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Volumn 44, Issue 5, 2013, Pages 809-850

Students' mathematical noticing

Author keywords

Algebraic reasoning; Discourse practices; Linear functions; Noticing

Indexed keywords


EID: 84887924939     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: 10.5951/jresematheduc.44.5.0809     Document Type: Article
Times cited : (45)

References (61)
  • 2
    • 67349156674 scopus 로고    scopus 로고
    • Gestures as semiotic resources in the mathematics classroom
    • doi:10.1007/s10649-008-9163-z
    • Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom Educational Studies in Mathematics, 70(2), 97-109. doi:10.1007/s10649-008-9163-z
    • (2009) Educational Studies in Mathematics , vol.70 , Issue.2 , pp. 97-109
    • Arzarello, F.1    Paola, D.2    Robutti, O.3    Sabena, C.4
  • 5
    • 54649084614 scopus 로고    scopus 로고
    • Proportional reasoning among 7th grade students with different curricular experiences
    • doi:10.1023/A:1003235712092
    • Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36(3), 247-273. doi:10.1023/A:1003235712092
    • (1998) Educational Studies in Mathematics , vol.36 , Issue.3 , pp. 247-273
    • Ben-Chaim, D.1    Fey, J.T.2    Fitzgerald, W.M.3    Benedetto, C.4    Miller, J.5
  • 9
    • 1842560749 scopus 로고    scopus 로고
    • Reflecting abstraction in context
    • R. Campbell (Ed. & Trans.), Sussex, United Kingdom: Psychology Press. (Original work published in 1977)
    • Campbell, R. (2001). Reflecting abstraction in context In R. Campbell (Ed. & Trans.), Studies in reflecting abstraction by Jean Piaget (pp. 1-27). Sussex, United Kingdom: Psychology Press. (Original work published in 1977)
    • (2001) Studies in Reflecting Abstraction by Jean Piaget , pp. 1-27
    • Campbell, R.1
  • 10
    • 84879640486 scopus 로고    scopus 로고
    • Chinese pedagogy and a pedagogy for learning Chinese
    • F. Marton, S. K. Tse, & W. M. Cheung (Eds.), Rotterdam, the Netherlands: Sense
    • Chik, P. P. M., & Marton, F. (2010). Chinese pedagogy and a pedagogy for learning Chinese. In F. Marton, S. K. Tse, & W. M. Cheung (Eds.), On the learning of Chinese (pp. 9-30). Rotterdam, the Netherlands: Sense.
    • (2010) On the Learning of Chinese , pp. 9-30
    • Chik, P.P.M.1    Marton, F.2
  • 11
    • 58549097867 scopus 로고    scopus 로고
    • An interpretive scheme for analyzing the identities that students develop in mathematics classrooms
    • Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education, 40(1), 40-68.
    • (2009) Journal for Research in Mathematics Education , vol.40 , Issue.1 , pp. 40-68
    • Cobb, P.1    Gresalfi, M.2    Hodge, L.L.3
  • 12
    • 0037251107 scopus 로고    scopus 로고
    • Learning about statistical covariation
    • Cobb, P., McClain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21(1), 1-78. doi:10.1207/S1532690XCI2101-1 (Pubitemid 36399978)
    • (2003) Cognition and Instruction , vol.21 , Issue.1 , pp. 1-78
    • Cobb, P.1    McClain, K.2    Gravemeijer, K.3
  • 13
    • 0012797003 scopus 로고    scopus 로고
    • A method for conducting longitudinal analyses of classroom videorecordings and transcripts
    • Cobb, P., & Whitenack, J. (1996). A method for conducting longitudinal analyses of classroom videorecordings and transcripts. Educational Studies in Mathematics, 30(3), 213-228. doi:10.1007/BF00304566 (Pubitemid 126054985)
    • (1996) Educational Studies in Mathematics , vol.30 , Issue.3 , pp. 213-228
    • Cobb, P.1    Whitenack, J.W.2
  • 14
    • 0039470401 scopus 로고    scopus 로고
    • Constructivist, emergent, and sociocultural perspectives in the context of developmental research
    • doi:10.1080/00461520.1996.965 3265
    • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175-190. doi:10.1080/00461520.1996.965 3265
    • (1996) Educational Psychologist , vol.31 , Issue.3-4 , pp. 175-190
    • Cobb, P.1    Yackel, E.2
  • 15
    • 38349035803 scopus 로고    scopus 로고
    • The influence of reasoning with emergent quantities on students' generalizations
    • doi:10.1080/07370000701632397
    • Ellis, A. B. (2007). The influence of reasoning with emergent quantities on students' generalizations. Cognition and Instruction, 25(4), 439-478. doi:10.1080/07370000701632397
    • (2007) Cognition and Instruction , vol.25 , Issue.4 , pp. 439-478
    • Ellis, A.B.1
  • 16
    • 64649097253 scopus 로고    scopus 로고
