메뉴 건너뛰기




Volumn 17, Issue 1-2, 2012, Pages 61-86

Fostering hooks and shifts: Tutorial tactics for guided mathematical discovery

Author keywords

Cognition; Design based research; Discovery; Education; Embodied interaction; Guided reinvention; Insight; Mathematics education; Natural user interface (NUI); Proportion; Proportional reasoning; Remote control; Semiotic cultural; Sociocultural; Symbolic artifact; Teaching; Technology; Virtual object

Indexed keywords

DATA VISUALIZATION; EDUCATION; EDUCATION COMPUTING; REMOTE CONTROL; STUDENTS; TEACHING;

EID: 84887536111     PISSN: 22111662     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10758-012-9192-7     Document Type: Article
Times cited : (44)

References (106)
  • 1
    • 84892670722 scopus 로고    scopus 로고
    • Toward a taxonomy of design genres: Fostering students' mathematical insight via perception-based and action-based experiences
    • (submitted).
    • Abrahamson, D. (submitted). Toward a taxonomy of design genres: Fostering students' mathematical insight via perception-based and action-based experiences. Educational Studies in Mathematics.
    • Educational Studies in Mathematics.
    • Abrahamson, D.1
  • 2
    • 57849126299 scopus 로고    scopus 로고
    • Embodied design: Constructing means for constructing meaning
    • Electronic supplementary material at
    • Abrahamson, D. (2009a). Embodied design: Constructing means for constructing meaning. Educational Studies in Mathematics, 70(1), 27-47. Electronic supplementary material at http://edrl.berkeley.edu/publications/ journals/ESM/Abrahamson-ESM/.
    • (2009) Educational Studies in Mathematics , vol.70 , Issue.1 , pp. 27-47
    • Abrahamson, D.1
  • 3
    • 70349811745 scopus 로고    scopus 로고
    • Orchestrating semiotic leaps from tacit to cultural quantitative reasoning - The case of anticipating experimental outcomes of a quasi-binomial random generator
    • Abrahamson, D. (2009b). Orchestrating semiotic leaps from tacit to cultural quantitative reasoning - the case of anticipating experimental outcomes of a quasi-binomial random generator. Cognition and Instruction, 27(3), 175-224.
    • (2009) Cognition and Instruction , vol.27 , Issue.3 , pp. 175-224
    • Abrahamson, D.1
  • 4
    • 84892675867 scopus 로고    scopus 로고
    • Coordinating visualizations of polysemous action: Values added for grounding proportion
    • (submitted), In F. Rivera, H. Steinbring, & A. Arcavi (Eds.), ZDM: The International Journal on Mathematics Education.
    • Abrahamson, D., Lee, R. G., Negrete, A. G., & Gutiérrez, J. F. (submitted). Coordinating visualizations of polysemous action: Values added for grounding proportion. In F. Rivera, H. Steinbring, & A. Arcavi (Eds.), Visualization as an epistemological learning tool [Special issue]. ZDM: The International Journal on Mathematics Education.
    • Visualization as an Epistemological Learning Tool [Special issue]
    • Abrahamson, D.1    Lee, R.G.2    Negrete, A.G.3    Gutiérrez, J.F.4
  • 5
    • 79960279845 scopus 로고    scopus 로고
    • Toward an embodied-interaction design framework for mathematical concepts
    • In P. Blikstein & P. Marshall (Eds.), (Vol. ''Full papers''). Ann Arbor, MI: IDC.
    • Abrahamson, D., & Trninic, D. (2011). Toward an embodied-interaction design framework for mathematical concepts. In P. Blikstein & P. Marshall (Eds.), Proceedings of the 10th annual interaction design and children conference (IDC 2011) (Vol. ''Full papers'', pp. 1-10). Ann Arbor, MI: IDC.
