A Study of the Use of the Van Hiele Model in the Teaching of Non-Euclidean Geometry to Prospective Elementary School Teachers in Taiwan, the Republic of China_

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題名：	A Study of the Use of the Van Hiele Model in the Teaching of Non-Euclidean Geometry to Prospective Elementary School Teachers in Taiwan, the Republic of China
書刊名：	臺中師院學報
作者：	吳德邦
出版日期：	1995
卷期：	9
頁次：	頁443-474
主題關鍵詞：	范析理模式；師範學院學生；非歐幾何學；學習成就；幾何思考；Van Hiele model；Non-Euclidean geometry
原始連結：	連回原系統網址
相關次數：	被引用次數:期刊(2) 博士論文(0) 專書(0) 專書論文(0) 排除自我引用:2 共同引用:0 點閱:19

　　　　　本研究之主要目的，係在使用由范析理(van Hiele)所發展出來的五段式學習模式於教學，以探討我國師範學院數學組學生在非歐幾何學的學習成就和幾何思考層次之成效。本研究之研究對象為臺中師範學院兩班數學組學生，每班各有二十六名。兩組學生接受等量的非歐幾何學教材和相同的教學時數，但使用不同的教學策略。控制組學生是採傳統講授式教學法;實驗組學生則施以范析理五段式學習模式教學法。本研究所獲得的結論如下:(a)我國師範學院數學組學生，在非歐幾何教學上，採用范析理五段式學習模式教學法比採用?統講授式教學法，更能產生較高的幾何思考層次;(b)我國師範學院數學組學生，在非歐何教學上，採用范析理五段學習模式教學法，其學習成就顯著高於採用傳統講授式教學法。從本研究歸納出來的建議如下:(a)應嘗試在其他的實驗研究中，修改實驗變因;而范析理五段式學習模式和傳統講授式的混教學法，亦值得嘗試研究;(b)本研究僅在探究使用范析理五段式學習模式對我國師範院數學組學生在非歐幾何教學上之成效;爾後亦可針對我國中小學學生，探究使用范析理五段式學習模式之成效，進行類似的研究;(c)本研究運用非歐幾何學的課程，來探討范析理五段式學習模式在學習成就和幾何思考之成效，亦可運用范析理的五段式學習模式在其他的幾何和數學領域，做更深、更廣的研究;(d)對我國師範學院數學組學生而言，學習幾何學是符合未來課堂教學之需求，亦是期望達成之目標。而范析理學習模式與研究者從事之實驗研究相似，可將其方法統整、應用於數學組學生之幾何教學上。

