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Volumn 12, Issue 3, 2010, Pages 227-252

A local instruction theory for the development of number sense

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EID: 77954078726     PISSN: 10986065     EISSN: 15327833     Source Type: Journal    
DOI: 10.1080/10986061003689618     Document Type: Article
Times cited : (24)

References (61)
  • 2
    • 0012533445 scopus 로고    scopus 로고
    • Identifying cyclic patterns of interaction to study individual and collective learning
    • Bowers, J., & Nickerson, S. (2001). Identifying cyclic patterns of interaction to study individual and collective learning. Mathematical Thinking and Learning, 3, 1-28.
    • (2001) Mathematical Thinking and Learning , vol.3 , pp. 1-28
    • Bowers, J.1    Nickerson, S.2
  • 3
    • 0002926797 scopus 로고    scopus 로고
    • Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction
    • Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. Elementary School Journal, 97, 3-20.
    • (1996) Elementary School Journal , vol.97 , pp. 3-20
    • Carpenter, T.P.1    Fennema, E.2    Franke, M.L.3
  • 5
    • 84963405339 scopus 로고    scopus 로고
    • The development of computational estimation: A neo-Piagetian analysis
    • Case, R., & Sowder, J. T. (2000). The development of computational estimation: A neo-Piagetian analysis. Cognition and Instruction, 7(2), 79-104.
    • (2000) Cognition and Instruction , vol.7 , Issue.2 , pp. 79-104
    • Case, R.1    Sowder, J.T.2
  • 6
    • 0001887934 scopus 로고    scopus 로고
    • Conducting teaching experiments in collaboration with teachers
    • In A. Kelly & R. Lesh (Eds.), Mahwah, NJ: Lawrence Erlbaum
    • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. Kelly & R. Lesh (Eds.), Hand-book of research design in mathematics and science education (pp. 307-333). Mahwah, NJ: Lawrence Erlbaum.
    • (2000) Hand-Book of Research Design In Mathematics and Science Education , pp. 307-333
    • Cobb, P.1
  • 7
    • 0039388067 scopus 로고    scopus 로고
    • Cognitive and situated learning perspectives
    • Cobb, P., & Bowers, J. (1999). Cognitive and situated learning perspectives. Educational Researcher, 28 (2), 4-15.
    • (1999) Educational Researcher , vol.28 , Issue.2 , pp. 4-15
    • Cobb, P.1    Bowers, J.2
  • 9
    • 0001902422 scopus 로고    scopus 로고
    • Symbolizing and mathematizing: The emergence of chains of signification in one first-grade classroom
    • In D. Kirshner, & J. A. Whitson (Eds.), Hillsdale, NJ: Lawrence Erlbaum
    • Cobb, P., Gravemeijer, K., Yackel, E., McClain, K., & Whitenack, J. (1997). Symbolizing and mathematizing: The emergence of chains of signification in one first-grade classroom. In D. Kirshner, & J. A. Whitson (Eds.), Situated cognition theory: social, semiotic, and neurological perspectives (pp. 151-233). Hillsdale, NJ: Lawrence Erlbaum.
    • (1997) Situated Cognition Theory: Social, Semiotic, and Neurological Perspectives , pp. 151-233
    • Cobb, P.1    Gravemeijer, K.2    Yackel, E.3    McClain, K.4    Whitenack, J.5
  • 10
    • 0039470401 scopus 로고    scopus 로고
    • Constructivist, emergent, and sociocultural perspectives in the context of developmental research
    • Cobb, P., & Yackel E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 175-190.
    • (1996) Educational Psychologist , vol.31 , pp. 175-190
    • Cobb, P.1    Yackel, E.2
  • 12
    • 24944582475 scopus 로고
    • Factors contributing to success in mathematical estimation in preservice teachers: Types of problems and previous mathematical experience
    • Gliner, G. S. (1991). Factors contributing to success in mathematical estimation in preservice teachers: Types of problems and previous mathematical experience. Educational Studies in Mathematics, 22, 595-606.
    • (1991) Educational Studies In Mathematics , vol.22 , pp. 595-606
    • Gliner, G.S.1
  • 13
    • 0000286146 scopus 로고    scopus 로고
    • How emergent models may foster the constitution of formal mathematics
    • Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1, 155-177.
