메뉴 건너뛰기




Volumn 110, Issue 3, 2010, Pages 279-300

Measuring middle grades teachers' understanding of rational numbers with the mixture rasch model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77749283789     PISSN: 00135984     EISSN: None     Source Type: Journal    
DOI: 10.1086/648979     Document Type: Article
Times cited : (29)

References (60)
  • 1
    • 0042739924 scopus 로고
    • Multiplication and division of fractions: The search for meaning
    • In J. T. Sowder & B. P. Schappelle (Eds.), Albany: State University of New York Press
    • Armstrong, B., & Bezuk, N. (1995). Multiplication and division of fractions: The search for meaning. In J. T. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 85-119). Albany: State University of New York Press.
    • (1995) Providing A Foundation for Teaching Mathematics in the Middle Grades , pp. 85-119
    • Armstrong, B.1    Bezuk, N.2
  • 2
    • 0003141787 scopus 로고
    • Prospective elementary and secondary teachers' understanding of division
    • Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.
    • (1990) Journal for Research in Mathematics Education , vol.21 , Issue.2 , pp. 132-144
    • Ball, D.L.1
  • 3
    • 2442594419 scopus 로고    scopus 로고
    • Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics
    • In J. Boaler (Ed.), Westport, CT: Ablex
    • Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 81-104). Westport, CT: Ablex.
    • (2000) Multiple Perspectives on Mathematics Teaching and Learning , pp. 81-104
    • Ball, D.L.1    Bass, H.2
  • 4
    • 0039180504 scopus 로고    scopus 로고
    • Research on teaching mathematics: The unsolved problem of teachers' mathematical knowledge
    • In V. Richardson (Ed.), (4th ed.). Washington, DC: American Educational Research Association
    • Ball, D., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers' mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed.). Washington, DC: American Educational Research Association.
    • (2001) Handbook of Research on Teaching
    • Ball, D.1    Lubienski, S.2    Mewborn, D.3
  • 5
    • 54049084937 scopus 로고    scopus 로고
    • Content knowledge for teaching: What makes it special?
    • Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
    • (2008) Journal of Teacher Education , vol.59 , Issue.5 , pp. 389-407
    • Ball, D.1    Thames, M.2    Phelps, G.3
  • 6
    • 21444437773 scopus 로고    scopus 로고
    • Conceptual units analysis of preservice elementary school teachers' strategies on a rational-number-as-operator task
    • Behr, M., Khoury, H., Harel, G., Post, T., & Lesh, R. (1997). Conceptual units analysis of preservice elementary school teachers' strategies on a rational-number-as-operator task. Journal for Research in Mathematics Education, 28(1), 48-69.
    • (1997) Journal for Research in Mathematics Education , vol.28 , Issue.1 , pp. 48-69
    • Behr, M.1    Khoury, H.2    Harel, G.3    Post, T.4    Lesh, R.5
  • 9
    • 85084901350 scopus 로고    scopus 로고
    • Learning to teach In D. Berliner & R. Calfee (Eds.), New York: MacMillan
    • Borko, H., & Putnam, R. (1996). Learning to teach. In D. Berliner & R. Calfee (Eds.), Handbook of educational psychology (pp. 673- 708). New York: MacMillan.
    • (1996) Handbook of Educational Psychology , pp. 673-708
    • Borko, H.1    Putnam, R.2
  • 11
    • 0001311877 scopus 로고
    • Splitting, similarity, and rate of change: A new approach to multiplication and exponential functions
    • In G. Harel & J. Confrey (Eds.), Albany: State University of New York Press
    • Confrey, J. (1994). Splitting, similarity, and rate of change: A new approach to multiplication and exponential functions. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 291-330). Albany: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 291-330
    • Confrey, J.1
  • 12
    • 21844504051 scopus 로고
    • Splitting, covariation, and their role in the development of exponential functions
    • Confrey, J., & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26(1), 66-86.
    • (1995) Journal for Research in Mathematics Education , vol.26 , Issue.1 , pp. 66-86
    • Confrey, J.1    Smith, E.2
  • 15
    • 26244458744 scopus 로고
    • Strategies used by secondary mathematics teachers to solve proportion problems
    • Fisher, L. (1988). Strategies used by secondary mathematics teachers to solve proportion problems. Journal for Research in Mathematics Education, 19(2), 157-168.
    • (1988) Journal for Research in Mathematics Education , vol.19 , Issue.2 , pp. 157-168
    • Fisher, L.1
  • 16
    • 0011396835 scopus 로고
    • Multiplication and division involving decimals: Preservice elementary teachers' performance and beliefs
    • Graeber, A., & Tirosh, D. (1988). Multiplication and division involving decimals: Preservice elementary teachers' performance and beliefs. Journal of Mathematical Behavior, 7, 263-280.
    • (1988) Journal of Mathematical Behavior , vol.7 , pp. 263-280
    • Graeber, A.1    Tirosh, D.2
  • 17
    • 0002473869 scopus 로고
    • Preservice teachers' misconceptions in solving verbal problems in multiplication and division
    • Graeber, A., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102.
