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Volumn 79, Issue 1, 2012, Pages 19-40

From visual reasoning to logical necessity through argumentative design

Author keywords

Argumentation and learning; Argumentation and proof; Socio cognitive conflict

Indexed keywords


EID: 82555189806     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-011-9335-0     Document Type: Article
Times cited : (37)

References (67)
  • 2
    • 77953173242 scopus 로고    scopus 로고
    • Argumentation and explanation in conceptual change: Indications from protocol analyses of peer-to-peer dialogue
    • Asterhan, C. S. C., & Schwarz, B. B. (2009). Argumentation and explanation in conceptual change: Indications from protocol analyses of peer-to-peer dialogue. Cognitive Science, 33, 374-400.
    • (2009) Cognitive Science , vol.33 , pp. 374-400
    • Asterhan, C.S.C.1    Schwarz, B.B.2
  • 5
    • 3943051545 scopus 로고    scopus 로고
    • Computer-mediated argumentative interactions for the co-elaboration of scientific notions
    • J. Andriessen, M. Baker, and D. Suthers (Eds.), Dordrecht: Kluwer Academic
    • Baker, M. (2003). Computer-mediated argumentative interactions for the co-elaboration of scientific notions. In J. Andriessen, M. Baker, & D. Suthers (Eds.), Arguing to learn: Confronting cognitions in computer-supported collaborative learning environments (pp. 47-70). Dordrecht: Kluwer Academic.
    • (2003) Arguing to Learn: Confronting Cognitions in Computer-Supported Collaborative Learning Environments , pp. 47-70
    • Baker, M.1
  • 11
    • 79952619847 scopus 로고    scopus 로고
    • Approaching theorems in grade VIII. Some mental processes underlying producing and proving conjectures, and conditions suitable to enhance them
    • P. Boero (Ed.), Rotterdam: Sense Publishers
    • Boero, P., Garuti, R., & Lemut, E. (2007). Approaching theorems in grade VIII. Some mental processes underlying producing and proving conjectures, and conditions suitable to enhance them. In P. Boero (Ed.), Theorems in schools: From history, epistemology and cognition to classroom practices (pp. 251-266). Rotterdam: Sense Publishers.
    • (2007) Theorems in Schools: From History, Epistemology and Cognition to Classroom Practices , pp. 251-266
    • Boero, P.1    Garuti, R.2    Lemut, E.3
  • 12
    • 0002975998 scopus 로고
    • Guided, cooperative learning and individual knowledge acquisition
    • L. B. Resnick (Ed.), Hillsdale, NJ: Lawrence Erlbaum
    • Brown, A., & Palincsar, A. (1989). Guided, cooperative learning and individual knowledge acquisition. In L. B. Resnick (Ed.), Knowing, learning and instruction: Essays in honor of Robert Glaser (pp. 393-451). Hillsdale, NJ: Lawrence Erlbaum.
    • (1989) Knowing, Learning and Instruction: Essays in Honor of Robert Glaser , pp. 393-451
    • Brown, A.1    Palincsar, A.2
  • 14
    • 0040577762 scopus 로고
    • Self-explanations: How students study and use examples in learning to solve problems
    • Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science, 13, 145-182.
    • (1989) Cognitive Science , vol.13 , pp. 145-182
    • Chi, M.T.H.1    Bassok, M.2    Lewis, M.W.3    Reimann, P.4    Glaser, R.5
  • 17
    • 53249128107 scopus 로고
    • Nonanalytic aspects of mathematics and their implication for research and education
    • Davis, P. J., & Anderson, J. A. (1979). Nonanalytic aspects of mathematics and their implication for research and education. SIAM Review, 21(1), 112-127.
    • (1979) SIAM Review , vol.21 , Issue.1 , pp. 112-127
    • Davis, P.J.1    Anderson, J.A.2
  • 20
    • 0042505472 scopus 로고    scopus 로고
    • Argumentation and conceptualisation in context: A case study on sun shadows in primary school
    • Douek, N. (1999). Argumentation and conceptualisation in context: A case study on sun shadows in primary school. Educational Studies in Mathematics, 39, 89-110.
