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Toward a Dynamic Theory of Graphing

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Book cover Uncertainty and Graphing in Discovery Work
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Abstract

Graphs and graphing are constitutive of the sciences. Although there are an increasing number of studies on graphing, few of these studies focus on graphs and graphing in the discovery sciences, where uncertainty is one of the core characteristics. The discovery sciences allow us to revisit existing psychological theories, which tend to theorize graphing as a mental skill and graphs as external representation. Graphing is bound up with the scientific inquiry as a whole and, therefore, cannot be understood independently of it when we take an cultural-historical activity theoretic stance. This theory was created to take into account the continuously changing nature of human activities. I articulate some categories that reflect this flow. If activity and everything is theorized to be in flow, this has consequences for theorizing everything else as well: graphs, tools, or subjects of activity.

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Notes

  1. 1.

    “At work” should be understood in both of the ways that this expression allows to be heard, that is, at work in the scientific laboratory and graphing doing its part in the overall work of doing scientific research.

  2. 2.

    The name of the model is suggestive of processes, whereby the world comes to be imaged on the retina and in the brain as if these were operating like a camera. Such a view is inconsistent with the fact that all perception involves efferent and afferent dimensions and cannot be understood as a simple, mirror- or camera-like process.

  3. 3.

    Anaerobic organisms do not need oxygen for growth; they may in fact die in the presence of oxygen.

  4. 4.

    There are 50 articles when a Boolean search is conducted in the entire Education and Educational Research database using “open inquiry ” and “science” as the search terms.

  5. 5.

    The noun culture and adjective cultural tend to be used indiscriminately to very different phenomena. Thus, there is talk about Western culture even though cultural practices even with respect to academia are very different in typically countries such as Canada, France, and Germany.

  6. 6.

    In cultural-historical activity theory , as in dialectical logic generally, the term moment is used to denote a part of a whole that cannot be understood independently of this whole and all the other parts that can be identified. In this book, I employ the term only in this way.

  7. 7.

    The asterisk is used to mark the transitional nature of the phenomenon denoted.

  8. 8.

    I agree with Wittgenstein (2000) that we do not need to term meaning because it gets into our way of appropriately describing how language actually operates and how it is deployed.

References

  • Apedoe, X., & Ford, M. (2010). The empirical attitude, material practice and design activities. Science & Education, 19, 165–186.

    Article  Google Scholar 

  • Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.

    Article  Google Scholar 

  • Bakhtin, M. (1981). The dialogic imagination. Austin: University of Texas.

    Google Scholar 

  • Bourdieu, P. (1980). Le sens pratique [The logic of practice]. Paris: Les Éditions de Minuit.

    Google Scholar 

  • Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32–42.

    Article  Google Scholar 

  • Carlone, H. B., Haun-Frank, J., & Webb, A. (2011). Assessing equity beyond knowledge- and skills-based outcomes: A comparative ethnography of two fourth-grade reform-based science classrooms. Journal of Research in Science Teaching, 48, 459–485.

    Article  Google Scholar 

  • Chin, C. A., & Brewer, W. F. (2010). Models of data: A theory of how people evaluate data. Cognition and Instruction, 19, 323–393.

    Article  Google Scholar 

  • Cobb, P., & Tzou, C. (2009). Supporting students’ learning about data generation. In W.-M. Roth (Ed.), Mathematical representation at the interface of body and culture (pp. 135–170). Charlotte: Information Age Publishing.

    Google Scholar 

  • Edgerton, S. (1985). The renaissance development of the scientific illustration. In J. Shirley & D. Hoeniger (Eds.), Science and the arts in the renaissance (pp. 168–197). Washington, DC: Folger Shakespeare Library.

    Google Scholar 

  • English, L. D. (2012). Data modeling with first-grade students. Educational Studies in Mathematics, 81, 15–30.

    Article  Google Scholar 

  • Falk, H., Brill, G., & Yarden, A. (2008). Teaching a biotechnology curriculum based on adapted primary literature. International Journal of Science Education, 30, 1841–1866.

    Article  Google Scholar 

  • Fogleman, J., McNeill, K. L., & Krajcik, J. (2011). Examining the effect of teachers’ adaptations of a middle school science inquiry-oriented curriculum unit on student learning. Journal of Research in Science Teaching, 48, 149–169.

    Article  Google Scholar 

  • Foucault, M. (1975). Surveiller et punir: Naissance de la prison [Discipline and punish: Birth of the prison]. Paris: Gallimard.

    Google Scholar 

  • Garfinkel, H. (1967). Studies in ethnomethodology. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Garfinkel, H., & Sacks, H. (1986). On formal structures of practical action. In H. Garfinkel (Ed.), Ethnomethodological studies of work (pp. 160–193). London: Routledge & Kegan Paul.