    • Hidden lessons: How a focus on slope-like properties of quadratic functions encouraged unexpected generalizations
    • doi:10.1016/j.jmathb.2008.11.002
    • Ellis, A. B., & Grinstread, P. (2008). Hidden lessons: How a focus on slope-like properties of quadratic functions encouraged unexpected generalizations. Journal of Mathematical Behavior, 27(4), 277-296. doi:10.1016/j.jmathb.2008.11.002
    • (2008) Journal of Mathematical Behavior , vol.27 , Issue.4 , pp. 277-296
    • Ellis, A.B.1    Grinstread, P.2
  • 17
    • 84887955200 scopus 로고    scopus 로고
    • On noticing teacher noticing
    • M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), New York, NY: Routledge
    • Erickson, F. (2010). On noticing teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 17-34). New York, NY: Routledge.
    • (2010) Mathematics Teacher Noticing: Seeing Through Teachers' Eyes , pp. 17-34
    • Erickson, F.1
  • 18
    • 0036533932 scopus 로고    scopus 로고
    • Testing the efficiency and independence of attentional networks
    • DOI 10.1162/089892902317361886
    • Fan, J., McCandliss, B. D., Sommer, T., Raz, A., & Posner, M. I. (2002). Testing the efficiency and independence of attentional networks. Journal of Cognitive Neuroscience, 14(3), 340-347. doi: 10.1162/089892902317361886 (Pubitemid 34267537)
    • (2002) Journal of Cognitive Neuroscience , vol.14 , Issue.3 , pp. 340-347
    • Fan, J.1    McCandliss, B.D.2    Sommer, T.3    Raz, A.4    Posner, M.I.5
  • 21
    • 0003663910 scopus 로고    scopus 로고
    • Cambridge, United Kingdom: Cambridge University Press doi:10.1017/CBO9780511527777
    • Ginsburg, H. (1997). Entering the child's mind. Cambridge, United Kingdom: Cambridge University Press. doi:10.1017/CBO9780511527777
    • (1997) Entering the Child's Mind
    • Ginsburg, H.1
  • 23
    • 0000833354 scopus 로고
    • Mathematics, metaphors, and human factors: Mathematical, technical, and pedagogical challenges in the educational use of graphical representation of functions
    • Goldenberg, P. E. (1988). Mathematics, metaphors, and human factors: Mathematical, technical, and pedagogical challenges in the educational use of graphical representation of functions. The Journal of Mathematical Behavior, 7(2), 135-173.
    • (1988) The Journal of Mathematical Behavior , vol.7 , Issue.2 , pp. 135-173
    • Goldenberg, P.E.1
  • 25
    • 84981922507 scopus 로고
    • Professional vision
    • doi:10.1525/ aa.1994.96.3.02a00100
    • Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606-633. doi:10.1525/ aa.1994.96.3.02a00100
    • (1994) American Anthropologist , vol.96 , Issue.3 , pp. 606-633
    • Goodwin, C.1
  • 26
    • 0042824240 scopus 로고    scopus 로고
    • Commentary: Alternative perspectives on transfer and transfer studies
    • DOI 10.1016/S0883-0355(99)00029-4, PII S0883035599000294
    • Hatano, G., & Greeno, J. G. (1999). Commentary: Alternative perspectives on transfer and transfer studies. International Journal of Educational Research, 57(7), 645-654. (Pubitemid 41167989)
    • (1999) International Journal of Educational Research , vol.31 , Issue.7 , pp. 645-654
    • Hatano, G.1    Greeno, J.G.2
  • 27
    • 0942303519 scopus 로고    scopus 로고
    • Choosing qualitative research: A primer for technology education researchers
    • Retrieved from
    • Hoepfl, M. C. (1997). Choosing qualitative research: A primer for technology education researchers. Journal of Technology Education, 9(1). Retrieved from http://scholar.lib.vt.edu/ejournals/JTE/v9n1/hoepfl.html
    • (1997) Journal of Technology Education , vol.9 , Issue.1
    • Hoepfl, M.C.1
  • 30
    • 0002351467 scopus 로고
    • Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns
    • G. Harel & J. Confrey (Eds.), Albany, NY: State University of New York Press
    • Kaput, J. J., & Maxwell-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, NY: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 235-287
    • Kaput, J.J.1    Maxwell-West, M.2
  • 31
    • 0010036012 scopus 로고
    • Ratio and proportion: Elementary didactical phenomenology
    • J. T. Sowder & B. P. Schappelle (Eds.), Albany, NY: State University of New York Press
    • Lamon, S. J. (1995). Ratio and proportion: Elementary didactical phenomenology. In J. T. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 167-198). Albany, NY: State University of New York Press.
