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Volumn 26, Issue 2, 2014, Pages 237-255

The identification and validation process of proportional reasoning attributes: An application of a cognitive diagnosis modeling framework

Author keywords

Assessment; Proportional reasoning; Proportions; Ratios

Indexed keywords


EID: 84901605633     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/s13394-013-0090-7     Document Type: Article
Times cited : (27)

References (37)
  • 1
    • 0003045626 scopus 로고
    • Halves, pieces and twoths: Constructing and using representational contexts in teaching fractions
    • T. P. Carpenter, E. Fennema, and T. A. Romberg (Eds.), Hillsdale: Erlbaum
    • Ball, D. (1993). Halves, pieces and twoths: Constructing and using representational contexts in teaching fractions. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 157-195). Hillsdale: Erlbaum.
    • (1993) Rational Numbers: An Integration of Research , pp. 157-195
    • Ball, D.1
  • 6
    • 0035729517 scopus 로고    scopus 로고
    • Mapping and development of intuitive proportional thinking
    • Christou, C., & Philippou, G. (2001). Mapping and development of intuitive proportional thinking. Journal of Mathematical Behavior, 20, 321-336.
    • (2001) Journal of Mathematical Behavior , vol.20 , pp. 321-336
    • Christou, C.1    Philippou, G.2
  • 7
    • 0141651953 scopus 로고    scopus 로고
    • A comparison of ratios and fractions and their roles as tools in proportional reasoning
    • Clark, M., Berenson, S., & Cavey, O. (2003). A comparison of ratios and fractions and their roles as tools in proportional reasoning. Journal of Mathematical Behavior, 22, 297-317.
    • (2003) Journal of Mathematical Behavior , vol.22 , pp. 297-317
    • Clark, M.1    Berenson, S.2    Cavey, O.3
  • 8
    • 54749155344 scopus 로고
    • Connecting research to teaching proportional reasoning
    • Cramer, K., & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86, 404-407.
    • (1993) Mathematics Teacher , vol.86 , pp. 404-407
    • Cramer, K.1    Post, T.2
  • 9
    • 0009980501 scopus 로고
    • Learning and teaching ratio and proportion: Research implications
    • D. Owens (Ed.), New York: Macmillan
    • Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 159-178). New York: Macmillan.
    • (1993) Research Ideas for the Classroom: Middle Grades Mathematics , pp. 159-178
    • Cramer, K.1    Post, T.2    Currier, S.3
  • 10
    • 65249100652 scopus 로고    scopus 로고
    • A cognitive diagnosis model for cognitively-based multiple-choice options
    • de la Torre, J. (2009). A cognitive diagnosis model for cognitively-based multiple-choice options. Applied Psychological Measurement, 33, 163-183.
    • (2009) Applied Psychological Measurement , vol.33 , pp. 163-183
    • de la Torre, J.1
  • 11
    • 77953743410 scopus 로고    scopus 로고
    • A note on the invariance of the DINA model parameters
    • de la Torre, J., & Lee, Y. S. (2010). A note on the invariance of the DINA model parameters. Journal of Educational Measurement, 47, 115-127.
    • (2010) Journal of Educational Measurement , vol.47 , pp. 115-127
    • de la Torre, J.1    Lee, Y.S.2
  • 12
    • 77954736976 scopus 로고    scopus 로고
    • Factors affecting the item parameter estimation and classification accuracy of the DINA model
    • de la Torre, J., Hong, Y., & Deng, W. (2010). Factors affecting the item parameter estimation and classification accuracy of the DINA model. Journal of Educational Measurement, 47, 227-249.
    • (2010) Journal of Educational Measurement , vol.47 , pp. 227-249
    • de la Torre, J.1    Hong, Y.2    Deng, W.3
  • 13
    • 84885828286 scopus 로고    scopus 로고
    • Ratio tables to promote proportional reasoning in the primary classroom
    • Dole, S. (2008). Ratio tables to promote proportional reasoning in the primary classroom. Australian Primary Mathematics Classroom, 13, 18-22.
    • (2008) Australian Primary Mathematics Classroom , vol.13 , pp. 18-22
    • Dole, S.1
  • 15
    • 79959317800 scopus 로고    scopus 로고
    • Middle school students' responses to two-tier tasks
    • Haja, S., & Clarke, D. (2011). Middle school students' responses to two-tier tasks. Mathematics Education Research Journal, 23, 67-76.
    • (2011) Mathematics Education Research Journal , vol.23 , pp. 67-76
    • Haja, S.1    Clarke, D.2
  • 16
    • 0000909733 scopus 로고
    • Qualitative and numerical reasoning about fractions and rate by seventh and eighth grade students
    • Heller, P., Post, T., Behr, M., & Lesh, R. (1990). Qualitative and numerical reasoning about fractions and rate by seventh and eighth grade students. Journal for Research in Mathematics Education, 21, 388-402.
    • (1990) Journal for Research in Mathematics Education , vol.21 , pp. 388-402