    Google Scholar 

  • Garfinkel, H., & Wieder, D. L. (1992). Two incommensurable, asymmetrically alternate technologies of social analysis. In G. Watson & R. M. Seiler (Eds.), Text in context: Contributions to ethnomethodology (pp. 175–206). Newbury Park: Sage.

    Google Scholar 

  • Garfinkel, H., Lynch, M., & Livingston, E. (1981). The work of a discovering science construed with materials from the optically discovered pulsar. Philosophy of the Social Sciences, 11, 131–158.

    Google Scholar 

  • Gregory, B. (1990). Inventing reality: Physics as language. New York: Wiley.

    Google Scholar 

  • Husserl, E. (1939). Erfahrung und Urteil: Untersuchungen zur Genealogie der Logik. Prague: Academia Verlagsbuchhandlung.

    Google Scholar 

  • Jordan, R. C., Ruibai-Villasenor, M., Hmelo-Silver, C. E., & Etkina, E. (2011). Laboratory materials: Affordances or constraints? Journal of Research in Science Teaching, 48, 1010–1025.

    Article  Google Scholar 

  • Latour, B. (1987). Science in action: How to follow scientists and engineers through society. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Latour, B. (1993). La clef de Berlin et d’autres leçons d’un amateur de sciences [The key to Berlin and other lessons from a science lover]. Paris: Éditions de la Découverte.

    Google Scholar 

  • Lave, J. (1993). The practice of learning. In S. Chaiklin & J. Lave (Eds.), Understanding practice: Perspectives on activity and context (pp. 3–32). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Leont’ev, A. N. (1983). Dejatel’nost’. Soznanie. Ličnost’. [Activity, consciousness, personality]. In Izbrannye psixhologičeskie proizvedenija (Vol. 2, pp. 94–231). Moscow: Pedagogika.

    Google Scholar 

  • Lindwal, O., & Lymer, G. (2008). The dark matter of lab work: Illuminating the negotiation of disciplined perception in mechanics. Journal of the Learning Sciences, 17, 180–224.

    Article  Google Scholar 

  • Livingston, E. (1986). The ethnomethodological foundations of mathematics. London: Routledge and Kegan Paul.

    Google Scholar 

  • Luria, A. R. (2003). Osnoby nejrolpsixologii [Foundations of neuropsychology] Moscow: Isdatel’skij Centr «Akademija».

    Google Scholar 

  • Lynch, M. (1998). The discursive production of uncertainty: The O. J. Simpson “dream team” and the sociology of knowledge machine. Social Studies of Science, 28, 829–868.

    Article  Google Scholar 

  • Mannheim, K. (2004). Beiträge zur Theorie der Weltanschauungs-Interpretation [Contributions to the theory of worldview interpretation]. In J. Strübing & B. Schnettler (Eds.), Methodologie interpretativer Sozialforschung: Klassische Grundlagentexte (pp. 103–153). Konstanz: UVK.

    Google Scholar 

  • McElhaney, K. W., & Linn, M. C. (2011). Investigations of a complex, realistic task: Intentional, unsystematic, and exhaustive experiments. Journal of Research in Science Teaching, 48, 745–770.

    Article  Google Scholar 

  • National Council for Teaching of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston: Author.

    Google Scholar 

  • National Research Council (NRC). (1996). National science education standards. Washington, DC: National Academy Press.

    Google Scholar 

  • Noss, R., Bakker, A., Hoyles, C., & Kent, P. (2007). Situating graphs as workplace knowledge. Educational Studies in Mathematics, 65, 367–384.

    Article  Google Scholar 

  • Preece, J., & Janvier, C. (1992). A study of the interpretation of trends in multiple curve graphs of ecological situations. School Science and Mathematics, 92, 299–306.

    Article  Google Scholar 

  • Ritchie, S. M., Sandhu, M., Sandhu, S., Tobin, K., Henderson, S., & Roth, W.-M. (2013). Emotional arousal of beginning physics teachers during extended experimental investigations. Journal of Research in Science Teaching, 50, 137–161.

    Article  Google Scholar 

  • Rorty, R. (1989). Contingency, irony, and solidarity. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Roth, W.-M. (2003a). Competent workplace mathematics: How signs become transparent in use. International Journal of Computers for Mathematical Learning, 8, 161–189.

    Article  Google Scholar 

  • Roth, W.-M. (2003b). Toward an anthropology of graphing. Dordrecht: Kluwer Academic.

    Book  Google Scholar 

  • Roth, W.-M. (2004). What is the meaning of meaning? A case study from graphing. Journal of Mathematical Behavior, 23, 75–92.