    • (2011) Proceedings of the 10th Annual Interaction Design and Children Conference (IDC 2011) , pp. 1-10
    • Abrahamson, D.1    Trninic, D.2
  • 7
    • 34047229672 scopus 로고    scopus 로고
    • Learning axes and bridging tools in a technology-based design for statistics
    • DOI 10.1007/s10758-007-9110-6
    • Abrahamson, D., & Wilensky, U. (2007). Learning axes and bridging tools in a technology-based design for statistics. International Journal of Computers for Mathematical Learning, 12(1), 23-55. (Pubitemid 46543641)
    • (2007) International Journal of Computers for Mathematical Learning , vol.12 , Issue.1 , pp. 23-55
    • Abrahamson, D.1    Wilensky, U.2
  • 8
    • 33745947524 scopus 로고    scopus 로고
    • I see what you are saying: Action as cognition in fMRI brain mapping practice
    • Alač, M., & Hutchins, E. (2004). I see what you are saying: Action as cognition in fMRI brain mapping practice. Journal of Cognition and Culture, 4(3), 629-661.
    • (2004) Journal of Cognition and Culture , vol.4 , Issue.3 , pp. 629-661
    • Alač, M.1    Hutchins, E.2
  • 9
    • 59649092532 scopus 로고    scopus 로고
    • What the body knows: Exploring the benefits of embodied metaphors in hybrid physical digital environments
    • In Ramduny-Ellis D.,Dix A J Gill S & Hare, J (Eds)
    • Antle, A. N., Corness, G., & Droumeva, M. (2009). What the body knows: Exploring the benefits of embodied metaphors in hybrid physical digital environments. In Ramduny-Ellis, D., Dix, A. J., Gill, S., & Hare, J. (Eds.), Physicality and interaction [Special issue]. Interacting with Computers, 21(1&2), 66-75.
    • (2009) Physicality and interaction [SPECial issue] Interacting with Computers , vol.21 , Issue.1-2 , pp. 66-75
    • Antle, A.N.1    Corness, G.2    Droumeva, M.3
  • 11
    • 28244496622 scopus 로고    scopus 로고
    • Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students' learning about statistical distribution
    • DOI 10.1007/s10649-005-5536-8
    • Bakker, A., & Hoffmann, M. H. G. (2005). Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students' learning about statistical distribution. Educational Studies in Mathematics, 60(3), 333-358. (Pubitemid 41699760)
    • (2005) Educational Studies in Mathematics , vol.60 , Issue.3 , pp. 333-358
    • Bakker, A.1    Hoffmann, M.H.G.2
  • 12
    • 54049084937 scopus 로고    scopus 로고
    • Content knowledge for teaching: What makes it special?
    • Ball, D. L., Thames, M. H., & 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.L.1    Thames, M.H.2    Phelps, G.3
  • 13
    • 3042545380 scopus 로고    scopus 로고
    • Action knowledge and symbolic knowledge: The computer as mediator
    • In D. Schön, B. Sanyal & W. Mitchell (Eds.), Cambridge, MA: MIT Press.
    • Bamberger, J. (1999). Action knowledge and symbolic knowledge: The computer as mediator. In D. Schön, B. Sanyal, & W. Mitchell (Eds.), High technology and low Income communities (pp. 235-262). Cambridge, MA: MIT Press.
    • (1999) High Technology and Low Income Communities , pp. 235-262
    • Bamberger, J.1
  • 14
    • 79957871137 scopus 로고    scopus 로고
    • Grounded cognition: Past, present, and future
    • Barsalou, L. W. (2010). Grounded cognition: past, present, and future. Topics in Cognitive Science, 2(4), 716-724.
    • (2010) Topics in Cognitive Science , vol.2 , Issue.4 , pp. 716-724
    • Barsalou, L.W.1
  • 18
    • 0009267184 scopus 로고
    • Empirical research in understanding probability
    • In R. Kapadia & M. Borovcnik (Eds.), Dordrecht: Kluwer
    • Borovcnik, M., & Bentz, H. -J. (1991). Empirical research in understanding probability. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 73-105). Dordrecht: Kluwer.
    • (1991) Chance Encounters: Probability in Education , pp. 73-105
    • Borovcnik, M.1    Bentz, H.-J.2
  • 19
    • 50949113926 scopus 로고    scopus 로고
    • Embodied semiotic activities and their role in the construction of mathematical meaning of motion graphs
    • Botzer, G., & Yerushalmy, M. (2008). Embodied semiotic activities and their role in the construction of mathematical meaning of motion graphs. International Journal of Computers for Mathematical Learning, 13(2), 111-134.
