메뉴 건너뛰기




Volumn 90, Issue 1, 2015, Pages 39-56

Inappropriately applying natural number properties in rational number tasks: characterizing the development of the natural number bias through primary and secondary education

Author keywords

Fraction; Natural number bias; Primary education; Rational number; Secondary education

Indexed keywords


EID: 84938333283     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-015-9613-3     Document Type: Article
Times cited : (44)

References (36)
  • 1
    • 70349947205 scopus 로고    scopus 로고
    • Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction
    • Clarke, D. M., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72, 127–138. doi:10.10007/s10649-009-9198-9
    • (2009) Educational Studies in Mathematics , vol.72 , pp. 127-138
    • Clarke, D.M.1    Roche, A.2
  • 2
    • 23044533336 scopus 로고    scopus 로고
    • Initial fraction learning by fourth- and fifth- grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum
    • Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth- grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33, 111–144.
    • (2002) Journal for Research in Mathematics Education , vol.33 , pp. 111-144
    • Cramer, K.A.1    Post, T.R.2    delMas, R.C.3
  • 3
    • 85139490904 scopus 로고    scopus 로고
    • The whole number bias in fraction magnitude comparisons with adults
    • Carlson L, Hoelscher C, Shipley TF, (eds), Cognitive Science Society, Austin
    • De Wolf, M., & Vosniadou, S. (2011). The whole number bias in fraction magnitude comparisons with adults. In L. Carlson, C. Hoelscher, & T. F. Shipley (Eds.), Proceedings of the 33rd annual conference of the cognitive science society (pp. 1751–1756). Austin: Cognitive Science Society.
    • (2011) Proceedings of the 33rd annual conference of the cognitive science society , pp. 1751-1756
    • De Wolf, M.1    Vosniadou, S.2
  • 4
    • 84938370771 scopus 로고    scopus 로고
    • [From natural to rational numbers. A curriculum analysis of 3 Flemish mathematics textbooks] (Unpublished master's thesis), Katholieke Universiteit Leuven, Faculteit Psychologie en Pedagogische Wetenschappen, Belgium
    • Debou, E., & Verschetze, L. (2012). De overgang van natuurlijke naar rationale getallen. Een curriculumanalyse van drie Vlaamse wiskundemethoden [From natural to rational numbers. A curriculum analysis of 3 Flemish mathematics textbooks] (Unpublished master's thesis). Belgium: Katholieke Universiteit Leuven, Faculteit Psychologie en Pedagogische Wetenschappen.
    • (2012) De overgang van natuurlijke naar rationale getallen. Een curriculumanalyse van drie Vlaamse wiskundemethoden
    • Debou, E.1    Verschetze, L.2
  • 5
    • 84885407996 scopus 로고    scopus 로고
    • A componential view of children’s difficulties in learning fractions
    • Gabriel, F., Coché, F., Szucs, D., Carette, V., Rey, B., & Content, A. (2013). A componential view of children’s difficulties in learning fractions. Frontiers in Psychology, 4, 1–12. doi:10.3389/fpsyg.2013.00715
    • (2013) Frontiers in Psychology , vol.4 , pp. 1-12
    • Gabriel, F.1    Coché, F.2    Szucs, D.3    Carette, V.4    Rey, B.5    Content, A.6
  • 6
    • 85015563689 scopus 로고    scopus 로고
    • Leerplannen
    • Gemeenschapsonderwijs. (2014). Leerplannen. Geraadpleegd op Retrieved from http://www.gemeenschapsonderwijs.be/sites/portaal_nieuw/Prikbordvoorleerkrachten/Basisonderwijs/leerplannen/Leerplannen%2020102011/Wiskunde%20-%20LO.pdf
    • (2014) Geraadpleegd op Retrieved from
  • 8
    • 13844262803 scopus 로고    scopus 로고
    • The growth of mathematics through conceptual restructuring
    • Greer, B. (2004). The growth of mathematics through conceptual restructuring. Learning and Instruction, 14, 541–548. doi:10.1016/j.learninstruc.2004.06.018
    • (2004) Learning and Instruction , vol.14 , pp. 541-548
    • Greer, B.1
  • 9
    • 0013467151 scopus 로고
    • On difficulties with fractions
    • Hasemann, C. (1981). On difficulties with fractions. Educational Studies in Mathematics, 12, 171–187. doi:10.1007/BF00386047
    • (1981) Educational Studies in Mathematics , vol.12 , pp. 171-187
    • Hasemann, C.1
  • 10
    • 77649173768 scopus 로고
    • Longitudinal data analysis using generalized linear models
    • Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22. doi:10.1093/biomet/73.1.13
    • (1986) Biometrika , vol.73 , pp. 13-22
    • Liang, K.Y.1    Zeger, S.L.2
  • 12
    • 49549099008 scopus 로고    scopus 로고