    • (1989) Journal for Research in Mathematics Education , vol.20 , Issue.1 , pp. 95-102
    • Graeber, A.1    Tirosh, D.2    Glover, R.3
  • 21
    • 34250212074 scopus 로고    scopus 로고
    • Mathematical knowledge of middle school teachers: Implications for the no child Left behind Act
    • Hill, H. (2007). Mathematical knowledge of middle school teachers: Implications for the No Child Left Behind Act. Educational Evaluation and Policy Analysis, 29(2), 95-114.
    • (2007) Educational Evaluation and Policy Analysis , vol.29 , Issue.2 , pp. 95-114
    • Hill, H.1
  • 22
    • 47949089037 scopus 로고    scopus 로고
    • Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students
    • Hill, H., Ball, D. L., & Schilling, S. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
    • (2008) Journal for Research in Mathematics Education , vol.39 , Issue.4 , pp. 372-400
    • Hill, H.1    Ball, D.L.2    Schilling, S.3
  • 23
    • 47949112984 scopus 로고    scopus 로고
    • Assessing elemental and structural validity: Data from teachers, non-teachers, and mathematicians
    • Hill, H., Dean, C., & Goffney, I. (2007). Assessing elemental and structural validity: Data from teachers, non-teachers, and mathematicians. Measurement: Interdisciplinary Research and Perspectives, 5(2-3), 81-92.
    • (2007) Measurement: Interdisciplinary Research and Perspectives , vol.5 , Issue.2-3 , pp. 81-92
    • Hill, H.1    Dean, C.2    Goffney, I.3
  • 24
    • 21144450961 scopus 로고    scopus 로고
    • Effects of teachers' mathematical knowledge for teaching on student achievement
    • Hill, H., Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
    • (2005) American Educational Research Journal , vol.42 , Issue.2 , pp. 371-406
    • Hill, H.1    Rowan, B.2    Ball, D.L.3
  • 25
    • 7044286358 scopus 로고    scopus 로고
    • Developing measures of teachers' mathematics knowledge for teaching
    • Hill, H., Schilling, S., & Ball, D. L. (2004). Developing measures of teacher's mathematics knowledge for teaching. Elementary School Journal, 105(1), 11-30. (Pubitemid 39427416)
    • (2004) Elementary School Journal , vol.105 , Issue.1 , pp. 11-30
    • Hill, H.C.1    Schilling, S.G.2    Ball, D.L.3
  • 26
    • 24944498066 scopus 로고    scopus 로고
    • You have to count the squares": Applying knowledge in pieces to learning rectangular area
    • Izsák, A. (2005). "You have to count the squares": Applying knowledge in pieces to learning rectangular area. Journal of the Learning Sciences, 14(3), 361-403.
    • (2005) Journal of the Learning Sciences , vol.14 , Issue.3 , pp. 361-403
    • Izsák, A.1
  • 27
    • 41549152487 scopus 로고    scopus 로고
    • Mathematical knowledge for teaching fraction multiplication
    • Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26, 95-143.
    • (2008) Cognition and Instruction , vol.26 , pp. 95-143
    • Izsák, A.1
  • 29
    • 0002303730 scopus 로고
    • Ratio and proportion: Cognitive foundations in unitizing and norming
    • In G. Harel & J. Confrey (Eds.), Albany: State University of New York Press
    • Lamon, S. J. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 89-120). Albany: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 89-120
    • Lamon, S.J.1
  • 32
    • 70449363892 scopus 로고    scopus 로고
    • Model selection methods for dichotomous mixture IRT models
    • Li, F., Cohen, A. S., Kim, S. H., & Cho, S. J. (2009). Model selection methods for dichotomous mixture IRT models. Applied Psychological Measurement, 33(5), 353-373.
    • (2009) Applied psychological measurement , vol.33 , Issue.5 , pp. 353-373
    • Li, F.1    Cohen, A.S.2    Kim, S.H.3    Cho, S.J.4
  • 33
    • 0036343909 scopus 로고    scopus 로고
    • Quantitative reasoning in a reconceived view of transfer
    • Lobato, J., & Siebert, D. (2002). Quantitative reasoning in a reconceived view of transfer. Journal of Mathematical Behavior, 21(1), 87-116.
    • (2002) Journal of Mathematical Behavior , vol.21 , Issue.1 , pp. 87-116
    • Lobato, J.1    Siebert, D.2
  • 36
    • 0001019640 scopus 로고
    • Modeling item responses when different subjects employ different solution strategies
    • Mislevy, R. J., & Verhelst, N. (1990). Modeling item responses when different subjects employ different solution strategies. Psychometrika, 55, 195-215.
    • (1990) Psychometrika , vol.55 , pp. 195-215
    • Mislevy, R.J.1    Verhelst, N.2
  • 38
    • 84993723797 scopus 로고    scopus 로고
    • National council of teachers of mathematics
    • Reston, VA: Author
    • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
    • (2000) Principles and Standards for School Mathematics
  • 40
    • 84970751365 scopus 로고
    • Rasch models in latent classes: An integration of two approaches to item analysis
    • Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271-282.
