Partially correct constructs illuminate students' inconsistent answers

Educational Studies in Mathematics

Volumn 75, Issue 1, 2010, Pages 65-87

  Ron, Gila ^a   Dreyfus, Tommy ^a   Hershkowitz, Rina ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Knowledge construction; Probability

Indexed keywords

EID: 77955843740     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-010-9241-x     Document Type: Article

References (38)

1. Abrahamson, D. (2009). Embodied design: constructing means for constructing meaning. Educational Studies in Mathematics, 70, 27-47.
2. Bikner-Ahsbahs, A. (2006). Semiotic sequence analysis-constructing epistemic types empirically. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 161-168). Prague: Charles University Faculty of Education.
3. Campbell, R. L. (2000). Reflecting abstraction in context. In R. L. Campbell (Ed.), Studies in reflecting abstraction (pp. 1-26). Hove: Psychology.
4. Davydov, V. V. (1990). Types of generalisation in instruction: Logical and psychological problems in the structuring of school curricula. In: J. Kilpatrick (Ed.), J. Teller (Trans.). Soviet studies in mathematics education, Vol. 2. Reston: National Council of Teachers of Mathematics. (Original work published 1972).
5. Dienes, Z. P. (1961). On abstraction and generalization. Harvard Educational Review, 31, 281-301.
6. diSessa, A. A., & Wagner, J. F. (2005). What coordination has to say about transfer. In J. Mestre (Ed.), Transfer of learning from a modern multi-disciplinary perspective (pp. 121-154). Greenwich: Information Age.
7. Dreyfus, T., & Kidron, I. (2006). Interacting parallel constructions: a solitary learner and the bifurcation diagram. Recherches en Didactique des Mathématiques, 26, 295-336.
8. Dreyfus, T., Hershkowitz, R., & Schwarz, B. B. (2001). Abstraction in context II: The case of peer interaction. Cognitive Science Quarterly, 1, 307-368.
9. Fischbein, E. (1975). The intuitive sources of probabilistic thinking. Dordrecht: Reidel.
10. Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgments in children and adolescents. Educational Studies in Mathematics, 22, 523-549.
11. Giest, H. (2005). Zum Verhältnis von Konstruktivismus und Tätigkeitsansatz in der Pädagogik [On the relationship between constructivism and activity theory in pedagogy]. In: F. Radis, M.-L. Braunsteiner, & K. Klement (Eds.), Badener VorDrucke [Baden PrePrints] (pp. 43-64). Baden/A.: Kompetenzzentrum für Forschung und Entwicklung (Schriftenreihe zur Bildungsforschung - Band 3).
12. Hershkowitz, R. (2009). Contour lines between a model as a theoretical framework and the same model as methodological tool. In B. B. Schwarz, T. Dreyfus, & R. Hershkowitz (Eds.), Transformation of knowledge through classroom interaction (pp. 273-280). London: Routledge.
13. Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32, 195-222.
14. Lecoutre, M. P. (1992). Cognitive models and problem spaces in 'purely random' situations. Educational Studies in Mathematics, 23, 557-568.
15. 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: Sharpe.
16. Mitchelmore, M., & White, P. (2007). Abstraction in mathematics learning. Mathematics Education Research Journal, 19, 1-9.
17. Nilsson, P. (2004). Students' ways of interpreting aspects of chance embedded in dice games. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3 (pp. 425-432). Bergen: Bergen University College.
18. Nilsson, P. (2007). Different ways in which students handle chance encounters in the explorative settings of a dice game. Educational Studies in Mathematics, 66, 273-292.
19. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht: Kluwer.
20. Ozmantar, M. F., & Monaghan, J. (2007). A dialectical approach to the formation of mathematical abstractions. Mathematics Education Research Journal, 19, 89-112.
21. Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children. New York: Norton (Original work published 1951).
22. Pontecorvo, C., & Girardet, H. (1993). Arguing and reasoning in understanding historical topics. Cognition and Instruction, 11, 365-395.
23. Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31, 602-625.
24. Pratt, D., & Noss, R. (2002). The microevolution of mathematical knowledge: The case of randomness. The Journal of the Learning Sciences, 11, 453-488.
25. Ron, G., Dreyfus, T., & Hershkowitz, R. (2006). Partial knowledge constructs. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 449-456). Prague: Charles University Faculty of Education.
26. Schnarch, D. (1998). Intuitions and schemata in probabilistic reasoning-the evolution with age of probabilistic misconceptions. Unpublished doctoral dissertation, Tel Aviv University.
27. Schwarz, B. B., Dreyfus, T., & Hershkowitz, R. (2009). The nested epistemic actions model of abstraction in context. In B. B. Schwarz, T. Dreyfus, & R. Hershkowitz (Eds.), Transformation of knowledge through classroom interaction (pp. 11-41). London: Routledge.
28. Shaughnessy, J. M. (2003). Research on students' understandings of probability. In J. Kilpatrick, G. W. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 216-226). Reston: NCTM.
29. Skemp, R. (1986). The psychology of learning mathematics (2nd ed.). Harmondsworth: Penguin.
30. Smith, J. P., diSessa, A. A., & Roschelle, J. (1993). Misconceptions reconceived: a constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3, 115-163.
31. Treffers, A., & Goffree, F. (1985). Rational analysis of realistic mathematics education-the Wiskobas program. In L. Streefland (Ed.), Proceedings of the 9th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 97-121). Utrecht: OW& OC.
32. Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 4, 207-232.
33. van den Heuvel-Panhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour. Freudenthal Institute CD-rom for ICME9. Utrecht: Utrecht University.
34. van Oers, B. (1998). The fallacy of decontextualization. Mind, Culture and Activity, 5, 135-142.
35. Vidakovic, D., Berenson, S., & Brandsma, J. (1998). Children's intuitions of probabilistic concepts emerging from fair play. In L. Pereina-Mendoza, L. Seu Kea, T. Wee Kee, & W. K. Wong (Eds.), Proceedings of the 5th International Conference on Teaching Statistics, Vol. 1 (pp. 67-73). Voorburg: International Statistical Institute Permanent Office.
36. Wagner, J. F. (2002). Constructing generalizations: An analysis of one student's progress toward a generalized understanding of the law of large numbers. In D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Wiegel, R. L. Bryant, & K. Nooney (Eds.), Proceedings of the 24th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 3 (pp. 1335-1338). Athens: PME-NA.
37. Wagner, J. F. (2003). The microgenesis of mathematical generalizations: Examining competing theories of conceptual change and transfer. Paper presented at the 2003 Annual Meeting of the American Educational Research Association. Chicago, IL.
38. Wagner, J. F. (2006). Transfer in pieces. Cognition and Instruction, 24, 1-71.