    • Heller, P.1    Post, T.2    Behr, M.3    Lesh, R.4
  • 18
    • 0002351467 scopus 로고
    • Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns
    • G. Harel and J. Confrey (Eds.), Albany: State University of New York Press
    • Kaput, J., & West, M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235-287). Albany: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 235-287
    • Kaput, J.1    West, M.2
  • 19
    • 0008772890 scopus 로고
    • Early adolescents' proportional reasoning on 'rate' problems
    • Karplus, R., Pulos, S., & Stage, E. (1983). Early adolescents' proportional reasoning on 'rate' problems. Educational Studies in Mathematics, 14, 219-233.
    • (1983) Educational Studies in Mathematics , vol.14 , pp. 219-233
    • Karplus, R.1    Pulos, S.2    Stage, E.3
  • 20
    • 54949096914 scopus 로고    scopus 로고
    • Rational numbers and proportional reasoning: Toward a theoretical framework for research
    • F. K. Lester (Ed.), Charlotte: Information Age
    • Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-668). Charlotte: Information Age.
    • (2007) Second Handbook of Research on Mathematics Teaching and Learning , pp. 629-668
    • Lamon, S.1
  • 22
    • 0009176767 scopus 로고
    • The effect of different approaches to algebra on students' perceptions of functional relationships
    • MacGregor, M., & Stacey, K. (1995). The effect of different approaches to algebra on students' perceptions of functional relationships. Mathematics Education Research Journal, 7, 69-85.
    • (1995) Mathematics Education Research Journal , vol.7 , pp. 69-85
    • MacGregor, M.1    Stacey, K.2
  • 24
    • 0041378204 scopus 로고    scopus 로고
    • Diagnostic assessment of children's proportional reasoning
    • Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children's proportional reasoning. Journal of Mathematical Behavior, 22, 335-368.
    • (2003) Journal of Mathematical Behavior , vol.22 , pp. 335-368
    • Misailidou, C.1    Williams, J.2
  • 26
    • 0001695025 scopus 로고
    • The development of proportional reasoning and the ratio concept: Part I - Differentiation of stages
    • Noelting, G. (1980a). The development of proportional reasoning and the ratio concept: Part I - Differentiation of stages. Educational Studies in Mathematics, 11, 217-253.
    • (1980) Educational Studies in Mathematics , vol.11 , pp. 217-253
    • Noelting, G.1
  • 27
    • 0002670025 scopus 로고
    • The development of proportional reasoning and the ratio concept: part II - problem structure at successive stages; problem solving strategies and the mechanism of adaptive restructuring
    • Noelting, G. (1980b). The development of proportional reasoning and the ratio concept: part II - problem structure at successive stages; problem solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11, 331-363.
    • (1980) Educational Studies in Mathematics , vol.11 , pp. 331-363
    • Noelting, G.1
  • 28
    • 78649580671 scopus 로고    scopus 로고
    • (Fish) food for thought: authority shifts in the interaction between mathematics and reality
    • Peled, I. (2010). (Fish) food for thought: authority shifts in the interaction between mathematics and reality. Mathematics Education Research Journal, 22, 108-120.
    • (2010) Mathematics Education Research Journal , vol.22 , pp. 108-120
    • Peled, I.1
  • 29
    • 0039153310 scopus 로고    scopus 로고
    • A review of recent research in the area of initial fraction concepts
    • Pitkethly, A., & Hunting, R. (1996). A review of recent research in the area of initial fraction concepts. Educational Studies in Mathematics, 30, 5-38.
    • (1996) Educational Studies in Mathematics , vol.30 , pp. 5-38
    • Pitkethly, A.1    Hunting, R.2
  • 30
    • 36749086530 scopus 로고    scopus 로고
    • Understanding the concepts of proportion and ratio constructed by two grade six students
    • Singh, P. (2000). Understanding the concepts of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics, 43, 271-292.
    • (2000) Educational Studies in Mathematics , vol.43 , pp. 271-292
    • Singh, P.1
  • 31
    • 0001889880 scopus 로고
    • Children's multiplying schemes
    • G. Harel and J. Confrey (Eds.), Albany: State University of New York Press
    • Steffe, L. (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: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 3-39
    • Steffe, L.1
  • 32
  • 33
    • 13944269902 scopus 로고    scopus 로고
    • Not everything is proportional: effects of age and problem type on propensities for overgeneralization
    • van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23, 57-86.
    • (2005) Cognition and Instruction , vol.23 , pp. 57-86
    • van Dooren, W.1    De Bock, D.2    Hessels, A.3    Janssens, D.4    Verschaffel, L.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.