以文找文

期刊論文
1.	Shaughnessy, J. M.、Burger, W. F.(1985)。Spadework prior to deduction in geometry。The Mathematics Teacher，78(6)，419-428。
2.	Senk, S. L.(1989)。Van Hiele Levels and Achievement in Writing Geometry Proofs。Journal for Research in Mathematics Education，20(3)，309-321。
3.	Usiskin, Z.、Senk, S.(1990)。Evaluating a test of van Hiele levels: A response to Crowley and Wilson。Journal for Research in Mathematics Education，21(3)，245-342。
4.	Chen, M.、Wu, D.(1986)。A review of the psychological foundation of mathematics education theory for elementary schools。Journal of Taichung Junior Teachers' College，15，471-484。
5.	Cox, P. L.(1985)。Informal geometry-more is needed。Mathematics Teacher，78(6)，404-405。
6.	Crowley, M. L.(1990)。Criterion-referenced reliability indices associated with the van Hiele geometry test。Journal for Research in Mathematics Education，21(3)，238-241。
7.	Flores, A.(1993)。Pythagoras meets van Hiele。School Science and Mathematics，93(30)，152-157。
8.	Fuys, D.(1985)。Van Hiele levels of thinking in geometry。Education and Urban Society，17(4)，447-462。
9.	Gutierrez, A.、Jaime, D.、Fortuny, J. M.(1991)。An alternative paradigm to evaluate the acquisition of the van Hiele levels。Journal for Research in Mathematics Education，22(3)，237-251。
10.	Hoffer, A.(1981)。Geometry is more than proof。Mathematics Teacher，74(1)，11-18。
11.	Mayberry, J. W.(1983)。The van Hiele levels of geometric thought in undergraduate preservice teachers。Journal for Research in Mathematics Education，14(1)，58-69。
12.	Suydam, M. N.(1985)。The shape of instruction in geometry: Some highlights from research。Mathematics Teacher，78(6)，481-486。
13.	Teppo, A.(1991)。Van Hiele levels of geometric thought revisited。Mathematics Teacher，84(3)，210-221。
14.	Usiskin, Z. P.(1972)。The effects of teaching Euclidean geometry via transformations on student achievement and attitudes in tenth grade geometry。Journal for Research in Mathematics Education，3(3)，249-259。
15.	Usiskin, Z. P.(1974)。Transformations in high school before 1970。Mathematics Teacher，67(5)，353-360。
16.	Usiskin, Z. P.(1980)。What should not be in the algebra and geometry curricula of average college-bound students。Mathematics Teacher，73(5)，412-424。
17.	van Hiele, P. M.(1974)。System separation and transfer。Educational Studies in Mathematics，5(4)，413-417。
18.	Usiskin, Z. P.、Coxford, A. F.(1972)。A transformational approach to tenth grade geometry。Mathematics Teacher，65(1)，21-29。
19.	Wilson, M.(1990)。Measuring a van Hiele geometry sequence: A reanalysis。Journal for Research in Mathematics Education，21(3)，230-237。
20.	Wilson, M.(1989)。A psychometric model of discontinuity in cognitive development。Psychological Bulletin，105(2)，276-289。
21.	Williams, E.(1980)。An investigation of senior high school students' understanding of the nature of mathematical proof。Journal for Research in Mathematics Education，11(2)，165-166。
22.	Burger, W. F.、Shaughnessy, J. M.(1986)。Characterizing the van Hiele levels of development in geometry。Journal for Research in Mathematics Education，17(1)，31-48。

會議論文
1.	Dees, R. L.(1982)。Sex differences in Geometry Achievement。The Annual Meeting of the American Educational Research Association。New York, NY。
2.	Fuys, D.、Geddes, D.(1984)。An investigation of van Hiele levels of thinking in geometry among sixth and ninth graders: Research findings and implications。The American Educational Research Association meeting in NEW Orleans, LA。

研究報告
1.	Burger, W. F.、Shaughnessy, J. M.(1986)。Assessing Children's intellectual growth in geometry。Covallis, OR：Oregon State University, Department of Mathematics。
2.	Burger, W. F.(1981)。Thought levels in geometry。Corvallis, OR：Oregon State University, Department of Mathematics。
3.	Mitchelmore, M. C.(1982)。Cooperative geometry research project。Mona, Jamaica：University of West Indies。
4.	Usiskin, Z. P.(1982)。Van Hiele levels and achievement in secondary school geometry。Chicago, IL：University of Chicago, Department of Education。

