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Volumn 2, Issue 2, 2004, Pages 287-304

Distinguishing two stages of mathematics conceptual learning

Author keywords

Abstraction; Concept development; Conceptual learning; Conceptualization; Epistemology; Learning; Mathematics learning; Stages of learning

Indexed keywords


EID: 18244365817     PISSN: 15710068     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10763-004-7479-4     Document Type: Conference Paper
Times cited : (56)

References (44)
  • 3
    • 84970382585 scopus 로고
    • Toward a solution of the learning paradox
    • Bereiter, C. (1985). Toward a solution of the learning paradox. Review of Educational Research, 55(2), 201-226.
    • (1985) Review of Educational Research , vol.55 , Issue.2 , pp. 201-226
    • Bereiter, C.1
  • 5
    • 18244366139 scopus 로고    scopus 로고
    • Modeling, symbolizing, and tool use in statistical data analysis
    • K. Gravemeijer, R. Lehrer, B. Van Oers & L. Verschaffel (Eds.), Dordrecht, The Netherlands: Kluwer
    • Cobb, P. (2002). Modeling, symbolizing, and tool use in statistical data analysis. In K. Gravemeijer, R. Lehrer, B. Van Oers & L. Verschaffel (Eds.), Symbolizing, modeling, and tool use in mathematics education (pp. 171-195). Dordrecht, The Netherlands: Kluwer.
    • (2002) Symbolizing, Modeling, and Tool Use in Mathematics Education , pp. 171-195
    • Cobb, P.1
  • 7
    • 0002573795 scopus 로고
    • Reflective abstraction in advanced mathematical thinking
    • D. Tall (Ed.), Dordrecht, The Netherlands: Kluwer
    • Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Dordrecht, The Netherlands: Kluwer.
    • (1991) Advanced Mathematical Thinking , pp. 95-123
    • Dubinsky, E.1
  • 8
    • 18244396424 scopus 로고
    • A theory and practice of learning college mathematics
    • A.H. Schoenfeld (Ed.), Hillsdale, NJ: Lawrence Erlbaum
    • Dubinsky, E. (1994). A theory and practice of learning college mathematics. In A.H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 221-243). Hillsdale, NJ: Lawrence Erlbaum.
    • (1994) Mathematical Thinking and Problem Solving , pp. 221-243
    • Dubinsky, E.1
  • 9
    • 0001995528 scopus 로고
    • Reflective abstraction and mathematics education: The genetic decomposition of induction and compactness
    • Dubinsky, E. & Lewin, R (1986). Reflective abstraction and mathematics education: The genetic decomposition of induction and compactness. Journal of Mathematical Behavior, 5, 55-92.
    • (1986) Journal of Mathematical Behavior , vol.5 , pp. 55-92
    • Dubinsky, E.1    Lewin, R.2
  • 10
    • 0002951974 scopus 로고
    • On the impossibility of acquiring "more powerful" structures
    • M. Piattelli-Palmarini (Ed.), Cambridge, MA: Harvard University
    • Fodor, J. (1980). On the impossibility of acquiring "more powerful" structures. In M. Piattelli-Palmarini (Ed.), Language and learning: The debate between Jean Piage t and Noam Chomsky (pp. 142-162). Cambridge, MA: Harvard University.
    • (1980) Language and Learning: the Debate between Jean Piage T and Noam Chomsky , pp. 142-162
    • Fodor, J.1
  • 13
    • 18244395385 scopus 로고    scopus 로고
    • Emergent models as an instructional design heuristic
    • K. Gravemeijer, R. Lehrer, B. Van Oers & L. Verschaffel (Eds.), Dordrecht, The Netherlands: Kluwer
    • Gravemeijer, K. & Stephan, M. (2002). Emergent models as an instructional design heuristic. In K. Gravemeijer, R. Lehrer, B. Van Oers & L. Verschaffel (Eds.), Symbolizing, modeling, and tool use in mathematics education (pp. 145-169). Dordrecht, The Netherlands: Kluwer.
    • (2002) Symbolizing, Modeling, and Tool Use in Mathematics Education , pp. 145-169
    • Gravemeijer, K.1    Stephan, M.2
  • 15
    • 18244383591 scopus 로고
    • Understanding for teaching for understanding
    • Kieren, T.E. (1990). Understanding for teaching for understanding. The Alberta Journal of Educational Research, XXXVI(3), 191-201.
    • (1990) The Alberta Journal of Educational Research , vol.36 , Issue.3 , pp. 191-201
    • Kieren, T.E.1
  • 16
    • 0003865799 scopus 로고    scopus 로고