    • (1995) Providing a Foundation for Teaching Mathematics in the Middle Grades , pp. 167-198
    • Lamon, S.J.1
  • 33
    • 33846165073 scopus 로고    scopus 로고
    • Recursive and explicit rules: How can we build student algebraic understanding?
    • doi:10.1016/j.jmathb.2006.11.004
    • Lannin, J., Barker, D., & Townsend, B. (2006). Recursive and explicit rules: How can we build student algebraic understanding? Journal of Mathematical Behavior, 25(4), 299-317. doi:10.1016/j.jmathb.2006.11.004
    • (2006) Journal of Mathematical Behavior , vol.25 , Issue.4 , pp. 299-317
    • Lannin, J.1    Barker, D.2    Townsend, B.3
  • 34
    • 17144392686 scopus 로고    scopus 로고
    • An initiation into algebra culture through generalization activities
    • In C. Bednarz, C. Kieran, & L. Lee (Eds.), Dordrecht, the Netherlands: Kluwer. doi: 10.1007/978-94-009-1732-3-6
    • Lee, L. (1996). An initiation into algebra culture through generalization activities. In C. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 87-106). Dordrecht, the Netherlands: Kluwer. doi: 10.1007/978-94-009-1732-3-6
    • (1996) Approaches to Algebra: Perspectives for Research and Teaching , pp. 87-106
    • Lee, L.1
  • 35
    • 84887889676 scopus 로고    scopus 로고
    • Reasoning about probabilistic phenomena: Lessons learned and applied in software design
    • Retrieved from
    • Lee, H. S., & Lee, J. T. (2009). Reasoning about probabilistic phenomena: Lessons learned and applied in software design. Technology Innovations in Statistics Education, 3(2). Retrieved from http://www. escholarship.org/uc/item/1b54h9s9
    • (2009) Technology Innovations in Statistics Education , vol.3 , Issue.2
    • Lee, H.S.1    Lee, J.T.2
  • 36
    • 14844327841 scopus 로고    scopus 로고
    • How "Focusing phenomena" in the instructional environment support individual students' generalizations
    • Lobato, J., Ellis, A. B., & Muñoz, R. (2003). How "focusing phenomena" in the instructional environment afford students' generalizations. Mathematical Thinking and Learning, 5(1), 1-36. doi:10.1207/S15327833MTL0501-01 (Pubitemid 36116843)
    • (2003) Mathematical Thinking and Learning , vol.5 , Issue.1 , pp. 1-36
    • Lobato, J.1    Ellis, A.B.2    Munoz, R.3
  • 37
  • 38
    • 33645965939 scopus 로고    scopus 로고
    • On some necessary conditions of learning
    • DOI 10.1207/s15327809jls1502-2
    • Marton, F., & Pang, M. F. (2006). On some necessary conditions of learning. The Journal of the Learning Sciences, 15(2), 193-220. doi: 10.1207/s15327809jls1502-2 (Pubitemid 43602585)
    • (2006) Journal of the Learning Sciences , vol.15 , Issue.2 , pp. 193-220
    • Marton, F.1    Pang, M.F.2
  • 39
    • 0842288565 scopus 로고    scopus 로고
    • Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention
    • doi:10.1023/A:1009973717476
    • Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243-267. doi:10.1023/A:1009973717476
    • (1998) Journal of Mathematics Teacher Education , vol.1 , Issue.3 , pp. 243-267
    • Mason, J.1
  • 41
    • 84993812284 scopus 로고    scopus 로고
    • Causal explanation, qualitative research, and scientific inquiry in education
    • doi: 10.3102/0013189X033002003
    • Maxwell, J. (2004). Causal explanation, qualitative research, and scientific inquiry in education. Educational Researcher, 33(2), 3-11. doi: 10.3102/0013189X033002003
    • (2004) Educational Researcher , vol.33 , Issue.2 , pp. 3-11
    • Maxwell, J.1
  • 42
    • 85055302044 scopus 로고    scopus 로고