學位論文
1.	Chang, K. Y.(1992)。Spatial and geometric reasoning abilities of college students(博士論文)。Boston University。
2.	Corley, T. L.(1990)。Students' levels of thinking as related to achievement in geometry(博士論文)。Arizona State University，Tempe。
3.	Crowley, M. L.(1989)。The design and evaluation of an instrument for assessing mastery van Hiele levels of thinking about quadrilaterals(博士論文)。University of Maryland，College Park。
4.	Eberle, R. S.(1989)。The effects of instruction on the van Hiele levels of geometric reasoning in preservice elementary teachers(碩士論文)。The University of Texas at Austin。
5.	Finnell, L.(1992)。Metacognition and the van Hiele model of thinking in geometry(博士論文)。Georgia State University。
6.	Elchick, L. M.(1992)。The effects of software type, mathematics achievement, spatial visualization, locus of control, independent time of the investigation, and van Hiele level on geometric conjecturing ability(博士論文)。Pennsylvania State University。
7.	Land, J. E.(1990)。Appropriateness of the van Hiele model for describing students' cognitive processes on algebra tasks as typified by college students' learning of functions(博士論文)。Boston University。
8.	Lewellen, H.(1992)。Conceptualization of geometric motions in elementary school children: An extension of the van Hiele model(博士論文)。Kent State University。
9.	McClendon, M. E.(1990)。Application of the van Hiele model in evaluating elementary teachers' understanding of geometric concepts and improving their attitudes toward teaching geometry(博士論文)。University of South Florida，Sarasota。
10.	Mayberry, J. W.(1981)。An investigation of the van Hiele levels of geometric thought in undergraduate preservice teachers(博士論文)。University of Georgia。
11.	Naraine, B.(1989)。Relationships among eye fixation variables on task-oriented viewing of angles, van Hiele levels, spatial ability, and dependence(博士論文)。Ohio State University，Columbus。
12.	Molina, D. D.(1990)。The applicability of the van Hiele theory to transformational geometry(博士論文)。The University of Texas at Austin。
13.	Molina, D. D.(1987)。The teaching of transformational geometry in the secondary schools(碩士論文)。The University of Texas at Austin。
14.	Walker, J. D.(1973)。The value of the non-Euclidean geometries as enrichment(博士論文)。George Peabody College for Teachers，Nashville。
15.	Van Hiele-Geldof, D.(1957)。De didaktick van de Meetkunde in de eerset klass van het V.H.M.O.(博士論文)。University of Utrecht。
16.	Wilson, M.(1984)。A psychometric model of hierarchical development of three theories(博士論文)。The University of Chicago。
17.	Wu, D.(1985)。A comparison of the mathematics education of elementary schools in Taiwan, the Republic of China, with that of Boston, U. S.(碩士論文)。National Taiwan Normal University，Taipei。

