Vygotskian theory and mathematics education: Resolving the conceptual-procedural dichotomy

European Journal of Psychology of Education

Volumn 19, Issue 1, 2004, Pages 19-43

  Schmittau, Jean ^a  

^a BINGHAMTON UNIVERSITY   (United States)

Author keywords

Constructivism; Mathematics curriculum; Scientific concepts

Indexed keywords

EID: 8344260581     PISSN: 02562928     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03173235     Document Type: Article

References (41)

1. Bakhurst, D. (1997). Activity, consciousness, and communication. In M. Cole, Y. Engeström, & O. Vasquez (Eds.), Mind, culture, and activity: Seminal papers from the Laboratory of Comparative Human Cognition (pp. 147-163). Cambridge, UK: Cambridge University Press. (Original work published in 1988)
2. Barnett, J.H. (1998). A brief history of algorithms in mathematics. In L.J. Morrow & M.J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 69-77). Reston, VA: National Council of Teachers of Mathematics.
3. Carraher, T.N., Carraher, D.W., & Schliemann, A.D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3, 21-29.
4. Carraher, T.N., Carraher, D.W., & Schliemann, A.D. (1983). Mathematics in the streets and schools. Unpublished manuscript, Universidade Federal de Peraambuco, Recife, Brazil.
5. Carroll, W.M., & Porter, D. (1998). Alternative algorithms for whole-numberr operations. In L.J. Morrow & M.J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 106-114). Reston, VA: National Council of Teachers of Mathematics.
6. Chi, M., Feltovich, P., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152.
7. Davydov, V.V. (1975). The psychological characteristics of the "prenumerical" period of mathematics instruction. In L.P. Steffe (Ed.), Soviet studies in the psychology of learning and teaching mathematics (vol. 7, pp. 109-206). Chicago: University of Chicago Press.
8. Davydov, V.V. (1988). The concept of theoretical generalization and problems of educational psychology. Studies in Soviet thought, 36, 169-202. (Original work published in 1972)
9. Davydov, V.V. (1990). Types of generalization in instruction: Logical and psychological problems in the structuring of school curricula. Reston, VA: National Council of Teachers of Mathematics. (Original work published in 1972)
10. Davydov, V.V. (1992). The psychological analysis of multiplication procedures. Focus on Learning Problems in Mathematics, 14(1), 3-67.
11. Davydov, V.V., Gorbov, S.F., Mikulina, G.G., & Saveleva, O.V. (1999). Mathematics: Class I. Binghamton, New York: State University of New York.
12. Davydov, V.V., Gorbov, S.F., Mikulina, G.G., & Saveleva, O.V. (2000). Mathematics: Class 2. Binghamton, New York: State University of New York.
13. Davydov, V.V., Gorbov, S.F., Mikulina, G.G., Savyelyeva, O.V., & Tabachnikova, N.L. (2001). Mathematics: 3rd Grade. Binghamton, New York: State University of New York.
14. Hanna, G. (1983). Rigorous proof in mathematics education. Toronto: Ontario Institute for Studies in Education.
15. Il'enkov, E.V. (1964). Skkola dolzhna uchit' myslit [The school should teach linking]. Voprosy Estetiki [Questions in Aesthetics], No. 6. Moskow: Iskusstvo.
16. Kamii, C. & Dominick, A. (1998). The harmful effects of algorithms in grades 1-4. In L.J. Morrow & M.J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 130-140). Reston, VA: National Council of Teachers of Mathematics.
17. Kouba, V.L., & Wearne, D. (2000). Whole number properties and operations. In E.A. Silver & P.A. Kenney (Eds.), Results from the seventh mathematics assessment of the National Assessment of Educational Progress (pp. 141-162). Reston, VA: National Council of Teachers of Mathematics.
18. Kouba, V.L., Zawojewski, J.S., & Strutchens, M.E. (1997). What do students know about numbers and operations? In P.A. Kenney & E.A. Silver (Eds.), Results from the sixth mathematics assessment of the National Assessment of Educational Progress (pp. 87-140). Reston, VA: National Council of Teachers of Mathematics.
