Abstract
Research on graphing presents its results as if knowing and understanding were something stored in peoples' minds independent of the situation that they find themselves in. Thus, there are no models that situate interview responses to graphing tasks. How, then, we question, are the interview texts produced? How do respondents begin and end utterances? And, what is the relation between words and gestures used as part of the communication? Based on a database developed in two studies with research scientists (N = 37), we developed a theoretical framework using cultural-historical activity theory for understanding the texts produced during interviews. Our framework addresses three major findings, whose implications are discussed in the paper. First, the interview text is the contingent and situated product of the entire activity system, including interviewer and other aspects of the setting; the interview text can therefore not be reduced to the cognitive properties of the individual interviewee. Second, the interpretation unfolds in time, shaping the way the graph itself is perceived; unlike a written text that accompanies a graph, the verbally produced interview text therefore has to be analyzed through a moving interpretive window without recourse to subsequently produced talk. Third, gestures, speech, and the perceptual aspects of the graph currently salient to the interviewee, have to be understood as expressions that are irreducible to one another, requiring comprehensive research reports to present all modes of concurrent expression.
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REFERENCES
Bakhtin, M.M.: 1993, Toward a Philosophy of the Act, University of Texas Press, Austin.
Berg, C.A. and Phillips, D.G.: 1994, ‘An investigation of the relationship between logical thinking structures and the ability to construct and interpret line graphs’ Journal of Research in Science Teaching 31, 323–344.
Boden, D.: 1994, The Business of Talk: Organization in Action, Polity Press, Cambridge.
Clement, J.: 1989, ‘The concept of variation and misconceptions in Cartesian graphing’ Focus on Learning Problems in Mathematics 11, 77–87.
Eco, U.: 1984, Semiotics and the Philosophy of Language, Indiana University Press, Bloomington.
Edgerton, S.: 1985, ‘The renaissance development of the scientific illustration’ in J. Shirley and D. Hoeniger (eds.), Science and the Arts in the Renaissance, Folger Shakespeare Library, Washington, DC, pp. 168–197.
Edwards, D. and Potter, J.: 1992, Discursive Psychology, Sage, London.
Engeström, Y.: 1987, Learning by Expanding: An Activity-Theoretical Approach to Developmental Research, Orienta-Konsultit, Helsinki, Finland.
Garfinkel, H.: 1991, ‘Respecification: Evidence for locally produced naturally accountable phenomena of order*, logic, reason, meaning, method, etc. in an as of the essential haec-ceity of immortal ordinary society. (I) – An announcement of studies’ in G. Button (ed.), Ethnomethodology and the Human Sciences, Cambridge University Press, Cambridge, England, pp. 10–19.
Goldin-Meadow, S.: 1997, ‘When gestures and words speak differently’ Current Directions in Psychological Science 6, 138–143.
Greeno, J.G.: 1989, ‘Situations, mental models, and generative knowledge’ in D. Klahr and K. Kotovsky (eds.), Complex Information Processing, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 285–318.
Hegel, G.W.F.: 1977, Phenomenology of the Spirit, in A.V. Miller (Trans.), Oxford University Press, Oxford.
Hershkowitz, R., Schwarz, B.B. and Dreyfus, T.: 2001, ‘Abstraction in context: Epistemic actions’ Journal for Research in Mathematics Education 32, 195–222.
Il'enkov, E.: 1977, Dialectical Logic: Essays in its History and Theory, in H.C. Creighton (Trans.), Progress, Moscow.
Il'enkov, E.: 1982, Dialectics of the Abstract and the Concrete in Marx's Capital, in Sergei Kuzyakov (Trans.), Progress, Moskow.
Janvier, C.: 1987, ‘Translation processes in mathematics education’ in C. Janvier (ed.), Problems of Representation in the Teaching and Learning of Mathematics, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 27–32.
Jordan, B. and Henderson, A.: 1995, ‘Interaction analysis: Foundations and practice’ Journal of the Learning Sciences 4, 39–103.
Kingsland, S.E.: 1995, Modeling Nature: Episodes in the History of Population Ecology (2nd ed.), University of Chicago Press, Chicago.
Latour, B.: 1987, Science in Action: Howto Follow Scientists and Engineers through Society, Open University Press, Milton Keynes, England.
Lave, J.: 1988, Cognition in Practice: Mind, Mathematics and Culture in Everyday Life, Cambridge University Press, Cambridge, England.
Lave, J., Murtaugh, M. and de la Rocha, O.: 1984, ‘The dialectic of arithmetic in grocery shopping’ in B. Rogoff and J. Lave (eds.), Everyday Cognition: Its Development in Social Context, Harvard University Press, Cambridge, MA, pp. 67–94.
Leinhardt, G., Zaslavsky, O. and Stein, M.K.: 1990, ‘Functions, graphs, and graphing: Tasks, learning, and teaching’ Review of Educational Research 60, 1–64.
