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題名：動態幾何環境下大學生幾何探索之研究
書刊名：臺灣數學教育期刊
作者：許舜淵／胡政德
作者(外文)：Xu, Shun-yuan／Hu, Cheng-te
出版日期：2014
卷期：1:1
頁次：頁49-77
主題關鍵詞：動態表徵；動態幾何環境；幾何探索；Dynamic representation；Dynamic geometry environment；Geometric investigation
原始連結：連回原系統網址new window
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  • 被引用次數被引用次數:期刊(1) 博士論文(0) 專書(0) 專書論文(0)
  • 排除自我引用排除自我引用:1
  • 共同引用共同引用:9
  • 點閱點閱:14
本研究目的在探索動態幾何環境下大學生幾何探索之思考運作模式。透過個案研究來進行探究並以質性分析來詮釋資料。研究結果顯示：（1）當學生觀察動態幾何軟體所產生動態表徵時，通常透過幾何思考後再做適當的拖曳行動；（2）動態表徵其外顯的行為和內在的數學性質會激發個體產生猜測，並在心智中模擬操作數學物件以及分析可能的動態行為來驗證猜測，進而產生宣告；（3）學生會依據模擬操作的複雜程度，再決定是否使用DGS具體操作以驗證幾何思考過程中的想法；（4）學生在動態幾何環境下進行幾何實驗並與幾何思考不斷地交互作用下探索幾何性質。
The aim of this study is to explore, in a dynamic geometry environment (DGE), the operation models of the geometric thinking of college students. To achieve this, we conducted a case study. We recorded the process of geometry exploration activities by math-major college students, interviewed them, and interpreted their operation models of thinking through a qualitative analysis. The results are summarized as follows: (1) When students observe the dynamic representations generated by dynamic geometry software (DGS), they seldom react immediately, and instead engage in geometric thinking before they carry out appropriate dragging. (2) The apparent actions and intrinsic mathematical properties of dynamic representations tend to inspire students’ conjectures. Students then mentally manipulate mathematical objects and analyze possible dynamic behaviors to confirm their conjectures. Finally, they are able to produce a declaration. This process is a basic model for geometric thinking. (3) Students manipulate mathematical objects mentally based on the complexity of operation, and then decide whether to use a DGS-specific claim or conjecture in geometric thinking. (4) Students explore geometry properties in DGE under the constant interactions between geometry experiments and geometric thinking.
期刊論文
1.陳英娥、林福來(19980600)。數學臆測的思維模式。科學教育學刊，6(2)，191-218。new window  延伸查詢new window
2.Arzarello, F.、Olivero, F.、Paola, D.、Robutti, O.(2002)。A cognitive analysis of dragging practises in Cabri environments。ZDM Mathematics Education，34(3)，66-72。  new window
3.Fischbein, E.(1993)。The theory of figural concepts。Educational Studies in Mathematics，24(2)，139-162。  new window
4.Hazzan, O.、Goldenberg, E. P.(1996)。Students' understanding of the notion of function in dynamic geometry environments。International Journal of Computers for Mathematical Learning，1(3)，263-291。  new window
5.Hölzl, R.(1996)。How does 'dragging' affect the learning of geometry。International Journal of Computers for Mathematical Learning，1(2)，169-187。  new window
6.Lopez-Real, F.、Leung, A.(2006)。Dragging as a conceptual tool in dynamic geometry environments。International Journal of Mathematical Education in Science and Technology，37(6)，665-679。  new window
7.Mariotti, M. A.(2000)。Introduction to proof: The mediation of a dynamic software environment。Educational Studies in Mathematics，44(1-3)，25-53。  new window
8.Pinto, M.、Tall, D.(2002)。Building formal mathematics on visual imagery: A case study and a theory。For the Learning of Mathematics，22(1)，2-10。  new window
9.Talmon, V.、Yerushalmy, M.(2004)。Understanding dynamic behavior: Parent-child relations in dynamic geometry environments。Educational Studies in Mathematics，57(1)，91-119。  new window
會議論文
1.Furinghetti, F.、Paola, D.(2003)。To produce conjectures and to prove them within a dynamic geometry environment: A case study。The 27th International Group for the Psychology of Mathematics Education Conference Held Jointly with the 25th PME-NA Conference。Honolulu, HI：CRDG, University of Hawaii。397-404。  new window
2.Mariotti, M. A.、Laborde, C.、Falcade, R.(2003)。Function and graph in DGS environment。The 27th International Group for the Psychology of Mathematics Education Conference Held Jointly with the 25th PME-NA Conference。Honolulu, HI：CRDG, University of Hawaii。237-244。  new window
3.Tall, D.(1998)。Information technology and mathematics education: Enthusiasms, Possibilities & Realities。The 8th International Congress on Mathematical Education。Seville：S.A.E.M. Thales。65-82。  new window
圖書
1.Lakatos, I.(1976)。Proofs and refutations: The logic of mathematical discovery。Cambridge University Press。  new window
2.Sorensen, Roy A.(1992)。Thought experiments。New York, NY：Oxford University Press。  new window
3.Vygotsky, L. S.、Cole, M.、John-Steiner, V.、Scribner, S.、Souberman, E.(1978)。Mind in society: The development of higher mental psychological processes。Harvard University Press。  new window
圖書論文
1.Battista, M. T.(2007)。The development of geometric and spatial thinking。Second handbook of research on mathematics teaching and learning。Charlotte, NC：Information Age。  new window
2.Duval, R.(1995)。Geometrical pictures: Kinds of representation and specific processing。Exploiting mental imagery with computers in mathematics education。New York, NY：Springer-Verlag。  new window
3.Duval, R.(1998)。Geometry from a cognitive point of view。Perspectives on the Teaching of Geometry for the 21st Century。Dordrecht：Kluwer Academic Publishers。  new window
4.Hoyles, C.、Jones, K.(1998)。Proof in dynamic geometry contexts。Perspectives on the teaching of geometry for the 21st century。Dordrecht：Kluwer Academic Publishers。  new window
5.Laborde, C.(1993)。The computer as part of the learning environment: The case of geometry。Learning from computers: Mathematics education and technology。Berlin：Springer-Verlag。  new window
6.Tall, D.(1999)。The chasm between thought experiment and mathematical proof。Mathematische bildung und neue technologien。Leipzig：B. G. Teubner Stuttgart。  new window
 
 
 
 
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