19. Kozulin, A. (1998). Psychological tools: A sociocultural approach to education. Cambridge, MA: Harvard University Press.
20. Krutetskii, V.A. (1969). An investigation of mathematical abilities in schoolchildren. In J. Kilpatrick & I. Wirszup (Eds.), Soviet Studies in the Psychology of Learning and Teaching Mathematics (Vol. II): The Structure of Mathematical Abilities (pp. 5-57). Chicago: University of Chicago Press.
21. Krutetskii, V.A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press. (Original work published in 1968, in Russian)
22. Langer, J. (1997). The power of mindful learning. Reading, MA: Addison-Wesley.
23. Lave, J. (1988). Cognition in practice. New York: Cambridge University Press.
24. Leontiev, A.N. (1981). The problem of activity in psychology. In J.B. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37-71). Armonk, New York: M.E. Sharpe. (Original work published in 1972)
25. Morrow, L.J. (1998). Whither algorithms? Mathematics educators express their views. In L.J. Morrow & M.J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 1-6). Reston, VA: National Council of Teachers of Mathematics.
26. National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
27. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
28. Novak, J.D., & Gowin, D.B. (1984). Learning how to learn. New York: Cambridge University Press.
29. Saxe, G.B. (1997). Selling candy: A study of cognition in context. In M. Cole, Y. Engeström, & O. Vasquez (Eds.), Mind, culture, and activity: Seminal papers from the Laboratory of Comparative Human Cognition (pp. 330-337). Cambridge, UK: Cambridge University Press. (Original work published in 1989)
30. Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American Educator, 26(2), 10-26.
31. Schmittau, J. (1993a). Connecting mathematical knowledge: A dialectical perspective. Journal of Mathematical Behavior, 12, 179-201.
32. Schmittau, J. (1993b). Vygotskian scientific concepts: Implications for mathematics education. Focus on Learning Problems in Mathematics, 15(2-3), 29-39.
33. Schmittau, J. (1994). Scientific concepts and pedagogical mediation: A comparative analysis of category structure in Russian and U.S. students. Paper presented at the Annual meeting of the American Educational Research Association, New Orleans, LA.
34. Schmittau, J. (2003a). Beyond constructivism and back to basics: A cultural historical alternative to the teaching of the base ten positional system. In B. Rainforth & J. Kugelmass (Eds.), Curriculum and instruction for all learners: Blending systematic and constructivist approaches in inclusive elementary schools. Baltimore, MD: Brookes Publishing Co.
35. Schmittau, J. (2003b). Cultural historical theory and mathematics education. In A. Kozulin, B. Gindis, S. Miller, & V. Ageyev (Eds.), Vygotsky's educational theory in cultural context. Cambridge, UK: Cambridge University Press.
36. Scribner, S. (1997). Mind in action: A functional approach to thinking. In M. Cole, Y. Engeström, & O. Vasquez (Eds.), Mind, culture, and activity: Seminal papers from the Laboratory of Comparative Human Cognition (pp. 354-368). Cambridge, UK: Cambridge University Press. (Original work published in 1992)
37. Thorndike, E.L. (1922). The psychology of arithmetic. New York: Macmillan.
38. Tikhomirov, L.S. (1981). The psychological consequences of computerization. In J.V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 256-278). Armonk, New York: M.E. Sharpe. (Original work published in 1972)
39. Vygotsky, L.S. (1986). Thought and language. Cambridge, MA: MIT Press. (Original work published in 1934)
40. Vygotsky, L.S., & Luria, A.R. (1993). Studies on the history of behavior: Ape, primitive, and child. Hillsdale, NJ: Erlbaum.
41. Willingham, D.T. (2002). Inflexible knowledge: The first step to expertise. American Educator, 26(4), 31-33, 48-49.