Abstract
Everyday Mathematics has contributed in important ways to long-standing debates about mathematical concepts, symbolic representation, and the role of contexts in thinking—the latter topic reaching back at least as far as Kant’s notion of scheme. The descriptive work plays a role, of course. But it is only by making sense of the observations that science moves forward. If over time the expression Everyday Mathematics drops from usage, I would be neither surprised nor disappointed. Eventually the field needs to become absorbed into the mainstream traditions of research in mathematics education. However it would be disappointing if it is remembered only for its descriptive and proscriptive aspects, without recognizing the contributions to research, theory, and the cultural context of learning and thinking.
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Notes
A quarter of the children repeated first grade; another quarter dropped out of school.
The majority of students from middle class on up attended private schools.
The investigation of school failure was carried out before the first street vendor study; it was published after it, however.
In fairness, I don’t believe that the authors fall into this trap in their section, “What is ‘real’ mathematics?” Their use of single quotation around the word real serves to distance them from the remarks made by supermarket shoppers.
The expression, “real number line” denotes not a number line that is real but instead a line on which the “real numbers” are located.
A place value number systems assigns values to each digit based on its left-to-right location along a string of digits. That is why the strings 253, 235, 523, 532, 325 and 352 represent unique values even though the digits are the same in each case.
Note that this law says nothing about procedures for adding two numbers. A + B = B + A is not a method.
They are the Field Axioms or more correctly, the commutative ring axioms (Bass 2008).
By semi-invented I mean those algorithms that are an amalgam of introduced conventions and the student’s own fashioning.
References
Aleksandrov, A. D. (1989). A general view of mathematics (S. H. Gould, T. Bartha & K. Kirsh, Trans.). In A. D. Aleksandrov, A. N. Kolmogorov & M. A. Lavrent’ev (Eds.), Mathematics, its content, methods, and meaning (pp. 1–64). Cambridge, MA: MIT Press.
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: toward a practice-based theory of professional education. In G. Sykes & L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). San Francisco: Jossey Bass.
Bass, H. (2008). On the field axioms and the commutative ring axioms. Email message to D. W. Carraher, Jan. 18, 2008. Ann Arbor, MI.
Carraher, D. W. (1984a). Oral and written mathematics. Invited presentation delivered at MRC Cognition and Brain Sciences Unit, Cambridge, UK, June.
Carraher, D. W. (1984b). Oral and written mathematics. Invited presentation delivered at MRC Unit, London, UK, June.
Carraher, T. N. (1989). Sociedade e inteligência. São Paulo: Cortez Editora.
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” in the school: the cultural contexts of learning mathematics.). Cadernos de Pesquisa, 42, 79–86.
Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology, 3(21), 21–29.
Carraher, T. N., & Schliemann, A. D. (1983). Fracasso escolar: uma questão social. (School failure: a social issue). Cadernos de Pesquisa, 45, 3–l9.
Carraher, D. W., & Schliemann, A. D. (2002). Is everyday mathematics truly relevant to mathematics education? In J. Moshkovich & M. Brenner (Eds.), Monographs of the Journal for Research in Mathematics Education (Vol. 11—Everyday and academic mathematics, pp. 131–153).
Carraher, D. W., Schliemann, A. D., & Schwartz, J. L. (2007). Early algebra is not the same as algebra early. In J. Kaput, D. W. Carraher & M. Blanton (Eds.), Algebra in the early grades. Mahwah: Erlbaum.
Cole, M., Gay, J., Glick, J., & Sharp, D. (1971). The cultural context of learning and thinking: an exploration in experimental anthropology. New York: Basic.
Gould, S. J. (1996). The mismeasure of man. New York: Norton.
Greiffenhagen, C., & Sharrock, W. (2008). School mathematics and its everyday other? Revisiting Lave’s ‘Cognition in Practice’. Educational Studies in Mathematics. DOI 10.1007/s10649-008-9115-7.
Labov, W. (1969). The logic of nonstandard English. Georgetown Monographs on Language and Linguistics, 22, 1–31.
Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge: Cambridge University Press.
Leacock, E. B. (1971). The culture of poverty: A critique. New York: Simon & Schuster.
Menninger, K. (1992). Number words and number symbols: A cultural history of numbers. New York: Dover.
Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.
Reed, H. J., & Lave, J. (1979). Arithmetic as a tool for investigating relations between culture and cognition. American Ethnologist, 6(3), 568–582.
Resnick, L. B. (1986). The development of mathematical intuition. In M. Perlmutter (Ed.) Perspectives on intellectual development: The Minnesota Symposium on Child Psychology, vol. 19 (pp. 159–194). Hillsdale: Erlbaum.
Resnick, L. B. (1987). Learning in school and out. Educational Researcher, 13–20.
Rosenhan, D. L. (1973). On being sane in insane places. Science, 179, 25–58.
Ryan, W. (1976). Blaming the victim (rev. ed.). New York: Vintage.
Saxe, G. B. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale: Erlbaum.
Schliemann, A. D., Araujo, C., Cassundé, M. A., Macedo, S., & Nicéas, L. (1998). Multiplicative commutativity in school children and street sellers. Journal for Research in Mathematics Education, 29(4), 422–435.
Scribner, S. (1984). Studying working intelligence. In B. Rogoff & J. Lave (Eds.), Everyday cognition: Its development and social context (pp. 9–40). Cambridge: Harvard University Press.
Vergnaud, G. (1979). The acquisition of arithmetical concepts. Educational Studies in Mathematics, 10(2), 263–274.
Vergnaud, G. (1985). Concepts et schèmes dans une théorie opératoire de la représentation. (Concepts and schemes in an operational theory of representation). Psychologie Française, 30(3/4), 245–251.
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Carraher, D.W. Beyond ‘blaming the victim’ and ‘standing in awe of noble savages’: a response to “Revisiting Lave’s ‘cognition in practice’”. Educ Stud Math 69, 23–32 (2008). https://doi.org/10.1007/s10649-008-9126-4
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DOI: https://doi.org/10.1007/s10649-008-9126-4