    Article  Google Scholar 

  • Roth, W.-M. (2005). Mathematical inscriptions and the reflexive elaboration of understanding: An ethnography of graphing and numeracy in a fish hatchery. Mathematical Thinking and Learning, 7, 75–109.

    Article  Google Scholar 

  • Roth, W.-M. (2007). Graphing Hagan Creek: A case of relations in sociomaterial practice. In E. Teubal, J. Dockrell, & L. Tolchinsky (Eds.), Notational knowledge: Historical and developmental perspectives (pp. 179–207). Rotterdam: Sense Publishers.

    Google Scholar 

  • Roth, W.-M. (2009a). Limits to general expertise: A study of in- and out-of-field graph interpretation. In S. P. Weingarten & H. O. Penat (Eds.), Cognitive psychology research developments (pp. 1–38). Hauppauge: Nova Science.

    Google Scholar 

  • Roth, W.-M. (2009b). Radical uncertainty in scientific discovery work. Science, Technology & Human Values, 34, 313–336.

    Article  Google Scholar 

  • Roth, W.-M. (2009c). On the inclusion of emotions, identity, and ethico-moral dimensions of actions. In A. Sannino, H. Daniels, & K. Gutiérrez (Eds.), Learning and expanding with activity theory (pp. 53–71). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Roth, W.-M. (2013). To event: Towards a post-constructivist approach to theorizing and researching curriculum as event*-in-the-making. Curriculum Inquiry, 43, 388–417.

    Article  Google Scholar 

  • Roth, W.-M. (2014). Reading activity, consciousness, personality dialectically: Cultural-historical activity theory and the centrality of society. Mind, Culture, and Activity, 21, 4–20. doi:10.1080/10749039.2013.771368.

    Article  Google Scholar 

  • Roth, W.-M., & Barton, A. C. (2004). Rethinking scientific literacy. New York: Routledge.

    Book  Google Scholar 

  • Roth, W.-M., & Bowen, G. M. (1999). Digitizing lizards or the topology of vision in ecological fieldwork. Social Studies of Science, 29, 719–764.

    Article  Google Scholar 

  • Roth, W.-M., & Bowen, G. M. (2003). When are graphs ten thousand words worth? An expert/expert study. Cognition and Instruction, 21, 429–473.

    Article  Google Scholar 

  • Roth, W.-M., & Lee, Y. J. (2007). “Vygotsky’s neglected legacy”: Cultural-historical activity theory. Review of Educational Research, 77, 186–232.

    Article  Google Scholar 

  • Roth, W.-M., & McGinn, M. K. (1998). Inscriptions: A social practice approach to “representations”. Review of Educational Research, 68, 35–59.

    Article  Google Scholar 

  • Roth, W.-M., McGinn, M. K., & Bowen, G. M. (1998). How prepared are preservice teachers to teach scientific inquiry? Levels of performance in scientific representation practices. Journal of Science Teacher Education, 9, 25–48.

    Article  Google Scholar 

  • Russell, C. B., & Weaver, G. C. (2011). A comparative study of traditional, inquiry-based, and research-based laboratory curricula: Impacts on understanding of the nature of science. Chemistry Education Research and Practice, 12, 57–67.

    Article  Google Scholar 

  • Stieff, M., Hegarty, M., & Deslongchamps, G. (2011). Identifying representational competence with multi-representational displays. Cognition and Instruction, 29, 123–145.

    Article  Google Scholar 

  • Tabachneck-Schijf, H. J. M., Leonardo, A. M., & Simon, H. A. (1997). CaMeRa: A computational model for multiple representations. Cognitive Science, 21, 305–350.

    Article  Google Scholar 

  • van der Valk, T., & de Jong, O. (2009). Scaffolding science teachers in open-inquiry teaching. International Journal of Science Education, 31, 829–850.

    Article  Google Scholar 

  • Vygotskij, L. S. (2005). Psychologija razvitija cheloveka [Psychology of human development]. Moscow: Eksmo.

    Google Scholar 

  • Wittgenstein, L. (1997). Philosophische Untersuchungen [Philosophical investigations] (2nd ed.). Oxford: Blackwell. (First published in 1953)

    Google Scholar 

  • Wittgenstein, L. (2000). Bergen text edition: Big typescript. http://www.wittgensteinsource.org/texts/BTEn/Ts-213. Accessed 30 Nov 2013.

  • Woolgar, S. (1990). Time and documents in researcher interaction: Some ways of making out what is happening in experimental science. In M. Lynch & S. Woolgar (Eds.), Representation in scientific practice (pp. 123–152). Cambridge, MA: MIT Press.

    Google Scholar 

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Roth, WM. (2014). Toward a Dynamic Theory of Graphing. In: Uncertainty and Graphing in Discovery Work. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7009-6_1

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