    • (2008) International Journal of Computers for Mathematical Learning , vol.13 , Issue.2 , pp. 111-134
    • Botzer, G.1    Yerushalmy, M.2
  • 20
    • 0003599607 scopus 로고    scopus 로고
    • (N. Balacheff, M. Cooper, R. Sutherland & V. Warfield, Trans.). Boston: Kluwer Academic Publishers
    • Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland & V. Warfield, Trans.). Boston: Kluwer Academic Publishers.
    • (1997) Theory of Didactical Situations in Mathematics
    • Brousseau, G.1
  • 21
    • 84963164715 scopus 로고
    • Epistemic forms and epistemic games: Structures and strategies to guide inquiry
    • Collins, A., & Ferguson, W. (1993). Epistemic forms and epistemic games: Structures and strategies to guide inquiry. Educational Psychologist, 28(1), 25-42.
    • (1993) Educational Psychologist , vol.28 , Issue.1 , pp. 25-42
    • Collins, A.1    Ferguson, W.2
  • 22
    • 0010191570 scopus 로고
    • An example of the passage from the concrete to the manipulation of formal systems
    • Diénès, Z. P. (1971). An example of the passage from the concrete to the manipulation of formal systems. Educational Studies in Mathematics, 3(3/4), 337-352.
    • (1971) Educational Studies in Mathematics , vol.3 , Issue.3-4 , pp. 337-352
    • Diénès, Z.P.1
  • 24
    • 38349071548 scopus 로고    scopus 로고
    • An interactional analysis of clinical interviewing
    • DiSessa, A. A. (2007). An interactional analysis of clinical interviewing. Cognition and Instruction, 25(4), 523-565.
    • (2007) Cognition and Instruction , vol.25 , Issue.4 , pp. 523-565
    • DiSessa, A.A.1
  • 27
    • 39149117510 scopus 로고    scopus 로고
    • Making authentic practices accessible to learners: Design challenges and strategies
    • In R. K. Sawyer (Ed.), Cambridge, MA: Cambridge University Press.
    • Edelson, D. C., & Reiser, B. J. (2006). Making authentic practices accessible to learners: Design challenges and strategies. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 335-354). Cambridge, MA: Cambridge University Press.
    • (2006) The Cambridge Handbook of the Learning Sciences , pp. 335-354
    • Edelson, D.C.1    Reiser, B.J.2
  • 29
    • 84860850451 scopus 로고    scopus 로고
    • Productive ambiguity in the learning of mathematics
    • Foster, C. (2011). Productive ambiguity in the learning of mathematics. For the Learning of Mathematics, 31(2), 3-7.
    • (2011) For the Learning of Mathematics , vol.31 , Issue.2 , pp. 3-7
    • Foster, C.1
  • 30
    • 3843077902 scopus 로고
    • Geometry between the devil and the deep sea
    • Freudenthal, H. (1971). Geometry between the devil and the deep sea. Educational Studies in Mathematics, 3(3/4), 413-435.
    • (1971) Educational Studies in Mathematics , vol.3 , Issue.3-4 , pp. 413-435
    • Freudenthal, H.1
  • 32
    • 0042370556 scopus 로고    scopus 로고
    • (W. N. Hailmann, Trans.). New York: Dover Publications. (Original work published 1885).
    • Froebel, F. (2005). The education of man (W. N. Hailmann, Trans.). New York: Dover Publications. (Original work published 1885).
    • (2005) The Education of Man
    • Froebel, F.1
  • 33
    • 84867732300 scopus 로고    scopus 로고
    • The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters
    • in press, doi: 10.1037/a0028389.
    • Fyfe, E. R., Rittle-Johnson, B., & DeCaro, M. S. (in press). The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters. Journal of Educational Psychology. doi: 10.1037/a0028389.
    • Journal of Educational Psychology.
    • Fyfe, E.R.1    Rittle-Johnson, B.2    DeCaro, M.S.3
  • 34
    • 84892673523 scopus 로고    scopus 로고
    • Seeing the graph vs. Being the graph: Gesture, engagement and awareness in school mathematics
    • In G. Stam & M. Ishino (Eds.), Amsterdam: John Benjamins.
