메뉴 건너뛰기




Volumn 37, Issue 3, 1998, Pages 251-274

The role of operation sense in transitions from arithmetic to algebraic thought

Author keywords

[No Author keywords available]

Indexed keywords


EID: 54649084346     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1023/A:1003602322232     Document Type: Conference Paper
Times cited : (40)

References (46)
  • 1
    • 0002100652 scopus 로고
    • Symbol sense: Informal sense-making in formal mathematics
    • Arcavi, A.: 1994, 'Symbol sense: Informal sense-making in formal mathematics', For the Learning of Mathematics 14 (3), 24-35.
    • (1994) For the Learning of Mathematics , vol.14 , Issue.3 , pp. 24-35
    • Arcavi, A.1
  • 2
    • 0001754927 scopus 로고
    • The effects of instruction on children's understanding of he 'equals' sign
    • Baroody, A.J. and Ginsburg, H.P.: 1983, 'The effects of instruction on children's understanding of he 'equals' sign', The Elementary School Journal 84, 199-212.
    • (1983) The Elementary School Journal , vol.84 , pp. 199-212
    • Baroody, A.J.1    Ginsburg, H.P.2
  • 3
    • 84963486131 scopus 로고
    • An integrated model of skills in solving elementary word problems
    • Briars, D.J. and Larkin, J.H.: 1984, 'An integrated model of skills in solving elementary word problems', Cognition and Instruction 1, 245-296.
    • (1984) Cognition and Instruction , vol.1 , pp. 245-296
    • Briars, D.J.1    Larkin, J.H.2
  • 6
    • 84989419241 scopus 로고
    • Mathematical concepts in everyday life
    • G.B. Saxe and M. Gearhart (eds.), Jossey-Bass, San Francisco
    • Carraher, T.N., Schliemann, A.D. and Carraher, D.W.: 1988, 'Mathematical concepts in everyday life', in G.B. Saxe and M. Gearhart (eds.), Children's Mathematics, Jossey-Bass, San Francisco, pp. 71-87.
    • (1988) Children's Mathematics , pp. 71-87
    • Carraher, T.N.1    Schliemann, A.D.2    Carraher, D.W.3
  • 7
    • 0003124075 scopus 로고
    • A constructivist alternative to the representational view of mind in mathematics education
    • Cobb, P., Yackel, E. and Wood, T.: 1992, 'A constructivist alternative to the representational view of mind in mathematics education', Journal for Research in Mathematics Education 23(1), 2-33.
    • (1992) Journal for Research in Mathematics Education , vol.23 , Issue.1 , pp. 2-33
    • Cobb, P.1    Yackel, E.2    Wood, T.3
  • 8
    • 21844504051 scopus 로고
    • Splitting, covaration, and their role in the development of exponential functions
    • Confrey, J. and Smith, E.: 1995, 'Splitting, covaration, 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
  • 11
    • 42549147889 scopus 로고    scopus 로고
    • Algebraic procedures used by 13-to-15-years olds
    • Demby, A.: 1997, 'Algebraic procedures used by 13-to-15-years olds', Educational Studies in Mathematics 33(1), 45-70.
    • (1997) Educational Studies in Mathematics , vol.33 , Issue.1 , pp. 45-70
    • Demby, A.1
  • 12
    • 0009257532 scopus 로고
    • Solving equations: The transition from arithmetic to algebra
    • Filloy, E. and Rojano, T.: 1989, 'Solving equations: The transition from arithmetic to algebra', For the learning of Mathematics 9(2), 19-25.
    • (1989) For the Learning of Mathematics , vol.9 , Issue.2 , pp. 19-25
    • Filloy, E.1    Rojano, T.2
  • 13
    • 21444451370 scopus 로고    scopus 로고
    • Young children's perceptions of mathematics in problem-solving environments
    • Franke, M.L. and Carey, D.A.: 1997, 'Young children's perceptions of mathematics in problem-solving environments', Journal for Research in Mathematics Education 28(1), 8-25.
