메뉴 건너뛰기




Volumn 18, Issue 1, 2006, Pages 103-123

The case of Bruce: A teacher's model of his students' algebraic thinking about equivalent expressions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77956443553     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03217431     Document Type: Article
Times cited : (6)

References (46)
  • 1
    • 84904247345 scopus 로고    scopus 로고
    • Paper presented at the Fourth Congress of the European Society for Research in Mathematics Education. Sant Feliu de Guíxols, Spain. Retrieved October 5, 2005, from
    • Attorps, I. (2005). Secondary school teachers' conceptions about algebra teaching. Paper presented at the Fourth Congress of the European Society for Research in Mathematics Education. Sant Feliu de Guíxols, Spain. Retrieved October 5, 2005, from: http://cerme4. crm. es/Papers%20definitius/12/attorps. pdf
    • (2005) Secondary school teachers' conceptions about algebra teaching
    • Attorps, I.1
  • 2
    • 0013064837 scopus 로고    scopus 로고
    • What do students hear? Facing challenges of distance, context, and desire in trying to hear children
    • In B. Biddle, T. Good, & I. Goodson (Eds.), Boston: Kluwer Academic Publishers
    • Ball, D. L. (1997). What do students hear? Facing challenges of distance, context, and desire in trying to hear children. In B. Biddle, T. Good, & I. Goodson (Eds.), International handbook of teachers and teaching (Vol. II, pp. 679-818). Boston: Kluwer Academic Publishers
    • (1997) International handbook of teachers and teaching , vol.2 , pp. 679-818
    • Ball, D.L.1
  • 3
    • 79951758113 scopus 로고    scopus 로고
    • A problem-solving approach to algebra: Accounting for the reasonings and notations developed by students
    • In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Melbourne, Australia: The University of Melbourne
    • Bednarz, N. (2001). A problem-solving approach to algebra: Accounting for the reasonings and notations developed by students. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra. Proceedings of the 12th ICMI Study Conference (pp. 69-78). Melbourne, Australia: The University of Melbourne
    • (2001) The future of the teaching and learning of algebra. Proceedings of the 12th ICMI Study Conference , pp. 69-78
    • Bednarz, N.1
  • 5
    • 0010922436 scopus 로고
    • Children's difficulties in beginning algebra
    • In A. Coxford (Ed.), Reston, VA: National Council of Teachers of Mathematics
    • Booth, L. (1988). Children's difficulties in beginning algebra. In A. Coxford (Ed.), The ideas of algebra, k-12 (pp. 20-32). Reston, VA: National Council of Teachers of Mathematics
    • (1988) The ideas of algebra, k-12 , pp. 20-32
    • Booth, L.1
  • 7
    • 26044483877 scopus 로고    scopus 로고
    • Teacher discussions of students' thinking: Meeting the challenge of attending to students' thinking
    • Chamberlin, M. T. (2005). Teacher discussions of students' thinking: Meeting the challenge of attending to students' thinking. Journal of Mathematics Teacher Education, 8(2), 141-170
    • (2005) Journal of Mathematics Teacher Education , vol.8 , Issue.2 , pp. 141-170
    • Chamberlin, M.T.1
  • 8
    • 0342675877 scopus 로고    scopus 로고
    • On teachers' mathematical knowledge and student exploration: A personal story about teaching a technologically supported approach to school algebra
    • Chazan, D. (1999). On teachers' mathematical knowledge and student exploration: A personal story about teaching a technologically supported approach to school algebra. International Journal of Computers for Mathematical Learning, 4(2-3), 121-149
    • (1999) International Journal of Computers for Mathematical Learning , vol.4 , Issue.2-3 , pp. 121-149
    • Chazan, D.1
  • 9
    • 33750570141 scopus 로고    scopus 로고
    • Teachers' knowledge and the teaching of algebra
    • In K. Stacey, H. Chick, & M. Kendal (Eds.), Norwood, MA: Kluwer Academic Publishers
    • Doerr, H. M. (2004). Teachers' knowledge and the teaching of algebra. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 267-290). Norwood, MA: Kluwer Academic Publishers
    • (2004) The future of the teaching and learning of algebra: The 12th ICMI study , pp. 267-290
    • Doerr, H.M.1
  • 10
    • 84904258730 scopus 로고    scopus 로고
    • Examining the tasks of teaching when using students' mathematical thinking
    • (in press)
    • Doerr, H. M. (in press). Examining the tasks of teaching when using students' mathematical thinking. Educational Studies in Mathematics.