    • Focusing attention on decoding for children with poor reading skills: A study of the Word Building intervention
    • doi:10.1207/S1532799XSSR0701-05
    • McCandliss, B. D., Beck, I., Sandak, R., & Perfetti, C. (2003). Focusing attention on decoding for children with poor reading skills: A study of the Word Building intervention. Scientific Studies of Reading, 7(1), 75-104. doi:10.1207/S1532799XSSR0701-05
    • (2003) Scientific Studies of Reading , vol.7 , Issue.1 , pp. 75-104
    • McCandliss, B.D.1    Beck, I.2    Sandak, R.3    Perfetti, C.4
  • 44
    • 84887920559 scopus 로고    scopus 로고
    • National Council of Teachers of Mathematics Retrieved from
    • National Council of Teachers of Mathematics (2010). Mathematics professional development brief [Research brief]. Retrieved from http://www.nctm.org/news/content.aspx?id=27191
    • (2010) Mathematics Professional Development Brief [Research Brief]
  • 45
    • 4444363091 scopus 로고    scopus 로고
    • Learning to see: Making sense of the mathematics of change in middle school
    • doi:10.1023/B:IJCO.0000040891.50250.7e
    • Noble, T., Nemirovsky, R., Dimattia, C., & Wright, T. (2004). Learning to see: Making sense of the mathematics of change in middle school. International Journal of Computers for Mathematical Learning, 9(2), 109-167. doi:10.1023/B:IJCO.0000040891.50250.7e
    • (2004) International Journal of Computers for Mathematical Learning , vol.9 , Issue.2 , pp. 109-167
    • Noble, T.1    Nemirovsky, R.2    Dimattia, C.3    Wright, T.4
  • 46
    • 0025318243 scopus 로고
    • The attention systems of the human brain
    • doi:10.1146/annurev.ne.13.030190.000325
    • Posner, M. I., & Petersen, S. E. (1990). The attention systems of the human brain. Annual Review of Neuroscience, 13, 25-42. doi:10.1146/annurev.ne. 13.030190.000325
    • (1990) Annual Review of Neuroscience , vol.13 , pp. 25-42
    • Posner, M.I.1    Petersen, S.E.2
  • 47
    • 77951243551 scopus 로고    scopus 로고
    • Middle school children's cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns
    • doi:10.1007/s11858-007-0062-z
    • Rivera, F., & Becker, J. (2008). Middle school children's cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns. ZDM, 40(1), 65-82. doi:10.1007/s11858-007-0062-z
    • (2008) ZDM , vol.40 , Issue.1 , pp. 65-82
    • Rivera, F.1    Becker, J.2
  • 48
    • 0000130954 scopus 로고    scopus 로고
    • A time for telling
    • Schwartz, D. L., & Bransford, J. D. (1998). A time for telling. Cognition and Instruction, 16(4), 475-522. doi:10.1207/s1532690xcil604-4 (Pubitemid 128368485)
    • (1998) Cognition and Instruction , vol.16 , Issue.4 , pp. 475-522
    • Schwartz, D.L.1    Bransford, J.D.2
  • 49
    • 84893759949 scopus 로고    scopus 로고
    • Situating the study of teacher noticing
    • M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), New York, NY: Routledge
    • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2010). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 3-13). New York, NY: Routledge.
    • (2010) Mathematics Teacher Noticing: Seeing Through Teachers' Eyes , pp. 3-13
    • Sherin, M.G.1    Jacobs, V.R.2    Philipp, R.A.3
  • 50
    • 84883830554 scopus 로고    scopus 로고
    • Reflections on the study of teacher noticing
    • M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), New York, NY: Routledge
    • Sherin, B., & Star, J. R. (2010). Reflections on the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes (pp. 66-78). New York, NY: Routledge.