    • Parts and ‘holes’: Gaps in rational number sense among children with vs. without mathematical learning disabilities
    • Mazzocco, M. M. M., & Devlin, K. T. (2008). Parts and ‘holes’: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11, 681–691. doi:10.1111/j.1467-7687.2008.00717.x
    • (2008) Developmental Science , vol.11 , pp. 681-691
    • Mazzocco, M.M.M.1    Devlin, K.T.2
  • 13
    • 84891682947 scopus 로고    scopus 로고
    • Modeling the developmental trajectories of rational number concept(s): A latent variable approach
    • McMullen, J., Laakkonen, E., Hannula-Sormunen, M. M., & Lehtinen, E. (2014). Modeling the developmental trajectories of rational number concept(s): A latent variable approach. Learning and Instruction. doi:10.1016/j.learninstruc.2013.12.004
    • (2014) Learning and Instruction
    • McMullen, J.1    Laakkonen, E.2    Hannula-Sormunen, M.M.3    Lehtinen, E.4
  • 14
    • 77954758096 scopus 로고    scopus 로고
    • Comparing the magnitude of two fractions with common components: Which representations are used by 10- and 12-year-olds?
    • Meert, G. J., Grégoire, J., & Noël, M.-P. (2010). Comparing the magnitude of two fractions with common components: Which representations are used by 10- and 12-year-olds? Journal of Experimental Child Psychology, 107, 244–259.
    • (2010) Journal of Experimental Child Psychology , vol.107 , pp. 244-259
    • Meert, G.J.1    Grégoire, J.2    Noël, M.-P.3
  • 15
    • 33750161942 scopus 로고    scopus 로고
    • Pipes, tubes, and beakers: New approaches to teaching the rational-number system
    • Donovan MS, Bransford JD, (eds), National Academic Press, Washington
    • Moss, J. (2005). Pipes, tubes, and beakers: New approaches to teaching the rational-number system. In M. S. Donovan & J. D. Bransford (Eds.), How students learn: Mathematics in the classroom (pp. 121–162). Washington: National Academic Press.
    • (2005) How students learn: Mathematics in the classroom , pp. 121-162
    • Moss, J.1
  • 16
    • 15944425784 scopus 로고    scopus 로고
    • Teaching and learning fraction and rational numbers: The origins and implications of whole number bias
    • Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40, 27–52. doi:10.1207/s15326985ep4001_3
    • (2005) Educational Psychologist , vol.40 , pp. 27-52
    • Ni, Y.1    Zhou, Y.-D.2
  • 17
    • 84879747887 scopus 로고    scopus 로고
    • The natural number bias and magnitude representation in fraction comparison by expert mathematicians
    • Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64–72. doi:10.1016/j.learninstruc.2013.05.003
    • (2013) Learning and Instruction , vol.28 , pp. 64-72
    • Obersteiner, A.1    Van Dooren, W.2    Van Hoof, J.3    Verschaffel, L.4
  • 18
    • 0003155810 scopus 로고
    • Curriculum implications of research on the learning, teaching and assessing of rational number concepts
    • Carpenter T, Fennema E, Romberg T, (eds), Lawrence Erlbaum, Hillsdale
    • Post, T., Cramer, K., Behr, M., Lesh, R., & Harel, G. (1993). Curriculum implications of research on the learning, teaching and assessing of rational number concepts. In T. Carpenter, E. Fennema, & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 327–361). Hillsdale: Lawrence Erlbaum.
    • (1993) Rational numbers: An integration of research , pp. 327-361
    • Post, T.1    Cramer, K.2    Behr, M.3    Lesh, R.4    Harel, G.5
  • 22
    • 24644465554 scopus 로고    scopus 로고
    • Never getting to zero: Elementary school students’ understanding of the infinite divisibility of number and matter
    • Smith, C. L., Solomon, G. E. A., & Carey, S. (2005). Never getting to zero: Elementary school students’ understanding of the infinite divisibility of number and matter. Cognitive Psychology, 51, 101–140. doi:10.1016/j.cogpsych.2005.03.001
    • (2005) Cognitive Psychology , vol.51 , pp. 101-140
    • Smith, C.L.1    Solomon, G.E.A.2    Carey, S.3
  • 23
    • 13844292565 scopus 로고    scopus 로고
    • The development of students’ understanding of the numerical value of fractions
    • Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and instruction, 14, 503--518. doi:10.1016/j.learninstruc.2004.06.015
    • (2004) Learning and instruction , vol.14 , pp. 503
    • Stafylidou, S.1    Vosniadou, S.2
  • 24
    • 79960050993 scopus 로고    scopus 로고
    • What fills the gap between discrete and dense? Greek and Flemish students’ understanding of density
