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1 年數朗 * 識識識來數行識識略歷不行數數數念數邏識數 * 朗理理 A Study of the Essence of Constructivism-based Mathematics Teaching PI-LANG WANG ABSTRACT The epistemological perspectives inherent in constructivism emphasize that knowledge is constructed within each individual s mind. The new perspectives of knowledge and learning have challenged the instruction traditionally adopted in most schools, and further initiated to reform and change the classroom instruction. It is assumed in traditional teaching that knowledge can be conveyed to learners by teachers via language, words, and symbols and learners can pick up exact copies of teachers knowledge for their own use. Constructivists criticize the naive assumption of instruction and reject the traditional teaching approach. The school teaching advocated by constructivists is an unique process characterized by active interaction between teacher and students for promoting concept development and deep understanding. The knowledge construction process cannot be performed as following prescription and cookbook. Compared with the essence of the reformed instruction practiced in Western countries, the current changes in mathematics teaching in primary schools in Taiwan are in nature on the superficial surface. As the mathematics teaching and learning still confined to traditional limitations, it is difficult to expect students to develop deep concept understanding and to construct logico-mathematical knowledge on their own. Keywords: constructivism-based mathematics teaching 1 2

2 數年北利論識歷了不理論更理論數年列說數說念念論數理理了數領理歷樂不了度理論力論論勵來識行例年聯立立了理論年六年立立識理論識行識識理不識年數數數了論論數易理連了年連年數數力力落數數異數數論落力例數數說理論理論說數歷識理論契理論數例說參數識數數略 3 4

3 數歷不識論識什識來識類識說來類不力識識說來理理理識不來識論識理論理年理說識識不不說識不說念念來說識行說識來識行念行識理不念識不識識行念理論識領不切了理理論來說理論理論不理論理論粒論說不理論類識識類陸來識不論不理識不識不立識說識念不識識立 5 6

4 數句識說念識不不念不說念念說不識理論行論立不了量念理論不說理論略說不行不索立立論力類類錄說論略聯論行論理念力念類不念識不不不念念念狀念什了識來數行不識識略不領數 7 8

5 數不力數歷理論參數年來數理論歷更識數量數例說年數年數數說數行年索數念什數念不更歷更什什理不論不論識立數念識年女練了行數了糖了糖糖例讀不論不立來來說令來說不不什不立來說了不來說見說不不論論說不說理不來了 9 10

6 數理說不說數了說數數來來說不說說了理數不了數數理數理數數念不來易練數了數更數了了更念率不來數車離車行了行車了了來說不不什了說來什不了來說不來說數不說不來不說數數說不行論參來說來了說什說數了說什說不什說說說了了不見說說什數 11 12

7 數說了弄了不說來了說來說來說什不數來數了了數了數令力數不力來樂不列不更什什年數量數量歷不什來不數年行年數量歷輪廓易易狀讀量欄數令數了讀令量論數念力行數數念行了六立類識數念了沈年量什什沈念年來說了說什說不不什說 13 14

8 數來了更沈說不量說了立來量度來不說不留旅量量說量不了不什了論論量不量說量量了不什不量不量不量不離論不論識識量來量量量量什來量度來量論說來量行量見見行說不不藍廊藍度量藍度來量量量說量樂了什類力藍度量量來量論來不 15 16

9 數力不量念異量識論念說藍度量念什什量年數數念來念不切狀念不數行數不數識切數數識數復練數數識數識不不數數數念數數略數數數念論念年歷數數了數勵歷數數更數論量數來數念不數數年數數年行數老老老說練切練數數老老練練六練料類數類易立立六異 17 18

10 數老數不什切樂例識不行不說識了來老狀樂樂菱綠說不老不來說說不不理數數數老不老老了識不不說不列力勵說說了不了來不老數數連便老來聯數量不六六六六老量數老老老不類數數數例說歷不歷不不不復練練數 19 20

11 數勵論不理數念數識數邏識數不數邏識數例不數數數數歷數念不若不不來來了論來說更說不不不邏不識領理不說行數數論數數數數不數例年數例說裡什什來錄說說裡來不論列例糖糖糖列數立行年數數識不識練類年數數了數行數論列列列列六例列 21 22

12 數列列列列六列列列了數例數更數年數列數省例來來來來了來了來量來來數 23 24

13 數不列列來了烈論數年論數論理念論歷論歷論論數論歷說略論理略數理論錄論數狀說略略不說例綠來綠什什綠論不說什不說說勵例連什什什度不來不論什什老更什說不不什不什什老不行說裡 25 26

14 數什說論說略易例說數數論數論數理念數論數理念數參數數數來不數練理論來念數數念論念年行了六了不數念數數量行參說行論數念不行數論論例不論不列不不理行不什說說念說不說不什不說老不行說念念念不理說不行不令不數 27 28

15 數識念論數識了不連什什什度不來不老不行說說了陸論立理論念識說了歷歷不度不理理念識度識更更復練練行識理數數念數邏識行數更更更數落不力論老老老不老切老論不了數易來不來不數不理論不立理論落流行不理論不力識不論歷度歷不不不 29 30

16 數參料樂數數參北數省北論數年度論 Coles, D. & Price, A. (1998). How does a constructivist perspective influence mathematics teaching? In M. Littledyke & L. Huxford (Eds.), Teaching the primary curriculum for constructive learning. London: David Fulton Publishers. Confrey, J. (1998). Voice and perspective: hearing epistemological innovation in students words. In M. Larochelle, N. Bednarz, & J. Garrison (Eds.), Constructivism and education. New York: Cambridge University Press. Crain, W. (1992). Theories of development: concepts and application. Englewood Clifffs, New Jerrsey: Prentice-Hall Inc. Fosnot, C. T. (1996). Constructivism: A psychological theory of learning. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice. New York: Teachers College Press. Fosnot, C. T. (1996). Teacher construct constructivism: The center for constructivist teaching/teacher preparation project. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice. New York: Teachers College Press. Kamii, C. (2000). Young children reinvent arithmetic: Implications of Piaget s Theory. New York: Teachers College Press. Lester, J. B. (1996). Is the algorithm all there is In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice. New York: Teachers College Press. Schifter, D. (1996). A constructivist perspective on teaching and learning Mathematics. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice. New York: Teachers College Press. von Glasersfeld, E. (1996). Introduction: Aspects of constructivism. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice. New York: Teachers College Press. von Glaseersfeld, E. (1998). Why constructivism must be radical. In M. Larochelle, N. Bednarz, & J. Garrison (Eds.), Constructivism and education. New York: Cambridge University Press

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