    • Educational Studies in Mathematics
    • Doerr, H.M.1
  • 11
    • 85140152287 scopus 로고    scopus 로고
    • A modeling perspective on teacher development
    • In R. Lesh & H. Doerr (Eds.), Mahwah, NJ: Lawrence Erlbaum Associates
    • Doerr, H., & Lesh, R. (2003). A modeling perspective on teacher development. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modeling perspective (pp. 125-140). Mahwah, NJ: Lawrence Erlbaum Associates
    • (2003) Beyond constructivism: A models and modeling perspective , pp. 125-140
    • Doerr, H.1    Lesh, R.2
  • 12
    • 21144469530 scopus 로고
    • Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept
    • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94-116
    • (1993) Journal for Research in Mathematics Education , vol.24 , Issue.2 , pp. 94-116
    • Even, R.1
  • 13
    • 77957709853 scopus 로고
    • Connectedness in teaching equivalent algebraic expressions: Novice versus expert teachers
    • Even, R., Tirosh, D., & Robinson, N. (1993). Connectedness in teaching equivalent algebraic expressions: Novice versus expert teachers. Mathematics Education Research Journal, 5(1), 50-59
    • (1993) Mathematics Education Research Journal , vol.5 , Issue.1 , pp. 50-59
    • Even, R.1    Tirosh, D.2    Robinson, N.3
  • 14
    • 0042433872 scopus 로고    scopus 로고
    • Relationships between research and the NCTM standards
    • Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics Education, 30(1), 3-19
    • (1999) Journal for Research in Mathematics Education , vol.30 , Issue.1 , pp. 3-19
    • Hiebert, J.1
  • 16
    • 77955757739 scopus 로고    scopus 로고
    • U.S.; Massachusetts: National Center for Improving Student Learning and Achievement in Mathematics and Science Dartmouth MA
    • Kaput, J. J. (2000). Teaching and learning a new algebra with understanding. U. S.; Massachusetts: National Center for Improving Student Learning and Achievement in Mathematics and Science Dartmouth MA
    • (2000) Teaching and learning a new algebra with understanding
    • Kaput, J.J.1
  • 17
    • 0001071316 scopus 로고
    • Concepts associated with the equality symbol
    • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326
    • (1981) Educational Studies in Mathematics , vol.12 , pp. 317-326
    • Kieran, C.1
  • 18
    • 0002050688 scopus 로고
    • The learning and teaching of school algebra
    • In D. Grouws (Ed.), New York: Macmillan Publishing Company
    • Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan Publishing Company
    • (1992) Handbook of research on mathematics teaching and learning , pp. 390-419
    • Kieran, C.1
  • 19
    • 85135996149 scopus 로고    scopus 로고
    • Research on the learning and teaching of algebra: A broadening of sources of meaning
    • In A. Gutierrez & P. Boero (Eds.), Rotterdam: Sense Publishers
    • Kieran, C. (2006). Research on the learning and teaching of algebra: A broadening of sources of meaning. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 11-49). Rotterdam: Sense Publishers
    • (2006) Handbook of research on the psychology of mathematics education: Past, present and future , pp. 11-49
    • Kieran, C.1
  • 24
    • 0002939675 scopus 로고    scopus 로고
    • Multi-tiered teaching experiments
    • In A. Kelly & R. Lesh (Eds.), Mahwah, NJ: Lawrence Erlbaum Associates
    • Lesh, R., & Kelly, A. (1999). Multi-tiered teaching experiments. In A. Kelly & R. Lesh (Eds.), Handbook of research in mathematics and science education (pp. 197-230). Mahwah, NJ: Lawrence Erlbaum Associates
    • (1999) Handbook of research in mathematics and science education , pp. 197-230
    • Lesh, R.1    Kelly, A.2
  • 25
    • 22044432138 scopus 로고    scopus 로고
    • Supporting innovation: The impact of a teacher's conceptions of functions on his implementation of a reform curriculum
    • Lloyd, G. M., & Wilson, M. (1998). Supporting innovation: The impact of a teacher's conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29(3), 248-274
    • (1998) Journal for Research in Mathematics Education , vol.29 , Issue.3 , pp. 248-274
    • Lloyd, G.M.1    Wilson, M.2
  • 26
    • 84877773864 scopus 로고    scopus 로고
    • Goals and content of an algebra curriculum for the compulsory years of schooling
    • In K. Stacey, H. Chick, & M. Kendal (Eds.), Norwood, MA: Kluwer Academic Publishers
    • MacGregor, M. (2004). Goals and content of an algebra curriculum for the compulsory years of schooling. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 313-328). Norwood, MA: Kluwer Academic Publishers
    • (2004) The future of the teaching and learning of algebra: The 12th ICMI study , pp. 313-328
    • McGregor, M.1
  • 27
    • 21144479639 scopus 로고
    • Cognitive models underlying students' formulation of simple linear equations