    • Gerofsky, S. (2011). Seeing the graph vs. being the graph: Gesture, engagement and awareness in school mathematics. In G. Stam & M. Ishino (Eds.), Integrating gestures (pp. 245-256). Amsterdam: John Benjamins.
    • (2011) Integrating Gestures , pp. 245-256
    • Gerofsky, S.1
  • 36
    • 46349101245 scopus 로고    scopus 로고
    • What is teaching mathematics to young children? A theoretical perspective and case study
    • Ginsburg, H. P., & Amit, M. (2008). What is teaching mathematics to young children? A theoretical perspective and case study. Journal of Applied Developmental Psychology, 29, 274-285.
    • (2008) Journal of Applied Developmental Psychology , vol.29 , pp. 274-285
    • Ginsburg, H.P.1    Amit, M.2
  • 38
    • 0001893583 scopus 로고
    • Levels of language in mathematical problem solving
    • In C. Janvier (Ed.), Hillsdale, NJ: Lawrence Erlbaum Associates.
    • Goldin, G. A. (1987). Levels of language in mathematical problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 59-65). Hillsdale, NJ: Lawrence Erlbaum Associates.
    • (1987) Problems of Representation in the Teaching and Learning of Mathematics , pp. 59-65
    • Goldin, G.A.1
  • 39
    • 3843071396 scopus 로고    scopus 로고
    • A scientific perspective on structured, task-based interviews in mathematics education research
    • In A. E. Kelly & R. A. Lesh (Eds.), Mahwah, NJ: Lawrence Erlbaum Associates.
    • Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517-545). Mahwah, NJ: Lawrence Erlbaum Associates.
    • (2000) Handbook of Research Design in Mathematics and Science Education , pp. 517-545
    • Goldin, G.A.1
  • 40
    • 84981922507 scopus 로고
    • Professional vision
    • Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 603-633.
    • (1994) American Anthropologist , vol.96 , Issue.3 , pp. 603-633
    • Goodwin, C.1
  • 42
  • 43
    • 51249181946 scopus 로고
    • Epistemological and methodological bases of naturalistic inquiry
    • Guba, E. G., & Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Technology Research and Development, 30(4), 233-252.
    • (1982) Educational Technology Research and Development , vol.30 , Issue.4 , pp. 233-252
    • Guba, E.G.1    Lincoln, Y.S.2
  • 45
    • 0002441829 scopus 로고    scopus 로고
    • Competing paradigms in qualitative research
    • In N. Denzin & Y. Lincoln (Eds.),Thousand Oaks, CA: SAGE.
    • Guba, E. G., & Lincoln, Y. S. (1998). Competing paradigms in qualitative research. In N. Denzin & Y. Lincoln (Eds.), The landscape of qualitative research: Theories and issues (pp. 195-220). Thousand Oaks, CA: SAGE.
    • (1998) The Landscape of Qualitative Research: Theories and Issues , pp. 195-220
    • Guba, E.G.1    Lincoln, Y.S.2
  • 47
    • 0000902482 scopus 로고
    • History and significance of the emic/etic distinction
    • Harris, M. (1976). History and significance of the emic/etic distinction. Annual Review of Anthropology, 5, 329-350.
    • (1976) Annual Review of Anthropology , vol.5 , pp. 329-350
    • Harris, M.1
  • 48
    • 84859266349 scopus 로고    scopus 로고
    • Identity struggles in the mathematics classroom: On learning mathematics as an interplay of mathematizing and identifying
    • doi:10.1016/j.ijer.2011.12.015 128-145
    • Heyd-Metzuyanim, E., & Sfard, A. (2012). Identity struggles in the mathematics classroom: on learning mathematics as an interplay of mathematizing and identifying. International Journal of Educational Research, 51-52, 128-145. doi:10.1016/j.ijer.2011.12.015.
    • (2012) International Journal of Educational Research , pp. 51-52
    • Heyd-Metzuyanim, E.1    Sfard, A.2
  • 54
    • 84986846070 scopus 로고
    • The child is a theoretician, not an inductivist
    • Karmiloff-Smith, A. (1988). The child is a theoretician, not an inductivist. Mind & Language, 3(3), 183-195.
