Use of multiplicative commutativity by school children and street sellers

Journal for Research in Mathematics Education

Volumn 29, Issue 4, 1998, Pages 422-435

  Schliemann, Analúcia D ^a   Araujo, Cláudia ^b   Cassundé, Maria Angela ^b   Macedo, Suzana ^b   Nicéas, Lenice ^b  

^a TUFTS UNIVERSITY   (United States)

^b FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

Arithmetic; Children's strategies; Cognitive development; Cross cultural studies; Elementary; K 8; Situated cognition; Social and cultural issues

Indexed keywords

EID: 22044438431     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: 10.2307/749859     Document Type: Article

References (25)

1. Bruner, J. (1962). On knowing: Essays for the left hand. Cambridge, MA: Harvard University Press.
2. Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1982). Na vida, dez; na escola, zero: Os contextos culturais da aprendizagem da matemática [A in life, F at school: The cultural context of mathematics learning]. Cadernos de Pesquisa [Research Journal], 42, 79-86.
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. (1987). Written and oral mathematics. Journal for Research in Mathematics Education, 18, 83-97.
5. Collins, A., Brown, J. S., & Newman, S. E. (1989). Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics. In L. B. Resnick (Ed.), Knowing, learning, and instruction (pp. 453-494). Hillsdale, NJ: Erlbaum.
6. Gelman, R. (1979). Preschool thought. American Psychologist, 44, 134-141.
7. Ginsburg, H. P., Posner, J. K., & Russell, R. L. (1981). The development of mental addition as a function of schooling and culture. Journal of Cross-Cultural Psychology, 12, 163-176.
8. Groen, G. J., & Resnick, L. B. (1977). Can pre-school children invent addition algorithms? Journal of Educational Psychology, 69, 645-652.
9. Guberman, S. (1993). Changing activities and skills: Links between the commercial transactions and arithmetical achievements of some Brazilian children. Symposium abstracts of the twelfth biennial meetings of the International Society for the Study of Behavioural Development (p. 199). Recife, Brazil: Universidade Federal de Pernambuco.
10. Hughes, M. (1986). Children and number. Oxford, UK: Blackwell.
11. Lave, J. (1977). Cognitive consequences of traditional apprenticeship training in Africa. Anthropology and Educational Quarterly, 7, 177-180.
12. Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge, UK: Cambridge University Press.
13. Nunes, T., & Bryant, P. E. (1992). Commutativity in multiplication. In W. Geeslin & K. Graham (Eds.), Proceedings of the sixteenth international conference for the Psychology of Mathematics Education (Vol. 3, p. 133). Durham: University of New Hampshire.
14. Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. New York: Cambridge University Press.
15. Petitto, A., & Ginsburg, H. (1982). Mental arithmetic in Africa and America: Strategies, principles, and explanations. International Journal of Psychology, 17, 81-102.
16. Piaget, J. (1952). The child's conception of number. New York: Norton.
17. Resnick, L. B. (1986). The development of mathematical intuition. In M. Perlmutter (Ed.), Minnesota Symposium on Child Psychology (Vol. 19, pp. 159-194). Hillsdale, NJ: Erlbaum.
18. Saxe, G. B. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale, NJ: Erlbaum.
19. Schliemann, A. D., & Acioly, N. M. (1989). Mathematical knowledge developed at work: The contribution of practice versus the contribution of schooling. Cognition and Instruction, 6, 185-221.
20. Schliemann, A. D., & Carraher, D. W. (1992). Proportional reasoning in and out of school. In P. Light & G. Butterworth (Eds.), Context and cognition. Hemel Hempstead, UK: Harvester-Wheatsheaf.
21. Schliemann, A. D., & Magalhães, V. P. (1990). Proportional reasoning: From shopping, to kitchens, laboratories, and, hopefully, schools. In G. Booker, P. Cobb, & T. N. de Mendicuti (Eds.), Proceedings of the fourteenth international conference for the Psychology of Mathematics Education (Vol. 3, pp. 67-73). Oaxtepec, Mexico: Program Committee of the 14th PME Conference.
22. Scribner, S. (1984). Studying working intelligence. In B. Rogoff & J. Lave (Eds.), Everyday cognition: Its development in social context (pp. 9-40). Cambridge, MA: Harvard University Press.
23. Scribner, S. (1986). Thinking in action: Some characteristics of practical thought. In R. Sternberg & D. Wagner (Eds.), Practical intelligence: Nature and origins of competence in the everyday world (pp. 13-30). New York: Cambridge University Press.
24. Vergnaud, G. (1981). L'Enfant, la mathématique et la réalité [Children, mathematics, and reality]. Bern, Switzerland: Peter Lang.
25. Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 141-161). Hillsdale, NJ: Erlbaum, and Reston, VA: National Council of Teachers of Mathematics.