    • MacGregor, M., & Stacey, K. (1993). Cognitive models underlying students' formulation of simple linear equations. Journal for Research in Mathematics Education, 24(3), 217-232
    • (1993) Journal for Research in Mathematics Education , vol.24 , Issue.3 , pp. 217-232
    • McGregor, M.1    Stacey, K.2
  • 28
  • 29
    • 33746675016 scopus 로고    scopus 로고
    • Cognitive models underlying algebraic and non-algebraic solutions to unequal partition problems
    • MacGregor, M., & Stacey, K. (1998). Cognitive models underlying algebraic and non-algebraic solutions to unequal partition problems. Mathematics Education Research Journal, 10(2), 46-60
    • (1998) Mathematics Education Research Journal , vol.10 , Issue.2 , pp. 46-60
    • McGregor, M.1    Stacey, K.2
  • 30
    • 84904264731 scopus 로고    scopus 로고
    • Language conceptions of algebra are idiosyncratic
    • In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Melbourne, The University of Melbourne
    • Menzel, B. (2001). Language conceptions of algebra are idiosyncratic. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra. Proceedings of the 12th ICMI Study Conference (pp. 446-453). Melbourne, The University of Melbourne
    • (2001) The future of the teaching and learning of algebra. Proceedings of the 12th ICMI Study Conference , pp. 446-453
    • Menzel, B.1
  • 33
    • 13844272995 scopus 로고    scopus 로고
    • Making sense of what students know: Examining the referents, relationships and modes students displayed in response to a decimal task
    • Moskal, B. M., & Magone, M. E. (2000). Making sense of what students know: Examining the referents, relationships and modes students displayed in response to a decimal task. Educational Studies in Mathematics, 43(3), 313-335
    • (2000) Educational Studies in Mathematics , vol.43 , Issue.3 , pp. 313-335
    • Moskal, B.M.1    Magone, M.E.2
  • 34
    • 0012673052 scopus 로고    scopus 로고
    • An investigation of teachers' beliefs of students' algebra development
    • Nathan, M. J., & Koedinger, K. R. (2000). An investigation of teachers' beliefs of students' algebra development. Cognition and Instruction, 18(2), 209-237
    • (2000) Cognition and Instruction , vol.18 , Issue.2 , pp. 209-237
    • Nathan, M.J.1    Koedinger, K.R.2
  • 35
    • 0003865799 scopus 로고    scopus 로고
    • Reston, VA: Author, National Council of Teachers of Mathematics
    • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author
    • (2000) Principles and standards for school mathematics
  • 39
    • 85016682871 scopus 로고    scopus 로고
    • A modeling approach for providing teacher development
    • In R. Lesh & H. Doerr (Eds.), Mahwah, NJ: Lawrence Erlbaum Associates
    • Schorr, R., & Lesh, R. (2003). A modeling approach for providing teacher development. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modeling perspective (pp. 141-158). Mahwah, NJ: Lawrence Erlbaum Associates
    • (2003) Beyond constructivism: A models and modeling perspective , pp. 141-158
    • Schorr, R.1    Lesh, R.2
  • 40
    • 84993729340 scopus 로고    scopus 로고
    • The role of assessment in a learning culture
    • Shepard, L. A. (2000). The role of assessment in a learning culture. Educational Researcher, 29(1), 4-14
    • (2000) Educational Researcher , vol.29 , Issue.1 , pp. 4-14
    • Shepard, L.A.1
  • 41
    • 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
  • 42
    • 0033074650 scopus 로고    scopus 로고
    • Learning the algebraic method of solving problems
    • Stacey, K., & MacGregor, M. (2000). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18(2), 149-167
    • (2000) Journal of Mathematical Behavior , vol.18 , Issue.2 , pp. 149-167
    • Stacey, K.1    McGregor, M.2
  • 44
    • 54649084431 scopus 로고    scopus 로고
    • Simplifying algebraic expressions: Teacher awareness and teaching approaches
    • Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51-64
    • (1998) Educational Studies in Mathematics , vol.35 , Issue.1 , pp. 51-64
    • Tirosh, D.1    Even, R.2    Robinson, N.3
  • 45
    • 0010730953 scopus 로고
    • Improvement of (didactical) assessment by improvement of problems: An attempt with respect to percentage
    • Van den Heuvel-Panhuizen, M. (1994). Improvement of (didactical) assessment by improvement of problems: An attempt with respect to percentage. Educational Studies in Mathematics, 27, 341-372
    • (1994) Educational Studies in Mathematics , vol.27 , pp. 341-372
    • Van den Heuvel-Panhuizen, M.1
  • 46
    • 63649149182 scopus 로고    scopus 로고
    • The role of arithmetic structure in the transition from arithmetic to algebra
    • Warren, E. (2003). The role of arithmetic structure in the transition from arithmetic to algebra. Mathematics Education Research Journal, 15(2), 122-137
    • (2003) Mathematics Education Research Journal , vol.15 , Issue.2 , pp. 122-137
    • Warren, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.