    • (1988) Mind & Language , vol.3 , Issue.3 , pp. 183-195
    • Karmiloff-Smith, A.1
  • 55
    • 0001921677 scopus 로고
    • Proportional reasoning of early adolescents
    • In R. Lesh & M. Landau (Eds.), New York: Academic Press.
    • Karplus, R., Pulos, S., & Stage, E. K. (1983). Proportional reasoning of early adolescents. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 45-89). New York: Academic Press.
    • (1983) Acquisition of Mathematics Concepts and Processes , pp. 45-89
    • Karplus, R.1    Pulos, S.2    Stage, E.K.3
  • 56
    • 0030298913 scopus 로고    scopus 로고
    • Adapting the environment instead of oneself
    • Kirsh, D. (1996). Adapting the environment instead of oneself. Adaptive Behavior, 4(3-4), 415-452.
    • (1996) Adaptive Behavior , vol.4 , Issue.3-4 , pp. 415-452
    • Kirsh, D.1
  • 57
    • 0000128591 scopus 로고
    • On distinguishing epistemic from pragmatic action
    • Kirsh, D., & Maglio, P. (1994). On distinguishing epistemic from pragmatic action. Cognitive Science, 18(4), 513-549.
    • (1994) Cognitive Science , vol.18 , Issue.4 , pp. 513-549
    • Kirsh, D.1    Maglio, P.2
  • 59
    • 54949096914 scopus 로고    scopus 로고
    • Rational numbers and proportional reasoning: Toward a theoretical framework for research
    • In F. K. Lester (Ed.), Charlotte, NC: Information Age Publishing.
    • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). Charlotte, NC: Information Age Publishing
    • (2007) Second Handbook of Research on Mathematics Teaching and Learning , pp. 629-667
    • Lamon, S.J.1
  • 60
    • 0002259262 scopus 로고
    • When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching
    • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29-63.
    • (1990) American Educational Research Journal , vol.27 , Issue.1 , pp. 29-63
    • Lampert, M.1
  • 62
    • 85071534621 scopus 로고    scopus 로고
    • Multiplying meaning: Visual and verbal semiotics in scientific text
    • In J. R. Martin & R. Veel (Eds.), London: Routledge.
    • Lemke, J. L. (1998). Multiplying meaning: Visual and verbal semiotics in scientific text. In J. R. Martin & R. Veel (Eds.), Reading science: Critical and functional perspectives on discourses of science (pp. 87-113). London: Routledge.
    • (1998) Reading Science: Critical and Functional Perspectives on Discourses of Science , pp. 87-113
    • Lemke, J.L.1
  • 63
    • 34247213413 scopus 로고    scopus 로고
    • Mathematics in the middle: Measure, picture, gesture, sign, and word
    • In M. Anderson, A. Sa'enz-Ludlow, S. Zellweger, & V. V. Cifarelli (Eds.), Ottawa: Legas.
    • Lemke, J. L. (2003). Mathematics in the middle: Measure, picture, gesture, sign, and word. In M. Anderson, A. Sa'enz-Ludlow, S. Zellweger, & V. V. Cifarelli (Eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 215-234). Ottawa: Legas.
    • (2003) Educational Perspectives on Mathematics as Semiosis: From thinking to interpreting to knowing , pp. 215-234
    • Lemke, J.L.1
  • 64
    • 84892672672 scopus 로고    scopus 로고
    • Polysemy of symbols: Signs of ambiguity
    • Mamolo, A. (2010). Polysemy of symbols: Signs of ambiguity. The Montana Mathematics Enthusiast, 7(2&3), 247-261.
    • (2010) The Montana Mathematics Enthusiast , vol.7 , Issue.2-3 , pp. 247-261
    • Mamolo, A.1
  • 65
    • 84855928296 scopus 로고    scopus 로고
    • Artifacts and signs after a Vygotskian perspective: The role of the teacher. ZDM: The international journal on
    • Mariotti, M. A. (2009). Artifacts and signs after a Vygotskian perspective: The role of the teacher. ZDM: The international Journal on. Mathematics Education, 41, 427-440.