    • Reston, VA: National Council of Teachers of Mathematics
    • National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
    • (2000) Principles and Standards for School Mathematics
  • 17
    • 0001549062 scopus 로고    scopus 로고
    • From fractions to rational numbers of arithmetic: A reorganization hypothesis
    • Olive, J. (1999). From fractions to rational numbers of arithmetic: A reorganization hypothesis. Mathematical Thinking and Learning, I, 279-314.
    • (1999) Mathematical Thinking and Learning, I , pp. 279-314
    • Olive, J.1
  • 18
  • 19
    • 0004268713 scopus 로고
    • (E. Duckworth, Trans.). New York: Columbia University Press
    • Piaget, J. (1970). Genetic epistemology (E. Duckworth, Trans.). New York: Columbia University Press.
    • (1970) Genetic Epistemology
    • Piaget, J.1
  • 20
    • 0004112394 scopus 로고
    • (B. Walsh, Trans.). Chicago: The University of Chicago
    • Piaget, J. (1971). Biology and knowledge (B. Walsh, Trans.). Chicago: The University of Chicago.
    • (1971) Biology and Knowledge
    • Piaget, J.1
  • 22
    • 0002010262 scopus 로고
    • Opening the debate: The psychogenesis of knowledge and its epistemological significance
    • M. Piattelli-Palmarini (Ed.), Cambridge, MA: Harvard University
    • Piaget, J. (1980b). Opening the debate: The psychogenesis of knowledge and its epistemological significance. In M. Piattelli-Palmarini (Ed.), Language and learning: The debate between Jean Piaget and Noam Chomsky (pp. 23-34). Cambridge, MA: Harvard University.
    • (1980) Language and Learning: the Debate between Jean Piaget and Noam Chomsky , pp. 23-34
    • Piaget, J.1
  • 24
    • 0004323850 scopus 로고    scopus 로고
    • (R.L. Campbell, Trans.). Philadelphia: Taylor and Francis
    • Piaget, J. (2001). Studies in reflecting abstraction (R.L. Campbell, Trans.). Philadelphia: Taylor and Francis.
    • (2001) Studies in Reflecting Abstraction
    • Piaget, J.1
  • 26
    • 0000125593 scopus 로고
    • Creating constructivist environments and constructing creative mathematics
    • Pirie, S.E.B. & Kieren, T.E. (1992). Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics, 23(5), 505-528.
    • (1992) Educational Studies in Mathematics , vol.23 , Issue.5 , pp. 505-528
    • Pirie, S.E.B.1    Kieren, T.E.2
  • 27
    • 0842288567 scopus 로고
    • On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin
    • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 26, 114-145.
    • (1991) Educational Studies in Mathematics , vol.26 , pp. 114-145
    • Sfard, A.1
  • 29
    • 0009258747 scopus 로고
    • The development of algebra: Confronting historical and psychological perspectives
    • Sfard, A. (1995). The development of algebra: Confronting historical and psychological perspectives. Journal of Mathematical Behavior, 14, 15-39.
    • (1995) Journal of Mathematical Behavior , vol.14 , pp. 15-39
    • Sfard, A.1
  • 30
    • 0002464572 scopus 로고    scopus 로고
    • Symbolizing mathematical reality into being - Or how mathematical discourse and mathematical objects create each other
    • P. Cobb, E. Yackel & K. McClain (Eds.), Mahwah, NJ: Lawrence Erlbaum
    • Sfard, A. (2000). Symbolizing mathematical reality into being - or how mathematical discourse and mathematical objects create each other. In P. Cobb, E. Yackel & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 37-98). Mahwah, NJ: Lawrence Erlbaum.
    • (2000) Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design , pp. 37-98
    • Sfard, A.1
  • 31
    • 24944477378 scopus 로고
    • The gains and pitfalls of reification - The case of algebra
    • Sfard, A. & Linchevski, L. (1994). The gains and pitfalls of reification - the case of algebra. Educational Studies in Mathematics, 26, 191-228.
    • (1994) Educational Studies in Mathematics , vol.26 , pp. 191-228
    • Sfard, A.1    Linchevski, L.2
  • 32
    • 8644222004 scopus 로고    scopus 로고
    • Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction
    • Simon, M.A., Tzur, R., Heinz, K. & Kinzel, M. (2004). Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction. Journal for Research in Mathematics Education, 35(5), 305-329.
