The nested epistemic actions model for abstraction in context

Transformation of Knowledge through Classroom Interaction

Volumn , Issue , 2009, Pages 11-41

  Schwarz, Baruch B ^a   Dreyfus, Tommy ^b   Hershkowitz, Rina ^c  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

^c WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952098781     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203879276     Document Type: Chapter

References (54)

1. Baker, M. (2003). Computer-mediated 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. 47-78). Dordrecht: Kluwer.
2. Campbell, R. L. (2000). Reflecting abstraction in context. In R. L. Campbell (Ed. and Trans.), Studies in reflecting abstraction (pp. 1-26). Hove, UK: Psychology Press.
3. Cobb, P., & Bauersfeld, H. (Eds.) (1995). The emergence of mathematical meaning: Interaction in classroom culture. Hillsdale, NJ: LEA.
4. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10(1-2), 113-163.
5. Davydov, V. V. (1990). Types of generalisation in instruction: Logical and psychological problems in the structuring of school curricula (Soviet studies in mathematics education, Vol. 2; J. Kilpatrick, Ed., J. Teller, Trans.). Reston, VA: National Council of Teachers of Mathematics. (Original work published 1972).
6. Dienes, Z. P. (1961). On abstraction and generalization. Harvard Educational Review, 31, 281-301.
7. diSessa, A. A. (1993). Towards an epistemology of physics. Cognition and Instruction, 10, 105-205.
8. Dooley, T. (2007). Construction of knowledge by primary pupils: The role of whole-class interaction. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of CERME 5 (pp. 1658-1668). Larnaca, Cyprus.
9. Dreyfus, T., & Kidron, I. (2006). Interacting parallel constructions: A solitary learner and the bifurcation diagram. Recherches en didactique des mathématiques, 26(3), 295-336.
10. Dreyfus, T., Hadas, N., Hershkowitz, R., & Schwarz B. B. (2006). Mechanisms for consolidating knowledge constructs. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for Psychology of Mathematics Education (Vol. 2, pp. 465-472). Prague: Charles University Faculty of Education.
11. Dreyfus, T., Hershkowitz, R., & Schwarz, B. B. (2001). Abstraction in context: The case of peer interaction. Cognitive Science Quarterly, 1, 307-358.
12. Dreyfus, T., & Tsamir, P. (2004). Ben's consolidation of knowledge structures about infinite sets. Journal of Mathematical Behavior, 23, 271-300.
13. Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht: Kluwer.
14. Fuchs, D., & Fuchs, L. S. (1998). Researchers and teachers working together to adapt instruction for diverse learners. Learning Disabilities Research and Practice, 13, 126-137.
15. Giest, H. (2005). Zum Verhältnis von Konstruktivismus und Tätigkeitsansatz in der Pädagogik. In F. Radis, M.-L. Braunsteiner, & K. Klement (Eds.), Badener VorDrucke (pp. 43-64). Baden/A.: Kompetenzzentrum für Forschung und Entwicklung (Schriftenreihe zur Bildungsforschung - Band 3).
16. Hadas, N., Hershkowitz, R., & Ron, G. (in press). Instructional design and research design principles in probability. Proceedings of the 5th International Colloquium on the Didactics of Mathematics. The University of Crete, Rethymnon, Crete, April 2008.
17. Hershkowitz, R., & Schwarz, B. B. (1999). Reflective processes in a technology-based mathematical classroom. Cognition and Instruction, 17, 66-91.
18. Hershkowitz, R., Dreyfus, T., Ben-Zvi, D., Friedlander, A., Hadas, N., Resnick, T., et al. (2002). Mathematics curriculum development for computerised environments: A designer-researcher-teacher-learner activity. In L. D. English (Ed.), Handbook of international research in mathematics education: Directions for the 21st century (pp. 657-694). Mahwah, NJ: Lawrence Erlbaum.
19. Hershkowitz, R., Hadas, N., Dreyfus, T., & Schwarz, B. (2007). Processes of abstraction from the diversity of individuals' constructing of knowledge to a group's 'shared knowledge'. Mathematics Education Research Journal, 19(2), 41-68.
20. Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 22, 195-222.
21. Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Lawrence Erlbaum.
22. Kidron, I. (2008). Abstraction and consolidation of the limit procept by means of instrumented schemes: The complementary role of three different frameworks. Educational Studies in Mathematics, 69(3), 197-216.
23. Kidron, I., & Dreyfus, T. (2007). Justification and interacting parallel constructions of knowledge. (Technical report available from the authors). Jerusalem College of Technology.
24. Kidron, I., & Dreyfus, T. (in press). Justification, enlightenment and the explanatory nature of proof. Proceedings of the ICMI Study 19 Conference on Proof and Proving in Mathematics Education. Taipei, Taiwan, May 2009.
25. Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229-269). Hillsdale, NJ: Erlbaum.