    • (1997) Journal for Research in Mathematics Education , vol.28 , Issue.1 , pp. 8-25
    • Franke, M.L.1    Carey, D.A.2
  • 14
    • 0002776706 scopus 로고
    • Research on whole number addition and subtraction
    • D. Grouws (ed.), MacMillan, New York
    • Fuson, K.C.: 1992a, 'Research on whole number addition and subtraction', in D. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, MacMillan, New York, pp. 243-275.
    • (1992) Handbook of Research on Mathematics Teaching and Learning , pp. 243-275
    • Fuson, K.C.1
  • 15
    • 0001886704 scopus 로고
    • Research on learning and teaching addition and subtraction of whole numbers
    • G. Leinhardt, R.T. Putnam and R.A. Hattrups (eds.), Erlbaum, Hillsdale, NJ
    • Fuson, K.C.: 1992b, 'Research on learning and teaching addition and subtraction of whole numbers', in G. Leinhardt, R.T. Putnam and R.A. Hattrups (eds.), The Analysis of Arithmetic for Mathematics Teaching, Erlbaum, Hillsdale, NJ, pp. 53-187.
    • (1992) The Analysis of Arithmetic for Mathematics Teaching , pp. 53-187
    • Fuson, K.C.1
  • 18
    • 0000834849 scopus 로고
    • A theory of developing competence with written mathematical symbols
    • Hiebert, J.: 1988, 'A theory of developing competence with written mathematical symbols', Educational Studies in Mathematics 19, 333-355.
    • (1988) Educational Studies in Mathematics , vol.19 , pp. 333-355
    • Hiebert, J.1
  • 21
    • 21144460314 scopus 로고
    • Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic classrooms
    • Hiebert, J. and Wearne, D.: 1993, 'Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic classrooms', American Educational Research Journal 30(2), 393-425.
    • (1993) American Educational Research Journal , vol.30 , Issue.2 , pp. 393-425
    • Hiebert, J.1    Wearne, D.2
  • 22
    • 85085448896 scopus 로고
    • Linking representations in the symbol systems of algebra
    • S. Wagner and C. Kieran (eds.), NCTM, Reston
    • Kaput, J.J.: 1989, 'Linking representations in the symbol systems of algebra, in S. Wagner and C. Kieran (eds.), Research Issues in the Learning and Teaching of Algebra, NCTM, Reston, pp. 167-194.
    • (1989) Research Issues in the Learning and Teaching of Algebra , pp. 167-194
    • Kaput, J.J.1
  • 23
    • 3042832439 scopus 로고
    • A research base supporting long term algebra reform?
    • D.T. Owens, M.K. Reed and G.M. Millsaps (eds.), Columbus, Ohio
    • Kaput, J.J.: 1995, 'A research base supporting long term algebra reform?', in D.T. Owens, M.K. Reed and G.M. Millsaps (eds.), Proceedings of PME-NA XVII, Columbus, Ohio, pp. 71-94.
    • (1995) Proceedings of PME-NA XVII , pp. 71-94
    • Kaput, J.J.1
  • 25
    • 0002050688 scopus 로고
    • The learning and teaching of school algebra
    • D.A. Grouws (ed.), MacMillan, New York
    • Kieran, C.: 1992, 'The learning and teaching of school algebra', in D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, MacMillan, New York, pp. 390-419.
    • (1992) Handbook of Research on Mathematics Teaching and Learning , pp. 390-419
    • Kieran, C.1
  • 26
    • 29444437281 scopus 로고
    • Recursion and the mathematical experience
    • L. Steffe (ed.), Springer-Verlag, New York
    • Kieren, T.E. and Pirie, S.E.B.: 1991, 'Recursion and the mathematical experience', in L. Steffe (ed.), The Epistemology of Mathematical Experience, Springer-Verlag, New York.
    • (1991) The Epistemology of Mathematical Experience
    • Kieren, T.E.1    Pirie, S.E.B.2