    • (1999) Educational Studies in Mathematics , vol.39 , pp. 89-110
    • Douek, N.1
  • 21
    • 82555181010 scopus 로고    scopus 로고
    • What counts as proof in the mathematics classroom?
    • M. Kourkoulos, G. Troulis, and C. Tzanakis (Eds.), Rethymnon, Crete: University of Crete
    • Dreyfus, T. (2004). What counts as proof in the mathematics classroom? In M. Kourkoulos, G. Troulis, & C. Tzanakis (Eds.), Proceedings of the 3rd Colloquium on the Didactics of Mathematics (pp. 114-132). Rethymnon, Crete: University of Crete.
    • (2004) Proceedings of the 3rd Colloquium on the Didactics of Mathematics , pp. 114-132
    • Dreyfus, T.1
  • 22
    • 1042300390 scopus 로고    scopus 로고
    • Geometry from a cognitive point of view
    • C. Mammana and V. Villani (Eds.), Dordrecht, The Netherlands: Kluwer Academic
    • Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century. An ICMI Study (pp. 37-62). Dordrecht, The Netherlands: Kluwer Academic.
    • (1998) Perspectives on the Teaching of Geometry for the 21st Century. An ICMI Study , pp. 37-62
    • Duval, R.1
  • 24
    • 33745931843 scopus 로고    scopus 로고
    • Challenging the traditional school approach to theorems: A hypothesis about the cognitive unity of theorems
    • In L. Puig, & A. Gutierrez (Eds.) Valencia: University of Valencia
    • Garuti, R., Boero, P., Lemut, E., & Mariotti, M. A. (1996). Challenging the traditional school approach to theorems: A hypothesis about the cognitive unity of theorems. In L. Puig, & A. Gutierrez (Eds.), Proceedings of 20th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 2, pp. 113-120). Valencia: University of Valencia.
    • (1996) Proceedings of 20th Conference of the International Group for the Psychology of Mathematics Education , vol.2 , pp. 113-120
    • Garuti, R.1    Boero, P.2    Lemut, E.3    Mariotti, M.A.4
  • 26
    • 4544296595 scopus 로고    scopus 로고
    • The role of surprise and uncertainty in promoting the need to prove in computerized environment
    • Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2001). The role of surprise and uncertainty in promoting the need to prove in computerized environment. Educational Studies in Mathematics, 44(1&2), 127-150.
    • (2001) Educational Studies in Mathematics , vol.44 , Issue.1-2 , pp. 127-150
    • Hadas, N.1    Hershkowitz, R.2    Schwarz, B.B.3
  • 28
    • 0002952407 scopus 로고
    • Some pedagogical aspects of proof
    • Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21, 6-13.
    • (1990) Interchange , vol.21 , pp. 6-13
    • Hanna, G.1
  • 31
    • 0039194780 scopus 로고
    • Psychological aspects of learning geometry
    • P. Nesher and J. Kilpatrick (Eds.), Cambridge: Cambridge University Press
    • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 70-95). Cambridge: Cambridge University Press.
    • (1990) Mathematics and Cognition , pp. 70-95
    • Hershkowitz, R.1
  • 32
    • 4244086056 scopus 로고    scopus 로고
    • Space and shape
    • A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, and C. Laborde (Eds.), Dordrecht: Kluwer Academic Press
    • Hershkowitz, R., Parzysz, B., & van Dormolen, J. (1996). Space and shape. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 161-204). Dordrecht: Kluwer Academic Press.
    • (1996) International Handbook of Mathematics Education , pp. 161-204
    • Hershkowitz, R.1    Parzysz, B.2    van Dormolen, J.3
  • 33
    • 0038272764 scopus 로고    scopus 로고
    • Reflective processes in a technology-based mathematics classroom
    • Hershkowitz, R., & Schwarz, B. B. (1999). Reflective processes in a technology-based mathematics classroom. Cognition and Instruction, 17, 66-91.