Lektorsky, V.A.: 1977, ‘The dialectic of subject and object and some problems of the methodology of science’ in Philosophy in the USSR: Problems of Dialectical Materialism, Moscow, pp. 100–112.
Lemke, J.L.: 1998, ‘Multiplying meaning: Visual and verbal semiotics in scientific text’ in J. R. Martin and R. Veel (eds.), Reading Science, Routledge, London, pp. 87–113.
Leont'ev, A.N.: 1978, Activity, Consciousness and Personality, Prentice-Hall, Englewood Cliffs, NJ.
Lynch, M.: 1991, ‘Method: measurement – Ordinary and scientific measurement as eth-nomethodological phenomena’ in G. Button (ed.), Ethnomethodology and the Human Sciences, Cambridge University Press, Cambridge, England, pp. 77–108.
Marx, K.: 1991, Das Kapital: Kritik der politischen Ökonomie, Erster Band, 1890, Akademie Verlag, Berlin.
Maynard, D.W. and Schaeffer, N.C.: 2000, ‘Toward a sociology of social scientifie knowledge: Survey research and ethnomethodology's asymmetric alternates’ Social Studies of Science 30, 323–370.
McNeill, D.: 1992, Hand and Mind: What Gestures Reveal about Thought, University of Chicago Press, Chicago.
McNeill, D.: 2002, May 3–5, Gesture and Language Dialectic, Paper presented at the conference of The Multimodality of Human Communication: Theories, Problems and Applications, Toronto, Canada.
Merleau-Ponty, M.: 1945, Phénoménologie de la perception, Gallimard, Paris.
Pinker, S.: 1990, ‘A theory of graph comprehension’ in R. Freedle (ed.), Artificial In-telligence and the Future of Testing, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 73–126.
Ricklefs, R.E.: 1990, Ecology (3rd ed.), Freeman, New York.
Ricoeur, P.: 1985, Time and Narrative (vol. 3), University of Chicago Press, Chicago.
Roth, W.-M.: 2003a, ‘Competent workplace mathematics: How signs become transparent in use’ International Journal of Computers for Mathematical Learning 8, 161–189.
Roth, W.-M.: 2003b, Toward an Anthropology of Graphing, Kluwer Academic Publisher, Dordrecht, The Netherlands.
Roth, W.-M.: in press, ‘Computerized databases and the reflexive elaboration of understanding: A case study of graphing in a fish hatchery’ Mathematical Thinking and Learning.
Roth, W.-M.: 2004, ‘Perceptual gestalts in workplace communication’ Journal of Pragmatics 36, 1037–1069.
Roth, W.-M. and Bowen, G.M.: 2001, ‘Professionals read graphs: A semiotic analysis’ Journal for Research in Mathematics Education 32, 159–194.
Roth, W.-M. and Bowen, G.M.: 2003, ‘When are graphs ten thousand words worth? An expert/expert study’ Cognition and Instruction 21, 429–473.
Roth, W.-M., Bowen, G.M. and McGinn, M.K.: 1999, ‘Differences in graph-related practices between high school biology textbooks and scientific ecology journals’ Journal of Research in Science Teaching 36, 977–1019.
Roth, W.-M. and Lawless, D.: 2002, ‘Signs, deixis, and the emergence of scientific explanation’ Semiotica 138, 95–130.
Saari, E. and Miettinen, R.: 2001, ‘Dynamics of change in research work: Constructing a new research area in a research group’ Science, Technology, & Human Values 26, 300–321.
Suchman, L. and Jordan, B.: 1990, ‘Interactional troubles in face-to-face survey interviews’ Journal of the American Statistical Association 85, 232–253.
Tabachneck-Schijf, H.J.M., Leonardo, A.M. and Simon, H.A.: 1997, ‘CaMeRa: A computational model for multiple representations’ Cognitive Science 21, 305–350.
Walkerdine, V.: 1988, The Mastery of Reason, Routledge, London.
Wheeler, S.C. III.: 1986, ‘Indeterminacy of French interpretation: Derrida and Davidson’ in E. Lepore (ed.), Truth and Interpretation, Blackwell, Oxford, pp. 477–494.
Williams, J.S., Wake, G.D. and Boreham, N.C.: 2001, ‘College mathematics and workplace practice: An activity theory perspective’ Research in Mathematics Education 3, 69–84.
Zaslavsky, O., Sela, H. and Leron, U.: 2002, ‘Being sloppy about slope: The effect of changing the scale’ Educational Studies in Mathematics 49, 119–140.
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Roth, WM., Lee, Y.J. Interpreting unfamiliar graphs: A generative, activity theoretic model. Educational Studies in Mathematics 57, 265–290 (2004). https://doi.org/10.1023/B:EDUC.0000049276.37088.e4
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DOI: https://doi.org/10.1023/B:EDUC.0000049276.37088.e4
