Interaction between Knowledge and Contexts on Understanding Abstract Mathematical Concepts

Journal of Experimental Child Psychology

Volumn 65, Issue 1, 1997, Pages 68-95

  Mevarech, Zemira R ^a   Stern, Elsbeth ^b  

^a BAR ILAN UNIVERSITY   (Israel)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031501365     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1006/jecp.1996.2352     Document Type: Article

References (43)

1. Anand, P., & Ross, S. M. (1987). Using computer-assisted instruction to personalize math leaning materials for elementary school children. Journal of Educational Psychology, 79, 72-79.
2. Bell, A., & Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics, 2, 34-42.
3. Carraher, T., Carraher, D., & Schliemann, A. (1985). Mathematics in the streets and schools. British Journal of Developmental Psychology, 3, 21-29.
4. Ceci, S. J., & Roazzi, A. (1993). The effects of context on cognition: Postcards from Brazil. In R. J. Steinberg & R. K. Wagner (Eds.). Mind in context: Interactionist perspectives on human intelligence pp. 74-101. USA: Cambridge University Press.
5. Cheng, P. W., & Holyoak, K. J. (1985). Pragmatic reasoning schemes. Cognitive Psychology, 19, 293-328.
6. Clement, J. (1989). The concept of variation and misconceptions in Cartesian graphing. Focus on Learning Problems in Mathematics, 11, 77-87.
7. Davis-Dorsey, J., Ross, S. M., & Morrison, G. R. (1991). The role of rewording and context personalization in the solving mathematical word problems. Journal of Educational Psychology, 83, 61-68.
8. De Corte, E., Verschaffel, L., & De Win, L. (1985). Influence of rewording verbal problems on children's problem representations and solutions. Journal of Educational Psychology, 77, 460-470.
9. Fischbein, E. (1992). Intuition and information processing in mathematics activity. International Journal of Educational Research, 16, 31-50.
10. Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. Cognitive Psychology, 16, 253-292.
11. Gelman, R., & Meek, E. (1983). Preschoolers' counting principle before skill. Cognition, 13, 343-359.
12. Greeno, J. G. (1989). A perspective on thinking. American Psychologist, 44, 134-141.
13. Hall, R., Kibler, D., Wenger, E., Truxaw, C. (1989). Exploring the episodic structure of algebra story problem solving. Cognition and Instruction, 6, 223-283.
14. Hembree, R. (1992). Experiments and Relational studies in problem solving: A meta-analysis. Journal for Research in Mathematics Education, 23, 242-273.
15. Hudson, T. (1983). Correspondences and numerical differences between disjoint sets. Child Development, 54, 84-90.
16. Janvier, C. (1990). Contextualization and mathematics for all. In T. Cooney, & C. Hirsch (Eds.) Teaching and learning mathematics in the 1990s pp. 183-193. Reston Virginia: National Council of Teachers of Mathematics.
17. Johnson-Laird, P. N. (1983). Mental models: Toward a cognitive science of language, inference, and consciousness. Cambridge, MA: Harvard University Press.
18. Kintsch, W. (1988). The role of knowledge in discourse comprehension: A construction-integration model. Psychological Review, 95, 163-182.
19. Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109-129.
20. Kotovsky, K., Hayes, J. R., & Simon, H. A. (1985). Why are some problems hard? Evidence from Tower of Hanoi. Cognitive Psychology, 17, 248-294.
21. Lave, J. (1988). Cognition in Practice: Mind, Mathematics and Culture in Everyday Life. NY: Cambridge University Press.
22. Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, Learning, and teaching. Review of Educational Research, 60, 1-64.
23. Mayer, R. E. (1983). Thinking, problem solving, cognition. NY: Freeman.
24. McDermott, L. C., Rosenquist, M. L., & van Zee, E. H. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American Journal Physics, 55, 503-513.
25. Mevarech, Z. R., & Kramarski, B. (in press). From verbal descriptions to graphic representations: Stability and change in students' alternative conceptions. Educational Studies in Mathematics.
26. Nunes, T., Schleimann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. USA: Cambridge University Press.
27. Raven, J. C. (1960). Standard Progressive Matrices. London: H. K. Lewis.
28. Resnick, L. B. (1987). Education and Learning to Think. Washington D.C.: National Academy Press.
29. Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist, 44, 162-169.
30. Saxe, G. B. (1991). Culture and cognitive development: Studies in mathematical understanding. NJ: Erlbaum.
31. Schoenfeld, A. H. (1985). Mathematical problem solving. NY: Academic Press.
32. Schoenfeld, A. H., Smith, J. P., & Arcavi, A. (1993). Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain. In R. Glaser (Ed.) Advances in instructional psychology, Vol. 4. pp. 55-175. NJ: Erlbaum.
33. Scribner, S. (1986). Thinking in action: some characteristics of practical thought. In R. J. Sternberg & R. K. Wagner (Eds.). Practical intelligence: nature and origins of competence in the everyday world (pp. 13-30). Cambridge, England: Cambridge University Press.
34. Siegler, R. S., & Jenkins, E. (1989). How Children Discover New Strategies. NJ: Erlbaum.
35. Smith, E. E., Langston, C., & Nisbett, R. E. (1992). The case for rules in reasoning. Cognitive Science, 16, 1-40.
36. Stern, E. (1993). What makes certain arithmetic word problems involving the comparison of sets so hard for children? Journal of Educational Psychology, 85, 7-23.
37. Stern, E., & Lenderhofer, A. (1992). The role of situational context in solving word problems. Cognitive Development, 7, 259-268.
38. Stern, E., & Mevarech, Z. R. (1996). Children's understanding of successive halving in practical and abstract contexts. Journal of Experimental Child Psychology, 61, 153-172.
39. Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal for Research in Mathematics Education, 20, 356-366.
40. Wainer, M. J. (1992). Understanding graphs and tables. Educational Researcher, 21, 14-23.
41. Wason, P. C., & Johnson-Laird, P. N. (1972). Psychology of reasoning: Structure and Content. Cambridge, MA: Harvard University Press.
42. Weaver III, C. A., & Kintsch, W. (1992). Enhancing students' comprehension of the conceptual structure of algebra word problems. Journal of Educational Psychology, 84, 419-428.
43. Wollman, W. (1983). Determining the sources of error in a translation from sentence to equation. Journal for Research in Mathematics Education, 14, 169-181.