    • (1999) Cognition and Instruction , vol.17 , pp. 66-91
    • Hershkowitz, R.1    Schwarz, B.B.2
  • 34
    • 0034239516 scopus 로고    scopus 로고
    • Hypothesis-testing in science: Group consensus and acquisition of conceptual and procedural knowledge
    • Howe, C., Toulmie, A., Duchak-Tanner, V., & Rattay, C. (2000). Hypothesis-testing in science: Group consensus and acquisition of conceptual and procedural knowledge. Learning and Instruction, 10, 361-391.
    • (2000) Learning and Instruction , vol.10 , pp. 361-391
    • Howe, C.1    Toulmie, A.2    Duchak-Tanner, V.3    Rattay, C.4
  • 35
    • 34547675801 scopus 로고    scopus 로고
    • Modeling mathematical argumentation: The importance of qualification
    • Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modeling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3-21.
    • (2007) Educational Studies in Mathematics , vol.66 , Issue.1 , pp. 3-21
    • Inglis, M.1    Mejia-Ramos, J.P.2    Simpson, A.3
  • 36
    • 63849164447 scopus 로고    scopus 로고
    • Energizing learning: The instructional power of conflict
    • Johnsson, D. W., & Johnsson, R. T. (2009). Energizing learning: The instructional power of conflict. Educational Research, 38(1), 37-51.
    • (2009) Educational Research , vol.38 , Issue.1 , pp. 37-51
    • Johnsson, D.W.1    Johnsson, R.T.2
  • 37
    • 84953051766 scopus 로고
    • Effects of guided cooperative questioning on children's knowledge construction
    • King, A., & Rosenshine, B. (1993). Effects of guided cooperative questioning on children's knowledge construction. Journal of Experimental Education, 61(2), 127-148.
    • (1993) Journal of Experimental Education , vol.61 , Issue.2 , pp. 127-148
    • King, A.1    Rosenshine, B.2
  • 39
    • 0008106994 scopus 로고
    • Designing tasks for learning geometry in computer-based environment, the case of Cabri-géomètre
    • L. Burton and B. Jaworski (Eds.), London: Chartwell-Bratt
    • Laborde, C. (1995). Designing tasks for learning geometry in computer-based environment, the case of Cabri-géomètre. In L. Burton & B. Jaworski (Eds.), Technology in mathematics teaching-A bridge between teaching and learning (pp. 35-68). London: Chartwell-Bratt.
    • (1995) Technology in Mathematics Teaching-A Bridge between Teaching and Learning , pp. 35-68
    • Laborde, C.1
  • 40
    • 33645949437 scopus 로고    scopus 로고
    • A case study of different types of arguments emerging from exploration in an interactive computerized environment
    • Lavy, I. (2006). A case study of different types of arguments emerging from exploration in an interactive computerized environment. Journal of Mathematical Behavior, 25, 153-169.
    • (2006) Journal of Mathematical Behavior , vol.25 , pp. 153-169
    • Lavy, I.1
  • 41
    • 0042027462 scopus 로고    scopus 로고
    • On the cognitive conflict as an instructional strategy for conceptual change: A critical appraisal
    • Limón, M. (2001). On the cognitive conflict as an instructional strategy for conceptual change: A critical appraisal. Learning & Instruction, 11, 357-380.
    • (2001) Learning & Instruction , vol.11 , pp. 357-380
    • Limón, M.1
  • 42
    • 8644280954 scopus 로고    scopus 로고
    • Introduction to proof: The mediation of a dynamic software environment
    • Mariotti, M. A. (2001). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1&2), 25-53.
    • (2001) Educational Studies in Mathematics , vol.44 , Issue.1-2 , pp. 25-53
    • Mariotti, M.A.1
  • 43
    • 0000852649 scopus 로고    scopus 로고
    • Who reasons well? Two studies of informal reasoning among children of different grade, ability, and knowledge level
    • Means, M. L., & Voss, J. F. (1996). Who reasons well? Two studies of informal reasoning among children of different grade, ability, and knowledge level. Cognition and Instruction, 14, 139-179.