    • (2009) Mathematics Education , vol.41 , pp. 427-440
    • Mariotti, M.A.1
  • 67
    • 24044524220 scopus 로고    scopus 로고
    • Physically distributed learning: Adapting and reinterpreting physical environments in the development of fraction concepts
    • DOI 10.1207/s15516709cog0000-15
    • Martin, T., & Schwartz, D. L. (2005). Physically distributed learning: Adapting and reinterpreting physical environments in the development of fraction concepts. Cognitive Science, 29(4), 587-625. (Pubitemid 41223556)
    • (2005) Cognitive Science , vol.29 , Issue.4 , pp. 587-625
    • Martin, T.1    Schwartz, D.L.2
  • 68
    • 67349197876 scopus 로고    scopus 로고
    • Three conjectures concerning the relationship between body activity and understanding mathematics
    • In R. Nemirovsky & M. Borba (Coordinators), Perceptuo-motor activity and imagination in mathematics learning (Research Forum). In N. A. Pateman, B. J. Dougherty & J. T. Zilliox (Eds.), Honolulu, Hawaii: Columbus, OH: Eric Clearinghouse for Science, Mathematics, and Environmental Education.
    • Nemirovsky, R. (2003). Three conjectures concerning the relationship between body activity and understanding mathematics. In R. Nemirovsky & M. Borba (Coordinators), Perceptuo-motor activity and imagination in mathematics learning (Research Forum). In N. A. Pateman, B. J. Dougherty & J. T. Zilliox (Eds.), Proceedings of the twenty seventh annual meeting of the international group for the psychology of mathematics education (Vol. 1, pp. 105-109). Honolulu, Hawaii: Columbus, OH: Eric Clearinghouse for Science, Mathematics, and Environmental Education.
    • (2003) Proceedings of the Twenty Seventh Annual Meeting of the International Group for the Psychology of Mathematics Education , vol.1 , pp. 105-109
    • Nemirovsky, R.1
  • 70
    • 33846571511 scopus 로고    scopus 로고
    • The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic
    • DOI 10.1023/A:1002943821419, Computational Environments in Mathematics Education
    • Noss, R., Healy, L., & Hoyles, C. (1997). The construction of mathematical meanings: Connecting the visual with the symbolic. Educational Studies in Mathematics, 33(2), 203-233. (Pubitemid 127095610)
    • (1997) Educational studies in mathematics , vol.33 , Issue.2 , pp. 203-233
    • Noss, R.1    Healy, L.2    Hoyles, C.3
  • 72
    • 23144461481 scopus 로고    scopus 로고
    • Embodied cognition as grounding for situatedness and context in mathematics education
    • Núñez, R. E., Edwards, L. D., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39, 45-65.
    • (1999) Educational Studies in Mathematics , vol.39 , pp. 45-65
    • Núñez, R.E.1    Edwards, L.D.2    Matos, J.F.3
  • 75
    • 0010690055 scopus 로고
    • Growth in mathematical understanding: How can we characterize it and how can we represent it?
    • Pirie, S. E. B., & Kieren, T. E. (1994). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in Mathematics, 26, 165-190.
    • (1994) Educational Studies in Mathematics , vol.26 , pp. 165-190
    • Pirie, S.E.B.1    Kieren, T.E.2
  • 78
    • 27944486500 scopus 로고    scopus 로고
    • The seen, the spoken, and the written: A semiotic approach to the problem of objectification of mathematical knowledge
    • Radford, L. (2002). The seen, the spoken, and the written: A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14-23.
    • (2002) For the Learning of Mathematics , vol.22 , Issue.2 , pp. 14-23
    • Radford, L.1
  • 79
    • 29144470673 scopus 로고    scopus 로고
    • Gestures, speech, and the sprouting of signs: a semiotic-cultural approach to students' types of generalization
    • Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization. Mathematical Thinking and Learning, 5(1), 37-70. (Pubitemid 36116844)
    • (2003) Mathematical Thinking And Learning , vol.5 , Issue.1 , pp. 37-70
    • Radford, L.1
  • 80
    • 84859269152 scopus 로고    scopus 로고
    • The eye as a theoretician: Seeing structures in generalizing activities
    • Radford, L. (2010). The eye as a theoretician: Seeing structures in generalizing activities. For the Learning of Mathematics, 30(2), 2-7.