  • 28
    • 0009254295 scopus 로고    scopus 로고
    • Students' understanding of algebraic notation: 11-15
    • MacGregor, M. and Stacey, K.: 1997, 'Students' understanding of algebraic notation: 11-15', Educational Studies in Mathematics 33(1), 1-19.
    • (1997) Educational Studies in Mathematics , vol.33 , Issue.1 , pp. 1-19
    • MacGregor, M.1    Stacey, K.2
  • 29
    • 0345781459 scopus 로고
    • Towards a computational theory of algebraic competenece
    • Matz, M.: 1980, 'Towards a computational theory of algebraic competenece', Journal of Mathematical Behavior 3(1), 93-166.
    • (1980) Journal of Mathematical Behavior , vol.3 , Issue.1 , pp. 93-166
    • Matz, M.1
  • 31
    • 0002814286 scopus 로고
    • Development of children's problem solving ability in arithmetic
    • H. Ginsburg (ed.), Academic Press, New York
    • Riley, M.S., Greeno, J.G. and Heller, J.I.: 1983, 'Development of children's problem solving ability in arithmetic', in H. Ginsburg (ed.), The Development of Mathematical Thinking, Academic Press, New York, pp. 153-196.
    • (1983) The Development of Mathematical Thinking , pp. 153-196
    • Riley, M.S.1    Greeno, J.G.2    Heller, J.I.3
  • 32
    • 0000268131 scopus 로고
    • From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge
    • G. Leinhardt, R.T. Putnam and R.A. Hattrups (eds.), Erlbaum, Hillsdale, NJ
    • Resnick, L.B.: 1992, 'From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge, in G. Leinhardt, R.T. Putnam and R.A. Hattrups (eds.), The Analysis of Arithmetic for Mathematics Teaching, Erlbaum, Hillsdale, NJ, pp. 373-429.
    • (1992) The Analysis of Arithmetic for Mathematics Teaching , pp. 373-429
    • Resnick, L.B.1
  • 33
    • 0002714678 scopus 로고
    • Learning to understand arithmetic
    • R. Glaser (ed.), Erlbaum, Hillsdale, NJ
    • Resnick, L.B. and Omanson, S.F.: 1987, 'Learning to understand arithmetic', in R. Glaser (ed.), Advances in Instructional Psychology Vol. 3, Erlbaum, Hillsdale, NJ, pp. 41-95.
    • (1987) Advances in Instructional Psychology Vol. 3 , pp. 41-95
    • Resnick, L.B.1    Omanson, S.F.2
  • 34
    • 0002493923 scopus 로고
    • Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain
    • R. Glaser (ed.) Erlbaum, Hillsdale, NJ
    • Schoenfeld, A.H., Smith, J.P and Arcavi, A.: 1993, 'Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain', in R. Glaser (ed.), Advances in Instructional Psychology Vol. 4, Erlbaum, Hillsdale, NJ.
    • (1993) Advances in Instructional Psychology Vol. 4
    • Schoenfeld, A.H.1    Smith, J.P.2    Arcavi, A.3
  • 35
    • 24944477378 scopus 로고
    • The gains and pitfalls of reification - The case of algebra
    • Sfard, A. and Linchevski, L.: 1994, 'The gains and pitfalls of reification - The case of algebra', Educational Studies in Mathematics 26, 191-228.
    • (1994) Educational Studies in Mathematics , vol.26 , pp. 191-228
    • Sfard, A.1    Linchevski, L.2
  • 36
    • 0010078170 scopus 로고    scopus 로고
    • An alternate route to the reification of function
    • Slavit, D.: 1997a, 'An alternate route to the reification of function', Educational Studies in Mathematics 33(3), 259-281.
    • (1997) Educational Studies in Mathematics , vol.33 , Issue.3 , pp. 259-281
    • Slavit, D.1
  • 37
    • 54749120290 scopus 로고    scopus 로고
    • Learning as sense-making and property-noticing
    • J.A. Dossey, J.O. Swafford, M. Parmantie and A.E. Dossey (eds.), ERIC Clearinghouse, Columbus, OH