    • (1996) Cognition and Instruction , vol.14 , pp. 139-179
    • Means, M.L.1    Voss, J.F.2
  • 47
    • 84984426468 scopus 로고
    • Socio-cognitive conflict and structure of individual and collective performances
    • Mugny, G., & Doise, W. (1978). Socio-cognitive conflict and structure of individual and collective performances. European Journal of Social Psychology, 8, 181-192.
    • (1978) European Journal of Social Psychology , vol.8 , pp. 181-192
    • Mugny, G.1    Doise, W.2
  • 48
    • 34547676442 scopus 로고    scopus 로고
    • How can the relationship between argumentation and proof be analyzed?
    • Pedemonte, B. (2007). How can the relationship between argumentation and proof be analyzed? Educational Studies in Mathematics, 66, 23-41.
    • (2007) Educational Studies in Mathematics , vol.66 , pp. 23-41
    • Pedemonte, B.1
  • 50
    • 0010424484 scopus 로고    scopus 로고
    • Why do we prove theorems?
    • Rav, Y. (1999). Why do we prove theorems? Philosophia Mathematica, 7, 5-41.
    • (1999) Philosophia Mathematica , vol.7 , pp. 5-41
    • Rav, Y.1
  • 51
    • 84925785842 scopus 로고    scopus 로고
    • Advancing mathematical activity: A practice-oriented view of mathematical thinking
    • Rasmussen, C., Zandieh, M., King, K., & Teppo, A. (2005). Advancing mathematical activity: A practice-oriented view of mathematical thinking. Mathematical Thinking and Learning, 7(1), 51-73.
    • (2005) Mathematical Thinking and Learning , vol.7 , Issue.1 , pp. 51-73
    • Rasmussen, C.1    Zandieh, M.2    King, K.3    Teppo, A.4
  • 52
    • 79960254205 scopus 로고    scopus 로고
    • A methodology for documenting collective activity
    • A. E. Kelly, R. A. Lesh, and J. Y. Baek (Eds.), New York: Routledge
    • Rasmussen, C., & Stephan, M. (2008). A methodology for documenting collective activity. In A. E. Kelly, R. A. Lesh, & J. Y. Baek (Eds.), Handbook of design research methods in education (pp. 195-215). New York: Routledge.
    • (2008) Handbook of Design Research Methods in Education , pp. 195-215
    • Rasmussen, C.1    Stephan, M.2
  • 53
    • 82555168809 scopus 로고    scopus 로고
    • Forms and uses of abduction
    • In M. Mariotti (Ed.)
    • Reid, D. (2003). Forms and uses of abduction. In M. Mariotti (Ed.), Proceedings of the third ESRME conference Bellaria Italy. (www. dm. unipi. it/~didattica/CERME3/proceedings/Groups/TG4/TG4_list. html).
    • (2003) Proceedings of the third ESRME conference Bellaria Italy
    • Reid, D.1
  • 55
    • 0001935817 scopus 로고
    • Observing sociocultural activity on three planes: Participatory appropriation, guided participation and apprenticeship
    • J. W. Wertsch, P. Riodel, and A. Alvarez (Eds.), Cambridge: Cambridge University Press
    • Rogoff, B. (1995). Observing sociocultural activity on three planes: Participatory appropriation, guided participation and apprenticeship. In J. W. Wertsch, P. del Rio, & A. Alvarez (Eds.), Sociocultural studies of mind (pp. 139-164). Cambridge: Cambridge University Press.
    • (1995) Sociocultural Studies of Mind , pp. 139-164
    • Rogoff, B.1
  • 56
    • 84885729612 scopus 로고    scopus 로고
    • Argumentation and learning
    • N. Muller-Mirza and A.-N. Perret-Clermont (Eds.), New York: Springer
    • Schwarz, B. B. (2009). Argumentation and learning. In N. Muller-Mirza & A.-N. Perret-Clermont (Eds.), Argumentation and education: Theoretical foundations and practices (pp. 91-126). New York: Springer.