    • (2010) For the Learning of Mathematics , vol.30 , Issue.2 , pp. 2-7
    • Radford, L.1
  • 82
    • 4043178469 scopus 로고    scopus 로고
    • Scaffolding complex learning: The mechanisms of structuring and problematizing student work
    • Scaffolding
    • Reiser, B. J. (2004). Scaffolding complex learning: The mechanisms of structuring and problematizing student work. Journal of the Learning Sciences, 13(3), 273-304. (Pubitemid 39063558)
    • (2004) Journal of the Learning Sciences , vol.13 , Issue.3 , pp. 273-304
    • Reiser, B.J.1
  • 84
    • 3843150847 scopus 로고    scopus 로고
    • Pronouns in mathematics talk: Power, vagueness and generalisation
    • Rowland, T. (1999). Pronouns in mathematics talk: Power, vagueness and generalisation. For the Learning of Mathematics, 19(2), 19-26.
    • (1999) For the Learning of Mathematics , vol.19 , Issue.2 , pp. 19-26
    • Rowland, T.1
  • 85
    • 84973740928 scopus 로고
    • Partners in cognition: Extending human intelligences with intelligent technologies
    • Salomon, G., Perkins, D. N., & Globerson, T. (1991). Partners in cognition: Extending human intelligences with intelligent technologies. Educational Researcher, 20(3), 2-9.
    • (1991) Educational Researcher , vol.20 , Issue.3 , pp. 2-9
    • Salomon, G.1    Perkins, D.N.2    Globerson, T.3
  • 86
    • 63849214661 scopus 로고    scopus 로고
    • Practices of quantification from a sociocultural perspective
    • In K. A. Demetriou & A. Raftopoulos (Eds.), NY: Cambridge University Press.
    • Saxe, G. B. (2004). Practices of quantification from a sociocultural perspective. In K. A. Demetriou & A. Raftopoulos (Eds.), Developmental change: Theories, models, and measurement (pp. 241-263). NY: Cambridge University Press.
    • (2004) Developmental Change: Theories, Models, and Measurement , pp. 241-263
    • Saxe, G.B.1
  • 87
    • 0030496487 scopus 로고    scopus 로고
    • Confirming allusions: Toward an empirical account of action
    • Schegloff, E. A. (1996). Confirming allusions: Toward an empirical account of action. The American Journal of Sociology, 102(1), 161-216.
    • (1996) The American Journal of Sociology , vol.102 , Issue.1 , pp. 161-216
    • Schegloff, E.A.1
  • 88
    • 85121571296 scopus 로고
    • Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain
    • In R. Glaser (Ed.), Hillsdale, NJ: Erlbaum.
    • Schoenfeld, A. H., Smith, J. P., & Arcavi, A. (1991). Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in instructional psychology (pp. 55-175). Hillsdale, NJ: Erlbaum.
    • (1991) Advances in Instructional Psychology , pp. 55-175
    • Schoenfeld, A.H.1    Smith, J.P.2    Arcavi, A.3
  • 89
    • 68749090151 scopus 로고    scopus 로고
    • Prediction in joint action: What, when, and where
    • Sebanz, N., & Knoblich, G. (2009). Prediction in joint action: What, when, and where. Topics in Cognitive Science, 1(2), 353-367.
    • (2009) Topics in Cognitive Science , vol.1 , Issue.2 , pp. 353-367
    • Sebanz, N.1    Knoblich, G.2
  • 91
    • 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
  • 92
    • 84892668927 scopus 로고
    • The silent music of mathematics
    • Skemp, R. R. (1983). The silent music of mathematics. Mathematics Teaching, 102(58), 287-288.
    • (1983) Mathematics Teaching , vol.102 , Issue.58 , pp. 287-288
    • Skemp, R.R.1
  • 95
    • 84858405076 scopus 로고
    • Misconceptions reconceived: A constructivist analysis of knowledge in transition
    • Smith, J. P., diSessa, A. A., & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. Journal of the Learning Sciences, 3(2), 115-163.
    • (1993) Journal of the Learning Sciences , vol.3 , Issue.2 , pp. 115-163
    • Smith, J.P.1    DiSessa, A.A.2    Roschelle, J.3
  • 96
    • 33646690598 scopus 로고    scopus 로고
    • Commentary: Sociocultural activity as a unit of analysis: How Vygotsky and Piaget converge in empirical research on collaborative cognition
    • In D. J. Bearison & B. Dorval (Eds.), Westport, CN: Ablex Publishing.