    • Slavit, D.: 1997b, 'Learning as sense-making and property-noticing', in J.A. Dossey, J.O. Swafford, M. Parmantie and A.E. Dossey (eds.), Proceedings of PME-NA XIX (Vol. 1), ERIC Clearinghouse, Columbus, OH, pp. 649-656.
    • (1997) Proceedings of PME-NA XIX , vol.1 , pp. 649-656
    • Slavit, D.1
  • 39
    • 0030305056 scopus 로고    scopus 로고
    • Symbolizing as a constructive activity in a computer microworld
    • Steffe, L.P. and Olive, J.: 1996, 'Symbolizing as a constructive activity in a computer microworld', Journal of Educational Computing Research 14(2), 113-138.
    • (1996) Journal of Educational Computing Research , vol.14 , Issue.2 , pp. 113-138
    • Steffe, L.P.1    Olive, J.2
  • 40
    • 0000364533 scopus 로고
    • Notations, conventions, and constraints: Contributions to effective uses of concrete materials in elementary mathematics
    • Thompson, P.W.: 1992, 'Notations, conventions, and constraints: Contributions to effective uses of concrete materials in elementary mathematics', Journal for Research in Mathematics Education 23(2), 123-147.
    • (1992) Journal for Research in Mathematics Education , vol.23 , Issue.2 , pp. 123-147
    • Thompson, P.W.1
  • 41
    • 0010424734 scopus 로고
    • Quantitative reasoning, complexity, and additive structures
    • Thompson, P.W.: 1993, 'Quantitative reasoning, complexity, and additive structures', Educational Studies in Mathematics 25(3), 165-208.
    • (1993) Educational Studies in Mathematics , vol.25 , Issue.3 , pp. 165-208
    • Thompson, P.W.1
  • 42
    • 0003130954 scopus 로고
    • Students, functions, and the undergraduate curriculum
    • E. Dubinsky, A.H. Schoenfeld and J. Kaput (eds.), American Mathematical Society, Providence, RI, and Mathematical Association of America, Washington, D.C.
    • Thompson, P.W.: 1994, 'Students, functions, and the undergraduate curriculum', in E. Dubinsky, A.H. Schoenfeld and J. Kaput (eds.), Research in Collegiate Mathematics Education I, American Mathematical Society, Providence, RI, and Mathematical Association of America, Washington, D.C.
    • (1994) Research in Collegiate Mathematics Education I
    • Thompson, P.W.1
  • 44
    • 85092073965 scopus 로고
    • A classification of cognitive tasks and operations of thought involved in addition and subtraction problems
    • T.P. Carpenter, J.M. Moser and T.A. Romberg (eds.), Erlbaum, Hillsdale, NJ
    • Vergnaud, G.: 1982, A classification of cognitive tasks and operations of thought involved in addition and subtraction problems', in T.P. Carpenter, J.M. Moser and T.A. Romberg (eds.), Addition and Subtraction: A Cognitive Perspective, Erlbaum, Hillsdale, NJ, pp. 39-59.
    • (1982) Addition and Subtraction: a Cognitive Perspective , pp. 39-59
    • Vergnaud, G.1
  • 45
    • 0001328390 scopus 로고
    • Multiplicative structures
    • J. Hiebert and M. Behr (eds.), Reston, NCTM
    • Vergnaud, G.: 1988, 'Multiplicative structures', in J. Hiebert and M. Behr (eds.), Number concepts and operations in the middle grades, Reston, NCTM, pp. 141-161.
    • (1988) Number Concepts and Operations in the middle Grades , pp. 141-161
    • Vergnaud, G.1
  • 46
    • 85068094137 scopus 로고
    • Cognitive science and algebra learning
    • A.H. Schoenfeld (ed.), Erlbaum, Hillsdale, NJ
    • Wenger, R.H.: 1987, 'Cognitive science and algebra learning', in A.H. Schoenfeld (ed.), Cognitive Science and Mathematics Education, Erlbaum, Hillsdale, NJ, pp. 217-251.
    • (1987) Cognitive Science and Mathematics Education , pp. 217-251
    • Wenger, R.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.