    • (2009) Argumentation and Education: Theoretical Foundations and Practices , pp. 91-126
    • Schwarz, B.B.1
  • 57
    • 36048936958 scopus 로고    scopus 로고
    • The role of task design and of argumentation in cognitive development during peer interaction. The case of proportional reasoning
    • Schwarz, B. B., & Linchevski, L. (2007). The role of task design and of argumentation in cognitive development during peer interaction. The case of proportional reasoning. Learning and Instruction, 17, 310-331.
    • (2007) Learning and Instruction , vol.17 , pp. 310-331
    • Schwarz, B.B.1    Linchevski, L.2
  • 58
    • 82555181008 scopus 로고    scopus 로고
    • Argumentation and reasoning
    • K. Littleton, C. Wood, and J. Kleine Staarman (Eds.), Bradford: Emerald Group
    • Schwarz, B. B., & Asterhan, C. S. C. (2010). Argumentation and reasoning. In K. Littleton, C. Wood, & J. Kleine Staarman (Eds.), International handbook of psychology in education (pp. 137-176). Bradford: Emerald Group.
    • (2010) International Handbook of Psychology in Education , pp. 137-176
    • Schwarz, B.B.1    Asterhan, C.S.C.2
  • 60
    • 0036457606 scopus 로고    scopus 로고
    • Classroom mathematical practices in differential equations
    • Stephan, M., & Rasmussen, C. (2002). Classroom mathematical practices in differential equations. Journal of Mathematical Behavior, 21, 459-490.
    • (2002) Journal of Mathematical Behavior , vol.21 , pp. 459-490
    • Stephan, M.1    Rasmussen, C.2
  • 61
    • 0004096846 scopus 로고
    • Cambridge: Cambridge University Press
    • Toulmin, S. (1958). The uses of argument. Cambridge: Cambridge University Press.
    • (1958) The Uses of Argument
    • Toulmin, S.1
  • 62
    • 0002381924 scopus 로고
    • The genesis of higher mental functions
    • J. V. Wertsch (Ed.), New York: Sharpe
    • Vygotsky, L. S. (1981). The genesis of higher mental functions. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 144-188). New York: Sharpe.
    • (1981) The Concept of Activity in Soviet Psychology , pp. 144-188
    • Vygotsky, L.S.1
  • 63
    • 63049083406 scopus 로고    scopus 로고
    • The teacher's role in promoting collaborative dialogue in the classroom
    • Webb, N. M. (2009). The teacher's role in promoting collaborative dialogue in the classroom. The British Journal of Educational Psychology, 79, 1-28.
    • (2009) The British Journal of Educational Psychology , vol.79 , pp. 1-28
    • Webb, N.M.1
  • 65
    • 0036459171 scopus 로고    scopus 로고
    • What we can learn from analyzing the teacher's role in collective argumentation
    • Yackel, E. (2002). What we can learn from analyzing the teacher's role in collective argumentation. Journal of Mathematical Behavior, 21, 423-440.
    • (2002) Journal of Mathematical Behavior , vol.21 , pp. 423-440
    • Yackel, E.1
  • 66
    • 0000018415 scopus 로고
    • The Geometric Supposer: Promoting thinking and learning
    • Yerushalmy, M., & Houde, R. A. (1986). The Geometric Supposer: Promoting thinking and learning. Mathematics Teacher, 79, 418-422.
    • (1986) Mathematics Teacher , vol.79 , pp. 418-422
    • Yerushalmy, M.1    Houde, R.A.2
  • 67
    • 0001426740 scopus 로고
    • Theorems for a price: Tomorrow's semi-rigorous mathematical culture
    • Zeilberger, D. (1993). Theorems for a price: Tomorrow's semi-rigorous mathematical culture. Notices of the American Mathematical Society, 40(8), 978-981.
    • (1993) Notices of the American Mathematical Society , vol.40 , Issue.8 , pp. 978-981
    • Zeilberger, D.1


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