26. Leont'ev, A. N. (1981). The problem of activity in psychology. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37-71). Armonk, NY: Sharpe.
27. Mitchelmore, M., & White, P. (2007). Abstraction in mathematics learning. Mathematics Education Research Journal, 19(2), 1-9.
28. Monaghan, J., & Ozmantar, M. F. (2006). Abstraction and consolidation. Educational Studies in Mathematics, 62, 233-258.
29. Neth, H., & Payne, S. J. (2002). Thinking by doing? Epistemic actions in the Tower of Hanoi. In W. D. Gray & C. D. Schunn (Eds.), 24th Annual Conference of the Cognitive Science Society (pp. 691-696). Mahwah, NJ: Lawrence Erlbaum.
30. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht: Kluwer.
31. Ozmantar, M. F., & Monaghan, J. (2007). A dialectical approach to the formation of mathematical abstractions. Mathematics Education Research Journal, 19(2), 89-112.
32. Packer, M. J., & Goicoechea, J. (2001). Sociocultural and constructivist theories of learning: Ontology, not just epistemology. Educational Psychologist, 35(4), 227-241.
33. Piaget, J. [and collaborators] (1977). Recherches sur l'abstraction réfléchissante [Research on reflective abstraction] (2 vols.). Paris: Presses Universitaires de France.
34. Pontecorvo, C., & Girardet, H. (1993). Arguing and reasoning in understanding historical topics. Cognition and Instruction, 11(3-4), 365-395.
35. Robertson, E. A., & Cohen, D. A. (2006). Understanding consolidation through the architecture of memories. The Neuroscientist, 12(3), 261-271.
36. Ron, G., Dreyfus, T., & Hershkowitz, R. (2006). Partial constructs for the probability area model. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th International Conference for the Psychology of Mathematics Education (Vol. 4, pp. 449-456). Prague: Charles University Faculty of Education.
37. Ron, G., Dreyfus, T., & Hershkowitz, R. (2007). Partially correct constructs illuminate students' inconsistent answers. (Technical report available from the authors). Tel Aviv University.
38. Rota, G.-C. (1997). Indiscrete thoughts. Basel: Birkhäuser.
39. Schwarz, B. B., & Hershkowitz, R. (2001). Production and transformation of computer artifacts towards the construction of mathematical meaning. Mind, Culture and Activity, 8(3), 250-267.
40. Schwarz, B. B., Dreyfus, T., Hadas, N., & Hershkowitz, R. (2004). Teacher guidance of knowledge construction. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th International Conference for the Psychology of Mathematics Education (Vol. 4, pp. 169-176). Bergen, Norway: Bergen University College.
41. Schwarz, B. B., Hershkowitz, R., & Azmon, S., (2006). The role of the teacher in turning claims to arguments. In J. Novotná, H. Moravá, M. Krátaká & N. Stehliková (Eds.), Proceedings of the 30th International Conference for the Psychology of Mathematics Education (Vol. 5, pp. 5-65-5-72) Prague: Charles University Faculty of Education.
42. Schwarz, B. B., Perret-Clermont, A-N., Trognon, A., & Marro, P. (2008). Learning processes within and between successive activities in a laboratory context. Pragmatics and Cognition, 16(1), 57-87.
43. Skemp, R. (1986). The psychology of learning mathematics. (2nd ed.). Harmondsworth, England: Penguin.
44. Stehlíková, N. (2003a). Emergence of mathematical knowledge structures: Introspection. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th International Conference for the Psychology of Mathematics Education (Vol. 4, pp. 251-258). Honolulu, HI: University of Hawaii.
45. Stehlíková, N. (2003b). Building a finite arithmetic structure: Interpretation in terms of abstraction in context. In M. A. Mariotti (Ed.), Proceedings of the 3rd Conference for European Research in Mathematics Education (on CD). Bellaria, Italy.
46. Steinbring, H. (2005). The construction of new mathematical knowledge in classroom interaction: An epistemological perspective. Berlin: Springer.
47. Tabach, M., Hershkowitz, R., & Schwarz, B. B. (2006). Construction and consolidation of algebraic knowledge within dyadic processes: A case study. Educational Studies in Mathematics, 63, 235-258.
48. Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics instruction: The Wiskobas project. Dordrecht: Reidel.
49. van Oers, B. (1998). The fallacy of decontextualisation. Mind, Culture and Activity, 5, 135-142.
50. Voigt, J. (1995). Thematic patterns of interaction and sociomathematics norms. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom culture (pp. 163-201). Hillsdale, NJ: Lawrence Erlbaum.
51. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, Eds.). Cambridge, MA: Harvard University Press. (Original work published 1930.)
52. Wagner, J. F. (2005). Transfer in pieces. Cognition and Instruction, 24(1), 1-71.
53. Wood, T., Williams, G., & McNeal, B. (2006). Children's mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222-255.
54. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458-477.