    • (1999) Mathematical Thinking and Learning , vol.1 , pp. 155-177
    • Gravemeijer, K.1
  • 14
    • 70349489584 scopus 로고    scopus 로고
    • Local instruction theories as a means of support for teachers in reform mathematics education
    • Gravemeijer, K. (2004). Local instruction theories as a means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6, 105-128.
    • (2004) Mathematical Thinking and Learning , vol.6 , pp. 105-128
    • Gravemeijer, K.1
  • 15
    • 36348980062 scopus 로고    scopus 로고
    • A hypothetical learning trajectory on measurement and flexible arithmetic
    • In M. Stephan, J. Bowers, P. Cobb, & K. Gravemeijer (Eds.), Reston, VA: National Council of Teachers of Mathematics
    • Gravemeijer, K., Bowers, J., & Stephan, M. (2003). A hypothetical learning trajectory on measurement and flexible arithmetic. In M. Stephan, J. Bowers, P. Cobb, & K. Gravemeijer (Eds.), Supporting students' development of measuring conceptions: Analyzing students' learning in social context (pp. 51-66). Reston, VA: National Council of Teachers of Mathematics.
    • (2003) Supporting Students' Development of Measuring Conceptions: Analyzing Students' Learning In Social Context , pp. 51-66
    • Gravemeijer, K.1    Bowers, J.2    Stephan, M.3
  • 16
    • 0000429268 scopus 로고
    • Number sense as situated knowing in a conceptual domain
    • Greeno, J. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22, 170-218.
    • (1991) Journal For Research In Mathematics Education , vol.22 , pp. 170-218
    • Greeno, J.1
  • 17
  • 19
    • 0036347128 scopus 로고    scopus 로고
    • Flexibility and inflexibility in accurate mental addition and subtraction: Two case studies
    • Heirdsfield, A. M., & Cooper, T. J. (2002). Flexibility and inflexibility in accurate mental addition and subtraction: Two case studies. Journal of Mathematical Behavior, 21, 57-74.
    • (2002) Journal of Mathematical Behavior , vol.21 , pp. 57-74
    • Heirdsfield, A.M.1    Cooper, T.J.2
  • 20
    • 10144260614 scopus 로고    scopus 로고
    • Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers
    • Heirdsfield, A. M., & Cooper, T. J. (2004). Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers. Journal of Mathematical Behavior, 23, 443-463.
    • (2004) Journal of Mathematical Behavior , vol.23 , pp. 443-463
    • Heirdsfield, A.M.1    Cooper, T.J.2
  • 22
    • 0040382699 scopus 로고
    • Teaching number sense
    • Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36, 6-11.
    • (1989) Arithmetic Teacher , vol.36 , pp. 6-11
    • Howden, H.1
  • 24
    • 0040675272 scopus 로고    scopus 로고
    • Promoting conceptual thinking in four upper-elementary mathematics classrooms
    • Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 102, 59-80.
    • (2001) The Elementary School Journal , vol.102 , pp. 59-80
    • Kazemi, E.1    Stipek, D.2
  • 26
    • 0038247248 scopus 로고
    • The development of procedural and conceptual knowledge in computation estimation
    • LeFevre, J., Greenham, S. L., & Waheed, N. (1993). The development of procedural and conceptual knowledge in computation estimation, Cognition and Instruction, 11(2), 95-132.
    • (1993) Cognition and Instruction , vol.11 , Issue.2 , pp. 95-132
    • Lefevre, J.1    Greenham, S.L.2    Waheed, N.3
  • 27
    • 0041060849 scopus 로고
    • Strategy use and estimation ability of college students
    • Levine, D. R. (1982). Strategy use and estimation ability of college students. Journal for Research in Mathematics Education, 13, 350-359.
    • (1982) Journal For Research In Mathematics Education , vol.13 , pp. 350-359
    • Levine, D.R.1
  • 28
    • 77954070386 scopus 로고    scopus 로고
    • Is mental calculation just strolling around in an imaginary number space?
    • In M. Beishuizen, K. P. E. Gravemeijer, & E. C. D. M. van Lieshout (Eds.), Utrecht, the Netherlands: Utrecht University
    • Lorenz, J. H. (1997). Is mental calculation just strolling around in an imaginary number space? In M. Beishuizen, K. P. E. Gravemeijer, & E. C. D. M. van Lieshout (Eds.), The role of context and models in the development of mathematical strategies and procedures (pp. 199-213). Utrecht, the Netherlands: Utrecht University.
