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Volumn 79, Issue 1, 2012, Pages 61-83

Levels of students' "conception" of fractions

Author keywords

Comparison; Equivalence; Fraction; Measurement; Part whole subconstruct; Procedural and conceptual understanding; Rasch model

Indexed keywords


EID: 82555174365     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-011-9338-x     Document Type: Article
Times cited : (60)

References (34)
  • 5
    • 82555168712 scopus 로고    scopus 로고
    • Didactical implications of children's difficulties in learning the fraction concept
    • Boulet, G. (1998). Didactical implications of children's difficulties in learning the fraction concept. Focus on Learning Problems in Mathematics, 21(3), 48-66.
    • (1998) Focus on Learning Problems in Mathematics , vol.21 , Issue.3 , pp. 48-66
    • Boulet, G.1
  • 6
    • 0000973077 scopus 로고
    • Role of conceptual knowledge in mathematical procedural learning
    • Byrnes, J. P., & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27, 777-786.
    • (1991) Developmental Psychology , vol.27 , pp. 777-786
    • Byrnes, J.P.1    Wasik, B.A.2
  • 7
    • 33846799328 scopus 로고    scopus 로고
    • Drawing on a theoretical model to study students' understandings of fraction
    • Charalambous, C., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students' understandings of fraction. Educational Studies in Mathematics, 64, 293-316.
    • (2007) Educational Studies in Mathematics , vol.64 , pp. 293-316
    • Charalambous, C.1    Pitta-Pantazi, D.2
  • 12
    • 0002573795 scopus 로고
    • Reflective abstraction in advance mathematical thinking
    • D. Tall (Ed.), Netherlands: Springer
    • Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-126). Netherlands: Springer.
    • (1991) Advanced Mathematical Thinking , pp. 95-126
    • Dubinsky, E.1
  • 14
    • 54649084690 scopus 로고    scopus 로고
    • The roles of reification and reflective abstraction in the development of abstract thought: Transitions from arithmetic to algebra
    • Goodson-Espy, T. (1998). The roles of reification and reflective abstraction in the development of abstract thought: Transitions from arithmetic to algebra. Educational Studies in Mathematics, 36, 219-245.
    • (1998) Educational Studies in Mathematics , vol.36 , pp. 219-245
    • Goodson-Espy, T.1
  • 15
    • 21344483370 scopus 로고
    • Duality, ambiguity and flexibility: A proceptual view of simple arithmetic
    • Gray, E., & Tall, D. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 26(2), 115-141.
    • (1994) Journal for Research in Mathematics Education , vol.26 , Issue.2 , pp. 115-141
    • Gray, E.1    Tall, D.2
  • 16
    • 78649565341 scopus 로고    scopus 로고
    • Abstraction as a natural process of mental compression
    • Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23-40.
    • (2007) Mathematics Education Research Journal , vol.19 , Issue.2 , pp. 23-40
    • Gray, E.1    Tall, D.2
  • 17
    • 77955045797 scopus 로고    scopus 로고
    • Individual differences in conceptual and procedural knowledge when learning fractions
    • Hallett, D., Nunes, T., & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal of Educational Psychology, 102(2), 395-406.
    • (2010) Journal of Educational Psychology , vol.102 , Issue.2 , pp. 395-406
    • Hallett, D.1    Nunes, T.2    Bryant, P.3
  • 20
    • 85065691630 scopus 로고
    • Conceptual and procedural knowledge in mathematics: An introduction analysis
    • J. Hiebert (Ed.), Hillsdale: Erlbaum
    • Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introduction analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale: Erlbaum.
    • (1986) Conceptual and Procedural Knowledge: The Case of Mathematics , pp. 1-27
    • Hiebert, J.1    Lefevre, P.2
  • 21
    • 0003314423 scopus 로고
    • Equivalent fractions: Their difficulty and educational implications
    • Kamii, C., & Clark, F. (1995). Equivalent fractions: Their difficulty and educational implications. The Journal of Mathematical Behavior, 14(4), 365-378.
    • (1995) The Journal of Mathematical Behavior , vol.14 , Issue.4 , pp. 365-378
    • Kamii, C.1    Clark, F.2
  • 24
    • 0002358189 scopus 로고
    • Rational and fractional numbers: From quotient fields to recursive understanding
    • T. P. Carpenter, E. Fennema, and T. A. Romberg (Eds.), New Jersey: Erlbaum
    • Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 49-84). New Jersey: Erlbaum.
    • (1993) Rational Numbers: An Integration of Research , pp. 49-84
    • Kieren, T.E.1
  • 26
    • 33745659696 scopus 로고    scopus 로고
    • A procedure for detecting pattern clustering in measurement design
    • M. Wilson and G. EngelhardJr (Eds.), Ablex Publishing: Greenwich
    • Marcoulides, G. A., & Drezner, Z. (1999). A procedure for detecting pattern clustering in measurement design. In M. Wilson & G. Engelhard Jr. (Eds.), Objective measurement: Theory into practice (Vol. 5, pp. 261-277). Ablex Publishing: Greenwich.
    • (1999) Objective Measurement: Theory into Practice , vol.5 , pp. 261-277
    • Marcoulides, G.A.1    Drezner, Z.2
  • 27
    • 0242474792 scopus 로고    scopus 로고
    • Semantic domains of rational numbers and the acquisition of fraction equivalence
    • Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26, 400-417.
    • (2001) Contemporary Educational Psychology , vol.26 , pp. 400-417
    • Ni, Y.1
  • 28
    • 0001695025 scopus 로고
    • The development of proportional reasoning and the ration concept. Part.1-Differentation of stages
    • Noelting, G. (1983). The development of proportional reasoning and the ratio concept. Part. 1-Differentation of stages. Educational Studies in Mathematics, 11, 217-253.
    • (1983) Educational Studies in Mathematics , vol.11 , pp. 217-253
    • Noelting, G.1
  • 30
    • 58449105010 scopus 로고    scopus 로고
    • The fundamental cycle of concept construction underlying various theoretical frameworks
    • Pegg, J., & Tall, D. (2005). The fundamental cycle of concept construction underlying various theoretical frameworks. International Reviews on Mathematical Education, 37(6), 468-475.
    • (2005) International Reviews on Mathematical Education , vol.37 , Issue.6 , pp. 468-475
    • Pegg, J.1    Tall, D.2
  • 31
    • 0035602865 scopus 로고    scopus 로고
    • Developing conceptual understanding and procedural skill in mathematics: An iterative process
    • Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93, 346-362.
    • (2001) Journal of Educational Psychology , vol.93 , pp. 346-362
    • Rittle-Johnson, B.1    Siegler, R.S.2    Alibali, M.W.3
  • 33
    • 0002546637 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, 22, 1-36.
    • (1991) Educational Studies in Mathematics , vol.22 , pp. 1-36
    • Sfard, A.1


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