On the relation of abstract and concrete in scientists' graph interpretations: A case study

Journal of Mathematical Behavior

Volumn 25, Issue 4, 2006, Pages 318-333

  Roth, Wolff Michael ^a   Hwang, SungWon ^b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b Hanyang University   (South Korea)

Author keywords

Abstract; Concrete; Consciousness; Dialectical logic; Generalization

Indexed keywords

EID: 33846135190     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2006.11.005     Document Type: Article

References (32)

1. Bourdieu, P. (1997). Méditations pascaliennes. Paris: Seuil (available in English as Pascalian mediations, Stanford: Stanford University Press, 2000).
2. Depraz N., Varela F., and Vermersch P. On becoming aware: A pragmatics of experiencing (2003), Benjamins, Amsterdam
3. Ericsson K.A., and Simon H.A. Protocol analysis: Verbal reports as data. revised ed. (1993), MIT Press, Cambridge, MA
4. Garfinkel H. Studies in ethnomethodology (1967), Prentice-Hall, Englewood Cliffs, NJ
5. Garfinkel H. Ethnomethodology's program: Working out Durkheim's aphorism (2002), Rowman & Littlefield, Lanham, NY
6. Hazzan O., and Zazkis R. Reducing abstraction: The case of school mathematics. Educational Studies in Mathematics 58 (2005) 101-119
7. Hegel, G. W. F. (1977). Phenomenology of spirit (A. V. Miller, Trans.). Oxford: Oxford University Press (German original published in 1807).
8. Heidegger, M. (1977). Sein und Zeit. Tübingen: Niemeyer. (Also used: Being and time (J. Stambaugh, Trans.). Albany: State University of New York Press, 1996).
9. Husserl, E. (1931). Ideas: General introduction to pure phenomenology (W. R. Boyce Gibson, Trans.). London: George Allen & Unwin.
10. Husserl, E. (2002). The origin of geometry. In M. Merleau-Ponty, Husserl at the limits of phenomenology: Including texts by Edmund Husserl (L. Lawlor & B. Bergo (Eds.), pp. 93-116). Evanston, IL: Northwestern University Press.
11. Janvier C. Translation processes in mathematics education. In: Janvier C. (Ed). Problems of representation in the teaching and learning of mathematics (1987), Lawrence Erlbaum Associates, Hillsdale, NJ 27-32
12. Jordan B., and Henderson A. Interaction analysis: Foundations and practice. The Journal of the Learning Sciences 4 (1995) 39-103
13. Jurow A.S. Generalizing in interaction: Middle school mathematics students making mathematical generalizations in a population-modeling project. Mind, Culture, and Activity 11 (2004) 279-300
14. Kant I. Werke V: Schriften zur Metaphysik und Logik Vol. 1 (1968), Suhrkamp, Frankfurt
15. Latour, B. (1993). La clef de Berlin et autres leçons d'un amateur de sciences [The key to Berlin and other lessons of a science lover]. Paris: Éditions la Découverte.
16. McNeill D. Gesture and language dialectic. Acta Linguistica Hafniensia 34 (2002) 7-37
17. Oxford English Dictionary (OED). (2005). Oxford University Press (online version).
18. Plato (360 BC). Phaedrus (B. Jowett, Trans.). URL: http://www.classicsarchive.com/P/books/Phaedrus__Trans_by_Ben._Jowett_-_ Plato/.
19. Ricœur P. From text to action: Essays in hermeneutics, II (1991), Northwestern University Press, Evanston, IL
20. Ricklefs R.E. Ecology. 3rd ed. (1990), Freeman, New York
21. Roth W.-M. Toward an anthropology of graphing (2003), Kluwer Academic Publishing, Dordrecht, The Netherlands
22. Roth W.-M. What is the meaning of meaning? A case study from graphing. Journal of Mathematical Behavior 23 (2004) 75-92
23. Roth W.-M. Doing qualitative research: Praxis of method (2005), Sense Publishers, Rotterdam
24. Roth W.-M., and Bowen G.M. 'Creative solutions' and 'fibbing results': Enculturation in field ecology. Social Studies of Science 31 (2001) 533-556
25. Roth W.-M., and Hwang S.W. Does mathematical learning occur in going from concrete to abstract or in going from abstract to concrete?. Journal of Mathematical Behavior 25 4 (2006)
26. Roth W.-M., and Lee. Interpreting unfamiliar graphs: A generative, activity-theoretic model. Educational Studies in Mathematics 57 (2004) 265-290
27. Roth W.-M., and Middleton. The making of asymmetries of knowing, identity, and accountability in the sequential organization of graph interpretation. Cultural Studies of Science Education 1 (2006) 11-81
28. Roth W.-M., Pozzer-Ardenghi L., and Han J. Critical graphicacy: Understanding visual representation practices in school science (2005), Springer-Kluwer, Dordrecht, The Netherlands
29. Saari E., and Miettinen R. Dynamics of change in research work: Constructing a new research area in a research group. Science, Technology, & Human Values 26 (2001) 300-321
30. Sriraman B. Reflective abstraction, uniframes and the formulation of generalizations. Journal of Mathematical Behavior 23 (2004) 205-222
31. Vygotsky L.S. Thought and language (1986), MIT Press, Cambridge, MA
32. Wilenski U. Abstract meditations on the concrete and concrete implications for mathematics education. In: Harel I., and Papert S. (Eds). Constructionism: Research reports and essays, 1985-1990 (1991), Ablex, Norwood, NJ 193-203