    • Vamvakoussi, X., Christou, K. P., Mertens, L., & Van Dooren, W. (2011). What fills the gap between discrete and dense? Greek and Flemish students’ understanding of density. Learning and Instruction, 21, 676–685. doi:10.1016/j.learninstruc.2011.03.005
    • (2011) Learning and Instruction , vol.21 , pp. 676-685
    • Vamvakoussi, X.1    Christou, K.P.2    Mertens, L.3    Van Dooren, W.4
  • 25
    • 84862993778 scopus 로고    scopus 로고
    • Naturally biased? In search for reaction time evidence for a natural number bias in adults
    • Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31, 344–355. doi:10.1016/j.jmathb.2012.02.001
    • (2012) The Journal of Mathematical Behavior , vol.31 , pp. 344-355
    • Vamvakoussi, X.1    Van Dooren, W.2    Verschaffel, L.3
  • 26
    • 13844264296 scopus 로고    scopus 로고
    • Understanding the structure of the set of rational numbers: A conceptual change approach
    • Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction, 14, 453–467. doi:10.1016/j.learninstruc.2004.06.013
    • (2004) Learning and Instruction , vol.14 , pp. 453-467
    • Vamvakoussi, X.1    Vosniadou, S.2
  • 27
    • 77951261035 scopus 로고    scopus 로고
    • How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation
    • Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and Instruction, 28, 181–209. doi:10.1080/07370001003676603
    • (2010) Cognition and Instruction , vol.28 , pp. 181-209
    • Vamvakoussi, X.1    Vosniadou, S.2
  • 29
    • 84940032894 scopus 로고    scopus 로고
    • Inhibiting natural knowledge in fourth graders: Towards a comprehensive test instrument. ZDM Mathematics Education. Advance online publication
    • Van Hoof, J., Janssen, R., Verschaffel, L., & Van Dooren, W. (2015). Inhibiting natural knowledge in fourth graders: Towards a comprehensive test instrument. ZDM Mathematics Education. Advance online publication.
    • (2015) & Van Dooren, W
    • Van Hoof, J.1    Janssen, R.2    Verschaffel, L.3
  • 30
    • 84879643447 scopus 로고    scopus 로고
    • Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks
    • Van Hoof, J., Lijnen, T., Verschaffel, L., & Van Dooren, W. (2013). Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks. Research in Mathematics Education, 15, 154–164. doi:10.1080/14794802.2013.797747
    • (2013) Research in Mathematics Education , vol.15 , pp. 154-164
    • Van Hoof, J.1    Lijnen, T.2    Verschaffel, L.3    Van Dooren, W.4
  • 31
    • 84898705805 scopus 로고    scopus 로고
    • In search for the natural number bias in secondary school students’ interpretation of the effect of arithmetical operations
    • Van Hoof, J., Vandewalle, J., Verschaffel, L., & Van Dooren, W. (2014). In search for the natural number bias in secondary school students’ interpretation of the effect of arithmetical operations. Learning and Instruction. doi:10.1016/j.learninstruc.2014.03.004
    • (2014) Learning and Instruction
    • Van Hoof, J.1    Vandewalle, J.2    Verschaffel, L.3    Van Dooren, W.4
  • 32
    • 85015560550 scopus 로고    scopus 로고
    • Eindtermen wiskunde: secundair onderwijs, eerste graad A-stroom
    • Vlaams Ministerie van Onderwijs en Vorming. (2011a). Eindtermen wiskunde: secundair onderwijs, eerste graad A-stroom. Retrieved from http://ond.vlaanderen.be/dvo/secundair/1stegraad/a-stroom/eindtermen/wiskunde.htm
    • (2011) Retrieved from
  • 33
    • 85015548387 scopus 로고    scopus 로고
    • Eindtermen wiskunde: secundair onderwijs, derde graad ASO
    • Vlaams Ministerie van Onderwijs en Vorming. (2011b). Eindtermen wiskunde: secundair onderwijs, derde graad ASO. Retrieved from http://ond.vlaanderen.be/dvo/secundair/3degraad/aso/eindtermen/wiskunde.htm
    • (2011) Retrieved from
  • 34
    • 7744223509 scopus 로고
    • Capturing and modelling the process of conceptual change
    • Vosniadou, S. (1994). Capturing and modelling the process of conceptual change. Learning and Instruction, 4, 45–69. doi:10.1016/0959-4752(94)90018-3
    • (1994) Learning and Instruction , vol.4 , pp. 45-69
    • Vosniadou, S.1
  • 36
    • 0001729316 scopus 로고
    • A cognitive approach to meaningful mathematics instruction: Testing a local theory using decimal numbers
    • Wearne, D., & Hiebert, J. (1988). A cognitive approach to meaningful mathematics instruction: Testing a local theory using decimal numbers. Journal for Research in Mathematics Education, 19, 371–384.
    • (1988) Journal for Research in Mathematics Education , vol.19 , pp. 371-384
    • Wearne, D.1    Hiebert, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.