    • (1997) The Role of Context and Models In the Development of Mathematical Strategies and Procedures , pp. 199-213
    • Lorenz, J.H.1
  • 32
    • 0003865799 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
  • 33
    • 0003601049 scopus 로고    scopus 로고
    • National Research Council, J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press
    • National Research Council (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
    • (2001) Adding it Up: Helping Children Learn Mathematics
  • 34
    • 36348987202 scopus 로고    scopus 로고
    • Reinventing solutions to systems of linear differential equations: A case of emergent models involving analytic expression
    • Rasmussen, C., & Blumenfeld, H. (2007). Reinventing solutions to systems of linear differential equations: A case of emergent models involving analytic expression. Journal of Mathematical Behavior, 26, 195-210.
    • (2007) Journal of Mathematical Behavior , vol.26 , pp. 195-210
    • Rasmussen, C.1    Blumenfeld, H.2
  • 35
    • 33750919237 scopus 로고    scopus 로고
    • Pedagogical content tools: Integrating student reasoning and mathematics in instruction
    • Rasmussen, C., & Marrongelle, K. (2006). Pedagogical content tools: Integrating student reasoning and mathematics in instruction. Journal for Research in Mathematics Education, 37, 388-420.
    • (2006) Journal For Research In Mathematics Education , vol.37 , pp. 388-420
    • Rasmussen, C.1    Marrongelle, K.2
  • 37
    • 21844486123 scopus 로고
    • Mental computation performance and strategies used by Japanese students in Grades 2, 4, 6, and 8
    • Reys, R. E., Reys, B. J., Nohda, N., & Emori, H. (1995). Mental computation performance and strategies used by Japanese students in Grades 2, 4, 6, and 8. Journal for Research in Mathematics Education, 26, 304-326.
    • (1995) Journal For Research In Mathematics Education , vol.26 , pp. 304-326
    • Reys, R.E.1    Reys, B.J.2    Nohda, N.3    Emori, H.4
  • 39
    • 21944452875 scopus 로고    scopus 로고
    • Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan
    • Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, 29, 225-237.
    • (1998) Journal For Research In Mathematics Education , vol.29 , pp. 225-237
    • Reys, R.E.1    Yang, D.C.2
  • 40
    • 0003358560 scopus 로고
    • Mathematical discussions
    • In E. von Glaserfeld (Ed.), Dordrecht, The Netherlands: Kluwer
    • Richards, J. (1991). Mathematical discussions. In E. von Glaserfeld (Ed.), Radical constructivism in mathematics education (pp. 13-51). Dordrecht, The Netherlands: Kluwer.
    • (1991) Radical Constructivism In Mathematics Education , pp. 13-51
    • Richards, J.1
  • 42
    • 0001806096 scopus 로고
    • Problem solving in context(s)
    • In R. Charles & E. Silver (Eds.), Reston, VA: National Council of Teachers of Mathematics
    • Schoenfeld, A. (1989). Problem solving in context(s). In R. Charles & E. Silver (Eds.), The teaching and assessing of mathematical problem solving, (pp. 82-92). Reston, VA: National Council of Teachers of Mathematics.
    • (1989) The Teaching and Assessing of Mathematical Problem Solving , pp. 82-92
    • Schoenfeld, A.1
  • 43
    • 0002242225 scopus 로고
    • Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics
    • In D.A. Grouws (Ed.), New York: MacMillan
    • Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York: MacMillan.
    • (1992) Handbook of Research On Mathematics Teaching and Learning , pp. 334-370
    • Schoenfeld, A.1
  • 44
    • 77954038933 scopus 로고    scopus 로고
    • There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning
    • Sfard, A. (2002). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 22, 1-36.
    • (2002) Educational Studies In Mathematics , vol.22 , pp. 1-36
    • Sfard, A.1
  • 45
    • 84861743096 scopus 로고
    • Strategy discovery and strategy generalization
    • In R. S. Siegler & E. Jenkins (Eds.), Hillsdale, NJ: Lawrence Erlbaum
    • Siegler, R., and Jenkins, E., (1989). Strategy discovery and strategy generalization. In R. S. Siegler & E. Jenkins (Eds.), How children discover new strategies (pp. 1-20). Hillsdale, NJ: Lawrence Erlbaum.