    • (2010) Mathematics Teacher Noticing: Seeing Through Teachers' Eyes , pp. 66-78
    • Sherin, B.1    Star, J.R.2
  • 51
    • 58649109367 scopus 로고    scopus 로고
    • Effects of video club participation on teachers' professional vision
    • doi:10.1177/0022487108328155
    • Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers' professional vision. Journal of Teacher Education, 60(1), 20-37. doi:10.1177/0022487108328155
    • (2009) Journal of Teacher Education , vol.60 , Issue.1 , pp. 20-37
    • Sherin, M.G.1    Van Es, E.A.2
  • 52
    • 85144391406 scopus 로고    scopus 로고
    • Quantitative reasoning and the development of algebraic reasoning
    • J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), New York, NY: Lawrence Erlbaum Associates
    • Smith, J. P., & Thompson, P. (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, NY: Lawrence Erlbaum Associates.
    • (2008) Algebra in the Early Grades , pp. 95-132
    • Smith, J.P.1    Thompson, P.2
  • 53
    • 0037548823 scopus 로고    scopus 로고
    • Disciplined perception: Learning to see in technoscience
    • M. Lampert & M. L. Blunk (Eds.), New York, NY: Cambridge University Press
    • Stevens, R., & Hall, R. (1998). Disciplined perception: Learning to see in technoscience. In M. Lampert & M. L. Blunk (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 107-149). New York, NY: Cambridge University Press.
    • (1998) Talking Mathematics in School: Studies of Teaching and Learning , pp. 107-149
    • Stevens, R.1    Hall, R.2
  • 54
    • 84955542803 scopus 로고
    • New York, NY: Cambridge University Press doi:10.1017/CBO9780511557842
    • Strauss, A. L. (1987). Qualitative analysis for social scientists. New York, NY: Cambridge University Press. doi:10.1017/CBO9780511557842
    • (1987) Qualitative Analysis for Social Scientists
    • Strauss, A.L.1
  • 56
    • 0002269268 scopus 로고
    • The development of the concept of speed and its relationship to concepts of rate
    • G. Harel & J. Confrey (Eds.), Albany, NY: SUNY Press
    • Thompson, P. W. (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, NY: SUNY Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 179-234
    • Thompson, P.W.1
  • 57
    • 0041579531 scopus 로고    scopus 로고
    • Intuitive rules: A way to explain and predict students' reasoning
    • doi:10.1023/A:1003436313032
    • Tirosh, D., & Stavy, R. (1999). Intuitive rules: A way to explain and predict students' reasoning. Educational Studies in Mathematics, 38(1), 51-66. doi:10.1023/A:1003436313032
    • (1999) Educational Studies in Mathematics , vol.38 , Issue.1 , pp. 51-66
    • Tirosh, D.1    Stavy, R.2
  • 58
    • 4544268394 scopus 로고    scopus 로고
    • The predictive power of intuitive rules: A critical analysis of the impact of "more A-more B" and "same A-same B."
    • doi:10.1023/B:EDUC.0000040379.26033.0d
    • van Dooren, W., de Bock, D., Weyer, D., & Verschaffel, L. (2004). The predictive power of intuitive rules: A critical analysis of the impact of "more A-more B" and "same A-same B." Educational Studies in Mathematics, 56(2/3), 179-207. doi:10.1023/B:EDUC.0000040379.26033.0d
    • (2004) Educational Studies in Mathematics , vol.56 , Issue.2-3 , pp. 179-207
    • Van Dooren, W.1    De Bock, D.2    Weyer, D.3    Verschaffel, L.4
  • 60
    • 84864672459 scopus 로고    scopus 로고
    • Affordances, constraints and attunements in mathematical activity
    • doi:10.1080/14794800008520128
    • Watson, A. (2004). Affordances, constraints and attunements in mathematical activity. Research in Mathematics Education, 6(1), 23-34. doi:10.1080/14794800008520128
    • (2004) Research in Mathematics Education , vol.6 , Issue.1 , pp. 23-34
    • Watson, A.1
  • 61
    • 84859639258 scopus 로고    scopus 로고
    • Madison, WI: Wisconsin Center for Education Research, University of Wisconsin-Madison
    • Woods, D., & Fassnacht, C. (2009). Transana (Version 2.41) [Computer software]. Madison, WI: Wisconsin Center for Education Research, University of Wisconsin-Madison. Available from http://www.transana.org
    • (2009) Transana (Version 2.41) [Computer Software]
    • Woods, D.1    Fassnacht, C.2


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