圖書
1.	Borg, W. R.、Gall, M. D.(1989)。Educational research, an introduction。NY：Longman。
2.	Billstein, R.、Libeskind, S.、Lott, J. W.(1993)。A Problem solving approach to mathematics for elementary school teachers。Menlo Park, CA：The Benjamin/Cummings Publishing Company, Inc.。
3.	Cederberg, J. N.(1989)。A course in modern geometries。New York：Springer-Varlag Inc.。
4.	Chen, M.、Wu, D.、Lee, Y.(1987)。A comparative study of mathematics education for elementary and secondary schools in the Republic of China with that of the U. S.。Taipei：Provincial Taiwan Institution for Elementary School Teachers' Inservice Education。
5.	Courant, R.、Robbins, H.(1958)。What is Mathematics: An elementary approach to ideas and methods。London：Oxford University Press。
6.	Freudenthal, H.(1973)。Mathematics as an educational task。Dordrecht, Holland：Reidel。
7.	Freudenthal, H.(1991)。Revisiting mathematics education: China lectures。Kluwer Academic Publishers。
8.	Heath, T. L.(1956)。The thirteen books of Euclid's elements。New York：Dover Publishing Inc.。
9.	Heath, T. L.(1921)。A history of Greek mathematics。Oxford：Clarendon Press。
10.	Fuys, D.、Geddes, D.、Tischler, R.(1988)。The van Hiele model of thinking in geometry among adolescents。Reston, VA：The National Council of Teachers of Mathematics, Inc.。
11.	Hoffer, A.(1979)。Geometry: A model of the universe。Manlo Park, CA：Addison-Wesley Publishing Company。
12.	Henderson, K. B.(1973)。Geometry in the mathematics curriculum: Thirty-sixth yearbook of the National Council of Teachers of Mathematics。Reston, VA：The National Council of Teachers of Mathematics。
13.	Lesh, R. A.、Landau, M.(1983)。Acquisition of mathematics concepts and processes。New York, NY：Academic Press。
14.	Liu, Hau(1991)。Geometric concepts misunderstood by elementary school teachers。
15.	Lin, C. J.(1992)。An analysis of the van Hiele level of geometric thought of children。Taichung：Su-hang Publishing Co.。
16.	Ministry of Education of the Republic of China(1985)。Curriculum standards for junior high school。Taipei：Cheng-Chung Publishing Co.。
17.	Ministry of Education of the Republic of China(1976)。Curriculum Standards for Elementary School。Taipei：Cheng-Chung Publishing Co.。
18.	Meserve, B. E.(1983)。Fundamental concepts of geometry。New York：Dover。
19.	Mcknight, C. C.、Crosswhite, F. J.、Dossey, J. A.、Kifer, E.、Swafford, J. O.、Travers, K. J.、Cooney, T. J.(1987)。The underachieving curriculum: Assessing schools mathematics from an international perspective。Champaign：Stipes Publishing Company。
20.	Ministry of Education of the Republic of China(1985)。Curriculum standards for high school。Taipei：Cheng-Chung Publishing Co.。
21.	National Research Council(1989)。Everybody counts: A report to the nation on the future of mathematics education。Washington, DC：National Academy Press。
22.	National Institute of Editing and Translating of the Republic of China(1979)。Mathematics textbooks of elementary school。Taipei：National Institute of Editing and Translating of the Republic of China。
23.	National Council of Teachers of Mathematics(1991)。Professional standards for teaching mathematics。Reston, VA：National Council of Teachers of Mathematics。
24.	National Council of Teachers of Mathematics(1989)。Curriculum and evaluation standards for school mathematics。Reston, Virginia：National Council of Teachers of Mathematics。
25.	National Council of Teachers of Mathematics, Inc.(1980)。An agenda for action: Recommendations for school mathematics of the 1980's。Reston, VA：National Council of Teachers of Mathematics。
26.	Senk, S. L.、Usiskin, Z.(1982)。Geometry proof writing: A new view of sex differences in mathematics ability。Chicago, IL：Department of Education, University of Chicago。
27.	O'Daffer, P. G.、Clemens, S. R.(1977)。Geometry: An investigative approach。Menlo Park, CA：Addison-Wesley Publishing Company。
28.	Troutan, A.、Lichtenberg, B.(1991)。Mathematics: A good beginning strategies for teaching children。Pacific Grove, CA：Brooks/Cole Publishing Company。
29.	Texas Education Agency(1990)。Guidelines for teaching geometry。Austin, TX：Texas Education Agency。
30.	Texas Education Agency(1988)。Proclamation 65 of the State Board of Education advertising for bids on textbooks。Austin, TX：Texas Education Agency。
31.	Texas Education Agency(1986)。Mathematics framework, kindergarten-grade 12。Austin, TX：Texas Education Agency。
32.	van Hiele, Pierre M.(1986)。Structure and Insight: A Theory of Mathematics Education。Academic Press。

單篇論文
1.	Fuys, D.，Geddes, D.，Tischler, R.(1984)。English translations of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele，Columbus, OH：ERIC Information Analysis Center for Science, Mathematics, and Environmental Education。(No. ED 287 697)。
2.	Lesh, R. A.，Mierkiewicz, Diane B.(1987)。Recent research concerning the development of spatial and geometric concepts，Columbus, OH：ERIC/ SMEAC。(No. ED 159 062)。
3.	Martin, J. L.，Bradbard, D. A.(1976)。Space and geometry: Papers from a research workshop，Columbus, OH：ERIC Center for Science, Mathematics and Environmental Education。(No. ED 132)。

其他
1.	Chang, K. Y.(1992)。Spatial and geometric reasoning abilities of college students。
2.	Finnell, L.(1993)。Metacognition and the van Hiele model of thinking in geometry。
3.	Elchick, L. M.(1992)。The effects of software type, mathematics achievement, spatial visualization, locus of control, independent time of the investigation, and van Hiele level on geometric conjecturing ability。
4.	Land, J. E.(1991)。Appropriateness of the van Hiele model for describing students' cognitive processes on algebra tasks as typified by college students' learning of functions。
5.	Lewellen, H.(1992)。Conceptualization of geometric motions in elementary school children: An extension of the van Hiele model。
6.	Mayberry, J. W.(1981)。An investigation of the van Hiele levels of geometric thought in undergraduate preservice teachers。
7.	Wilson, M.(1984)。A psychometric model of hierarchical development of three theories。