    • (1990) Applied Psychological Measurement , vol.14 , pp. 271-282
    • Rost, J.1
  • 41
    • 0002657726 scopus 로고    scopus 로고
    • Logistic mixture models
    • In W. J. van der Linden & R. K. Hambleton (Eds.), New York: Springer
    • Rost, J. (1997). Logistic mixture models. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 449-463). New York: Springer.
    • (1997) Handbook of Modern Item Response Theory , pp. 449-463
    • Rost, J.1
  • 44
    • 84973848880 scopus 로고
    • Those who understand: Knowledge growth in teaching
    • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
    • (1986) Educational Researcher , vol.15 , Issue.2 , pp. 4-14
    • Shulman, L.S.1
  • 45
    • 21144471172 scopus 로고
    • Prospective elementary teachers' knowledge of division
    • Simon, M. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254.
    • (1993) Journal for Research in Mathematics Education , vol.24 , Issue.3 , pp. 233-254
    • Simon, M.1
  • 46
    • 0003114978 scopus 로고
    • Competent reasoning with rational numbers
    • Smith, J. P. (1995). Competent reasoning with rational numbers. Cognition and Instruction, 13(1), 3-50.
    • (1995) Cognition and Instruction , vol.13 , Issue.1 , pp. 3-50
    • Smith, J.P.1
  • 49
    • 0001679235 scopus 로고
    • Children's construction of number sequences and multiplying schemes
    • In J. Hiebert & M. Behr (Eds.), Reston, VA: National Council of Teachers of Mathematics; Hillsdale, NJ: Erlbaum
    • Steffe, L. (1988). Children's construction of number sequences and multiplying schemes. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in middle grades (pp. 119-140). Reston, VA: National Council of Teachers of Mathematics; Hillsdale, NJ: Erlbaum.
    • (1988) Number Concepts and Operations in Middle Grades , pp. 119-140
    • Steffe, L.1
  • 50
    • 38249013863 scopus 로고
    • Schemes of action and operation involving composite units. Learning and individual differences
    • Steffe, L. P. (1992). Schemes of action and operation involving composite units. Learning and Individual Differences: A Multidisciplinary Journal in Education, 4(3), 259-309.
    • (1992) A Multidisciplinary Journal in Education , vol.4 , Issue.3 , pp. 259-309
    • Steffe, L.P.1
  • 51
    • 0001889880 scopus 로고
    • Children's multiplying schemes
    • In G. Harel & 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
  • 52
    • 0035729603 scopus 로고    scopus 로고
    • A new hypothesis concerning children's fractional knowledge
    • Steffe, L. (2001). A new hypothesis concerning children's fractional knowledge. Journal of Mathematical Behavior, 20(3), 267-307.
    • (2001) Journal of Mathematical Behavior , vol.20 , Issue.3 , pp. 267-307
    • Steffe, L.1
  • 53
    • 0042881175 scopus 로고    scopus 로고
    • Fractional commensurate, composition, and adding schemes learning trajectories of jason and Laura: Grade 5
    • Steffe, L. (2003). Fractional commensurate, composition, and adding schemes learning trajectories of Jason and Laura: Grade 5. Journal of Mathematical Behavior, 22(3), 237-295.
    • (2003) Journal of Mathematical Behavior , vol.22 , Issue.3 , pp. 237-295
    • Steffe, L.1
  • 54
    • 34247566085 scopus 로고    scopus 로고
    • On the construction of learning trajectories of children: The case of commensurate fractions
    • Steffe, L. (2004). On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking and Learning, 6(2), 129-162.
    • (2004) Mathematical Thinking and Learning , vol.6 , Issue.2 , pp. 129-162
    • Steffe, L.1
  • 55
    • 0002269268 scopus 로고
    • The development of the concept of speed and its relationship to concepts of rate
    • In G. Harel & J. Confrey (Eds.), Albany: State University of New York Press
    • Thompson, P. (1994). The development of the concept of speed and its relationship to concepts of rate. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 179-234). Albany: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 179-234
    • Thompson, P.1
  • 56
  • 57
    • 22844453632 scopus 로고    scopus 로고
    • Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions
    • Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.
    • (2000) Journal for Research in Mathematics Education , vol.31 , Issue.1 , pp. 5-25
    • Tirosh, D.1
  • 58
    • 0346306445 scopus 로고
    • Evoking cognitive conflict to explore preservice teachers' thinking about division
    • Tirosh, D., & Graeber, A. (1990). Evoking cognitive conflict to explore preservice teachers' thinking about division. Journal for Research in Mathematics Education, 21(2), 98-108.
    • (1990) Journal for Research in Mathematics Education , vol.21 , Issue.2 , pp. 98-108
    • Tirosh, D.1    Graeber, A.2
  • 59
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.