    • (1989) How Children Discover New Strategies , pp. 1-20
    • Siegler, R.1    Jenkins, E.2
  • 46
    • 21844488292 scopus 로고
    • Reconstructing mathematics pedagogy from a constructivist perspective
    • Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114-145.
    • (1995) Journal For Research In Mathematics Education , vol.26 , pp. 114-145
    • Simon, M.1
  • 47
    • 33746186990 scopus 로고    scopus 로고
    • Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory
    • Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6, 91-104.
    • (2004) Mathematical Thinking and Learning , vol.6 , pp. 91-104
    • Simon, M.A.1    Tzur, R.2
  • 48
    • 85144391406 scopus 로고    scopus 로고
    • Quantitative reasoning and the development of algebraic reasoning
    • In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), New York: Erlbaum
    • Smith, J. P., & Thompson, P. W. (2008). Quantitative reasoning and the development of algebraic reasoning. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 95-132). New York: Erlbaum.
    • (2008) Algebra In the Early Grades , pp. 95-132
    • Smith, J.P.1    Thompson, P.W.2
  • 50
    • 38949193724 scopus 로고    scopus 로고
    • The mathematical education and development of teachers
    • In F. K. Lester (Ed.), Charlotte, NC: Information Age Publishing
    • Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157-223). Charlotte, NC: Information Age Publishing.
    • (2007) Second Handbook of Research On Mathematics Teaching and Learning , pp. 157-223
    • Sowder, J.T.1
  • 52
    • 0010036255 scopus 로고
    • The development of concepts and strategies used in computational estimation
    • Sowder, J. T., & Wheeler, M. M. (1989). The development of concepts and strategies used in computational estimation. Journal for Research in Mathematics Education, 20, 130-146.
    • (1989) Journal For Research In Mathematics Education , vol.20 , pp. 130-146
    • Sowder, J.T.1    Wheeler, M.M.2
  • 54
    • 0010424734 scopus 로고
    • Quantitative reasoning, complexity, and additive structures
    • Thompson, P. W. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25, 165-208.
    • (1993) Educational Studies In Mathematics , vol.25 , pp. 165-208
    • Thompson, P.W.1
  • 55
    • 0012881236 scopus 로고
    • Calculational and conceptual orientations toward teaching mathematics
    • In D. B. Aichele & A. F. Coxford (Eds.), Reston, VA: National Council of Teachers of Mathematics
    • Thompson, A. G., Philipp, R. A., Thompson, P. W., & Boyd, B. A. (1994). Calculational and conceptual orientations toward teaching mathematics. In D. B. Aichele & A. F. Coxford (Eds.), Professional development for teachers of mathematics (pp.79-92). Reston, VA: National Council of Teachers of Mathematics.
    • (1994) Professional Development For Teachers of Mathematics , pp. 79-92
    • Thompson, A.G.1    Philipp, R.A.2    Thompson, P.W.3    Boyd, B.A.4
  • 56
    • 3843119950 scopus 로고    scopus 로고
    • The didactical use of models in Realistic Mathematics Education: An example from a longitudinal trajectory on percentage
    • van den Heuvel-Panhuizen, M. (2003). The didactical use of models in Realistic Mathematics Education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9-35.
    • (2003) Educational Studies In Mathematics , vol.54 , pp. 9-35
    • van den Heuvel-Panhuizen, M.1
  • 57
    • 34547195458 scopus 로고    scopus 로고
    • Elementary school students' mental computation proficiencies
    • Varol, F., & Farran, D. (2007). Elementary school students' mental computation proficiencies. Early Childhood Education Journal, 35(1), 89-94.
    • (2007) Early Childhood Education Journal , vol.35 , Issue.1 , pp. 89-94
    • Varol, F.1    Farran, D.2
  • 58
    • 77954048988 scopus 로고    scopus 로고
    • Proceedings of the Tenth Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education. Retrieved from
    • Whitacre, I. (2007). Preservice teachers' number sensible mental computation strategies. Proceedings of the Tenth Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education. Retrieved from http://sigmaa.man.org/rume/crume2007/papers/whitacre.pdf
    • (2007) Preservice Teachers' Number Sensible Mental Computation Strategies
    • Whitacre, I.1
  • 61
    • 21344474293 scopus 로고    scopus 로고
    • Sociomathematical norms, argumentation, and autonomy in mathematics
    • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458-477.
    • (1996) Journal For Research In Mathematics Education , vol.27 , pp. 458-477
    • Yackel, E.1    Cobb, P.2


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