    • Stetsenko, A. (2002). Commentary: Sociocultural activity as a unit of analysis: How Vygotsky and Piaget converge in empirical research on collaborative cognition. In D. J. Bearison & B. Dorval (Eds.), Collaborative cognition: Children negotiating ways of knowing (pp. 123-135). Westport, CN: Ablex Publishing.
    • (2002) Collaborative Cognition: Children Negotiating Ways of Knowing , pp. 123-135
    • Stetsenko, A.1
  • 97
    • 0037548823 scopus 로고    scopus 로고
    • Disciplined perception: Learning to see in technoscience
    • In M. Lampert & M. L. Blunk (Eds.), New York: 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: Cambridge University Press.
    • (1998) Talking Mathematics in School: Studies of Teaching and Learning , pp. 107-149
    • Stevens, R.1    Hall, R.2
  • 99
    • 84862614483 scopus 로고    scopus 로고
    • Learning trajectory based instruction
    • doi:10.3102/0013189x12442801.
    • Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction. Educational Researcher, 41(5), 147-156. doi:10.3102/0013189x12442801.
    • (2012) Educational Researcher , vol.41 , Issue.5 , pp. 147-156
    • Sztajn, P.1    Confrey, J.2    Wilson, P.H.3    Edgington, C.4
  • 101
    • 84892669044 scopus 로고    scopus 로고
    • Embodied interaction as designed mediation of conceptual performance
    • in press, In D. Martinovic & V. Freiman (Eds.)
    • Trninic, D., & Abrahamson, D. (in press). Embodied interaction as designed mediation of conceptual performance. In D. Martinovic & V. Freiman (Eds.), Visual mathematics and cyberlearning
    • Visual mathematics and cyberlearning
    • Trninic, D.1    Abrahamson, D.2
  • 102
    • 21844487017 scopus 로고
    • Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity
    • Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77-101.
    • (1995) European Journal of Psychology of Education , vol.10 , Issue.1 , pp. 77-101
    • Vérillon, P.1    Rabardel, P.2
  • 103
    • 84892670392 scopus 로고    scopus 로고
    • (submitted)., (Manuscript submitted toward presentation at the annual meeting of the American Educational Research Association, San Francisco
    • Waismeyer, B. C., & Abrahamson, D. (submitted). Quantitative analysis of tutorial tactics for embodied interaction, (Manuscript submitted toward presentation at the annual meeting of the American Educational Research Association, San Francisco, 2013).
    • (2013) Quantitative Analysis of Tutorial Tactics for Embodied Interaction
    • Waismeyer, B.C.1    Abrahamson, D.2
  • 104
    • 42149091864 scopus 로고    scopus 로고
    • Debugging an artifact, instrumenting a bug: Dialectics of instrumentation and design in technology-rich learning environments
    • DOI 10.1007/s10758-007-9119-x
    • White, T. (2008). Debugging an artifact, instrumenting a bug: Dialectics of instrumentation and design in technology-rich learning environments. International Journal of Computers for Mathematical Learning, 13(1), 1-26. (Pubitemid 351543655)
    • (2008) International Journal of Computers for Mathematical Learning , vol.13 , Issue.1 , pp. 1-26
    • White, T.1
  • 105
    • 0002614978 scopus 로고
    • Representations in distributed cognitive tasks
    • Zhang, J., & Norman, D. A. (1994). Representations in distributed cognitive tasks. Cognitive Science, 18, 87-122.
    • (1994) Cognitive Science , vol.18 , pp. 87-122
    • Zhang, J.1    Norman, D.A.2
  • 106
    • 33749608088 scopus 로고    scopus 로고
    • Distributed cognition, representation, and affordance
    • DOI 10.1075/pc.14.2.12zha
    • Zhang, J., & Patel, V. L. (2006). Distributed cognition, representation, and affordance. In Harnad, S., & Dror, I. E. (Eds.), Distributed cognition [Special issue]. Pragmatics & Cognition, 14(2), 333-341. (Pubitemid 44541570)
    • (2006) Pragmatics and Cognition , vol.14 , Issue.2 , pp. 333-341
    • Zhang, J.1    Patel, V.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.