圖書論文
1.	Clements, D. H.、Battista, M. T.(1992)。Geometry and spatial Reasoning。Handbook of research on mathematics teaching and learning。Reston, VA：National Council of Teachers of Mathematics, Inc.。
2.	Coxford, A. F. Jr.(1973)。A transformation approach to Euclidean geometry。Geometry in the mathematics curriculum (36th) Yearbook of the National Council of Teachers of Mathematics。Reston, VA：National Council of Teachers of Mathematics。
3.	Crowley, M. L.(1987)。The van Hiele model of the development of geometric thought。Learning and teaching geometry, k-12, 1987 Yearbook of the National Council of Teachers of Mathematics。Reston, Va：NCTM。
4.	Coxford, A. F.(1978)。Research directions in geometry。Recent research concerning the development of spatial and geometric concepts。Columbus, OH：ERIC/SMEA。
5.	Hoffer, A.(1983)。Van Hiele based research。Acquisition of mathematical concepts and processes。New York, NY：Academic Press。
6.	Hershkowitz, R.、Bruckheimer, M.、Vinner, S.(1987)。Activities with teacher based on cognitive research。Learning and teaching geometry, k-12。Reston, VA：The National Council of Teachers of Mathematics。
7.	Hershkowitz, R.、Bruckheimer, M.、Vinner, S.(1987)。Activities with teacher based on cognitive research。Learning and teaching geometry。Reston, VA：The National Council of Teachers of Mathematics。
8.	Hoffer, A.(1988)。Geometry and visual thinking。Teaching mathematics in grades k-8。Boston, MA：Allyn and Bacon, Inc.。
9.	Lindquist, M. M.、Shulte, A. P.(1987)。Learning and teaching geometry, k-12。1987 yearbook of the National Council of Teachers of Mathematics。Reston, VA：The National Council of Teachers of Mathematics。
10.	Usiskin, Z. P.(1987)。Resolving the continuing dilemmas in school geometry。Learning and teaching geometry, k-12, 1987 Yearbook of the National Council of Teachers of Mathematics。Reston, VA：The National Council of Teacher。
11.	Van Hiele, P. M.(1984)。A child's thought and geometry。English translations of selected writings of Dina van Hiele-Geldorf and Pierre M. van Hiele。Columbus, OH：ERIC Information Analysis Center for Science, Mathematics, and Environmental Education。
12.	van Hiele, P. M.(1984)。English summary。English translations of selected writings of Dina van Hiele-Geldorf and Pierre M. van Hiele。Columbus, OH：ERIC Information Analysis Center for Science, Mathematics, and Environmental Education。
13.	van Hiele, P. M.、van Hiele-Geldof, D.(1958)。A method of initiation into geometry。Report on methods of initiation into geometry。Groningen：J. B. Wolters。
14.	van Hiele-Geldof, D.(1984)。The didactics of geometry in the lowest class of secondary school。English translations of selected writing of Dina van Hiele-Geldorf and Pierre M. van Hiele。Columbus, OH：ERIC Information Analysis Center for Science, Mathematics, and Environmental Education。
15.	van Hiele-Geldof, D.(1984)。The didactics of geometry as a learning process for adults。English translations of selected writings of Dina van Hiele-Geldorf and Pierre M. van Hiele。Columbus, OH：ERIC Information Analysis Center for Science, Mathematics, and Environmental Education。
16.	Wirszup, I.(1976)。Breakthroughs in the psychology of learning and teaching geometry。Space and geometry: Papers from a research workshop。Columbus, OH：ERIC Center for Science, Mathematics and Environmental Education。

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