714。
5.
Healy, Lulu、Hoyles, Celia(2000)。A study of proof conceptions in algebra。Journal for research in mathematics education,31(4),396-428。
6.
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。
7.
Kintsch, Walter(1988)。The role of knowledge in discourse comprehension: A construction-integration model。Psychological Review,95(2),163-182。
8.
Meyer, B. J. F.、Freedle, R. O.(1984)。Effects of discourse type on recall。American Educational Research Journal,21(1),121-143。
9.
Seidenberg, P. L.(1989)。Relating Text-processing Research to Reading and Writing Instruction for Learning Disabled Students。Learning Disabilities Focus,5(1),4-12。
10.
McNamara, D. S.、Kintsch, E.、Songer, N. B.、Kintsch, W.(1996)。Are Good Texts Always Better? Text Coherence, Background Knowledge, and Levels of Understanding in Learning from Text。Cognition and Instruction,14,1-43。
11.
McGee, L. M.(1982)。Awareness of Text Structure。Reading Research Quarterly,17,581-590。
12.
Herbst, P.(2002)。Establishing a Custom of Proving in American School Geometry: Evolution of the Two-column Proof in the Early Twentieth Century。Educational Studies in Mathematics,49,283-312。
13.
Heinze, A.、Cheng, Y. H.、Yang, K. L.(2004)。Students' Performance in Reasoning and Proof in Taiwan and Germany: Results, Paradoxes and Open Questions。Zentralblatt für Didaktik der Mathematik,36(5),162-171。
14.
Housman, D.、Porter, M.(2003)。Proof Schemes and Learning Strategies of Above-average Mathematics Students。Educational Studies in Mathematics,53(2),139-158。
會議論文
1.
Tall, D.(1998)。The Cognitive Development of Proof: Is Mathematical Proof for All or for Some?。0。
2.
Kaplan, R. B.、Ostler, S.(1982)。Contrastive Rhetoric Revisited。0。
3.
Yang, K. L.、Wang, L. W.(2008)。Propositions Posed under a Proof without Its Proposition。0。
4.
Cheng, Y. H.、Lin, F. L.(2007)。The Effectiveness and Limitation of Reading and Coloring Strategy in Learning Geometry Proof。0。113-120。
研究報告
1.
Mullis, I. V. S.、Martin, M. O.、Gonzalez, E. J.、Gregory, K. D.、Garden, R. A.、O'Connor, K. M.、Chrostowski, S. J.、Smith, T. A.(2000)。TIMSS 1999 International Mathematics Report。Boston, MA。
圖書
1.
Miles, Matthew B.、Huberman, A. Michael(1984)。Qualitative data analysis: A sourcebook of new methods。Sage Publications。
2.
Lin, F. L.、Tsao, L. C.(1999)。Exam Maths Re-examined。Rethinking the Mathematics Curriculum。London, UK。
3.
Goldman, S.、Varma, S.、Cote, N.(1996)。Extending Capacity-constrained Construction Integration: Toward "Smarter" and Flexible Models of Text Comprehension。Models of Understanding Text。Mahwah, NJ。
4.
Borasi, R.、Siegel, M.(2000)。Reading Counts: Expanding the Role of Reading in Mathematics Classrooms。New York, NY:Teachers College Press。
其他
1.
Yang, K. L.,Lin, F. L.,Wu, J. D.(2008)。Re-investigating Characteristics of Mathematical Conjecturing,0。
圖書論文
1.
Duval, R.(1998)。Geometry from a Cognitive Point of View。Perspective on the Teaching of Geometry for the 21st Century。Dordrecht:Kluwer。
2.
Harel, G.、Sowder, L.(1998)。Student's Proof Schemes: Results from Exploratory Studies。Research on Collegiate Mathematics Education。Providence, RI:American Mathematical Society。
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