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Volumn , Issue , 2013, Pages 27-50

Advanced mathematical-thinking at any age: Its nature and its development

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Indexed keywords


EID: 84925695758     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9781315045955     Document Type: Chapter
Times cited : (48)

References (15)
  • 1
    • 0003599607 scopus 로고    scopus 로고
    • (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Eds. & Trans.). Dordrecht, The Netherlands: Kluwer Academic
    • Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Eds. & Trans.). Dordrecht, The Netherlands: Kluwer Academic.
    • (1997) Theory of Didactical Situations in Mathematics
    • Brousseau, G.1
  • 2
    • 84925741030 scopus 로고
    • Meaning and skill—maintaining the balance
    • Brownell, W. A. (1956). Meaning and skill—Maintaining the balance. Arithmetic Teacher, 3,129-136.
    • (1956) Arithmetic Teacher , vol.3 , pp. 129-136
    • Brownell, W.A.1
  • 3
    • 33745591680 scopus 로고    scopus 로고
    • Developing students’ proportional reasoning: A chinese perspective
    • B. Litwiller & G. Bright (Eds.), Reston, VA: National Council of Teachers of Mathematics
    • Cai, J., & Sun, W. (2002). Developing students’ proportional reasoning: A Chinese perspective. In B. Litwiller & G. Bright (Eds.), Making sense o f fractions, ratios, and proportions (pp. 195-205). Reston, VA: National Council of Teachers of Mathematics.
    • (2002) Making Sense O F Fractions, Ratios, and Proportions , pp. 195-205
    • Cai, J.1    Sun, W.2
  • 5
    • 0346600308 scopus 로고
    • The role of mathematics transformation and practice in mathematical development
    • L. P. Steffe (Ed.), New York: Springer-Verlag
    • Cooper, R. (1991). The role of mathematics transformation and practice in mathematical development. In L. P. Steffe (Ed.), Epistemological foundations in mathematical experience (pp. 102-123). New York: Springer-Verlag.
    • (1991) Epistemological Foundations in Mathematical Experience , pp. 102-123
    • Cooper, R.1
  • 6
  • 8
    • 0002573795 scopus 로고
    • Reflective abstraction in advanced mathematical thinking
    • D. Tall (Ed.), Dordrecht, The Netherlands: Kluwer Academic
    • Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-102). Dordrecht, The Netherlands: Kluwer Academic.
    • (1991) Advanced Mathematical Thinking , pp. 95-102
    • Dubinsky, E.1
  • 10
    • 1642330208 scopus 로고    scopus 로고
    • Blending the best of the twentieth century to achieve a mathematics equity pedagogy in the twenty-first century
    • M. J. Burke & F. R. Curcio (Eds.), Reston, VA: National Council of Teachers of Mathematics
    • Fuson, K. C., De La Cruz, Y., Smith, S. T., Cicero, A. M. L., Hudson, K., Pilar, R., et al. (2000). Blending the best of the twentieth century to achieve a mathematics equity pedagogy in the twenty-first century. In M. J. Burke & F. R. Curcio (Eds.), Learning mathematics fo r a new century (pp. 197-212). Reston, VA: National Council of Teachers of Mathematics.
    • (2000) Learning Mathematics Fo R a New Century , pp. 197-212
    • Fuson, K.C.1    De La Cruz, Y.2    Smith, S.T.3    Cicero, A.M.L.4    Hudson, K.5    Pilar, R.6
  • 11
    • 0000872159 scopus 로고
    • Conceptual entities
    • D. Genter & A. L. Stevens (Eds.), Hillsdale, NJ: Lawrence Erlbaum Associates, Inc
    • Greeno, J. (1983). Conceptual entities. In D. Genter & A. L. Stevens (Eds.), Mental models (pp. 227-252). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
    • (1983) Mental Models , pp. 227-252
    • Greeno, J.1
  • 12
    • 0010070825 scopus 로고
    • Nonconservation of multiplication and division involving decimals
    • Greer, B. (1987). Nonconservation of multiplication and division involving decimals. Journal for Research in Mathematics Education, 18, 37-45.
    • (1987) Journal for Research in Mathematics Education , vol.18 , pp. 37-45
    • Greer, B.1
  • 13
    • 0032372165 scopus 로고    scopus 로고
    • Two dual assertions: The first on learning and the second on teaching (or vice versa)
    • Harel, G. (1998). Two dual assertions: The first on learning and the second on teaching (or vice versa). The American Mathematical Monthly, 105, 497-507.
    • (1998) The American Mathematical Monthly , vol.105 , pp. 497-507
    • Harel, G.1
  • 14
    • 4243702904 scopus 로고    scopus 로고
    • Students’ understanding of proofs: A historical analysis and implications for the teaching of geometry and linear algebra
    • Harel, G. (1999). Students’ understanding of proofs: A historical analysis and implications for the teaching of geometry and linear algebra. Linear Algebra and Its Applications, 302 -303, 601-613.
    • (1999) Linear Algebra and Its Applications, 302 -303 , pp. 601-613
    • Harel, G.1
  • 15
    • 33947725910 scopus 로고    scopus 로고
    • The development of mathematical induction as a proof scheme: A model for da7?-based instruction
    • S. Campbell & R. Zazkis (Eds.), Westport, CT: Ablex
    • Harel, G. (2001). The development of mathematical induction as a proof scheme: A model for DA7?-based instruction. In S. Campbell & R. Zazkis (Eds.), Learning and teaching number theory (pp. 185-212). Westport, CT: Ablex.
    • (2001) Learning and Teaching Number Theory , pp. 185-212
    • Harel, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.