    • (2004) Journal for Research in Mathematics Education , vol.35 , Issue.5 , pp. 305-329
    • Simon, M.A.1    Tzur, R.2    Heinz, K.3    Kinzel, M.4
  • 33
    • 0001889880 scopus 로고
    • Children's multiplying schemes
    • G. Harel & J. Confrey (Eds.), Albany, NY: State University of New York Press
    • Steffe, L.P. (1994). Children's multiplying schemes. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3-39). Albany, NY: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 3-39
    • Steffe, L.P.1
  • 34
    • 0009596605 scopus 로고    scopus 로고
    • A new hypothesis concerning children's fractional knowledge
    • Steffe, L.P. (2002). A new hypothesis concerning children's fractional knowledge. Journal of Mathematical Behavior, 20, 1-41.
    • (2002) Journal of Mathematical Behavior , vol.20 , pp. 1-41
    • Steffe, L.P.1
  • 36
    • 18244410475 scopus 로고    scopus 로고
    • Didactic objects and didactic models in radical constructivism
    • K. Gravemeijer, R. Lehrer, B. Van Oers & L. Verschaffel (Eds.), Dordrecht The Netherlands: Kluwer
    • Thompson, P.W. (2002). Didactic objects and didactic models in radical constructivism. In K. Gravemeijer, R. Lehrer, B. Van Oers & L. Verschaffel (Eds.), Symbolizing, modeling, and tool use in mathematics education (pp. 197-220). Dordrecht, The Netherlands: Kluwer.
    • (2002) Symbolizing, Modeling, and Tool Use in Mathematics Education , pp. 197-220
    • Thompson, P.W.1
  • 38
    • 22644452255 scopus 로고    scopus 로고
    • An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning
    • Tzur, R. (1999). An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning. Journal for Research in Mathematics Education, 30(4), 390-416.
    • (1999) Journal for Research in Mathematics Education , vol.30 , Issue.4 , pp. 390-416
    • Tzur, R.1
  • 39
    • 0033074792 scopus 로고    scopus 로고
    • An integrated research on children's construction of meaningful, symbolic, partitioning-related conceptions, and the teacher's role in fostering that learning
    • Tzur, R. (2000). An integrated research on children's construction of meaningful, symbolic, partitioning-related conceptions, and the teacher's role in fostering that learning. Journal of Mathematical Behavior, 18(2), 123-147.
    • (2000) Journal of Mathematical Behavior , vol.18 , Issue.2 , pp. 123-147
    • Tzur, R.1
  • 40
    • 0842266964 scopus 로고    scopus 로고
    • Re-evaluating assessment in light of an integrated model of mathematics teaching and learning
    • M. van den Heuvel-Panhuizen (Ed.), Utrecht, The Netherlands: Freudenthal Institute and Utrecht University
    • Tzur, R. (2001). Re-evaluating assessment in light of an integrated model of mathematics teaching and learning. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Annual Meeting of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 319-326). Utrecht, The Netherlands: Freudenthal Institute and Utrecht University.
    • (2001) Proceedings of the 25th Annual Meeting of the International Group for the Psychology of Mathematics Education , vol.4 , pp. 319-326
    • Tzur, R.1
  • 41
    • 0842312241 scopus 로고    scopus 로고
    • Teacher and students' joint production of a reversible fraction conception
    • Tzur, R. (2004). Teacher and students' joint production of a reversible fraction conception. Journal of Mathematical Behavior, 23, 93-114.
    • (2004) Journal of Mathematical Behavior , vol.23 , pp. 93-114
    • Tzur, R.1
  • 43
    • 0001784057 scopus 로고
    • Abstraction, re-presentation, and reflection: An interpretation of experience and Piaget's approach
    • L.P. Steffe (Ed.), New York: Springer
    • von Glasersfeld, E. (1991). Abstraction, re-presentation, and reflection: An interpretation of experience and Piaget's approach. In L.P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 45-67). New York: Springer.
    • (1991) Epistemological Foundations of Mathematical Experience , pp. 45-67
    • Von Glasersfeld, E.1


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