Exploring Probability in School pp 297-324 | Cite as

# Teaching and Learning the Mathematization of Uncertainty: Historical, Cultural, Social and Political Contexts

Chapter

## Keywords

Mathematics Education Subjective Probability Political Context National Curriculum School Subject
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- Ahlgren, A., & Garfield, J. (1991). Analysis of the probability curriculum. In R. Kapadia & M. Borovcnik (Eds.),
*Chance Encounters: Probability in Education*(pp. 107–134). Dordrecht, The Netherlands: Kluwer.Google Scholar - Amir, G. S., & Williams, J. S. (1999). Cultural influences on children's probabilistic thinking.
*Journal of Mathematical Behavior*,*18*(1), 85–107.CrossRefGoogle Scholar - Bennett, D. J. (1998).
*Randomness*. Cambridge, MA: Harvard University Press.Google Scholar - Bernstein, P. L. (1996).
*Against the gods: The remarkable story of risk*. New York: Wiley.Google Scholar - Best, J. (2001).
*Damned lies and statistics*. Berkeley, CA: University of California Press.Google Scholar - Biggs, N. L. (1979). The roots of combinatorics.
*Historia Mathematica, 6*, 109–136.CrossRefGoogle Scholar - Borovcnik, M., & Peard, R. (1996). Probability. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.),
*International handbook of mathematics education*(Part 1, pp. 239–287). Dordrecht, The Netherlands: Kluwer.Google Scholar - California Department of Education (2000).
*Mathematics framework for California public schools*. Sacramento, CA: Author.Google Scholar - Chaitin, G. J. (1975). Randomness and mathematical proof.
*Scientific American, 232*, 47–52.CrossRefGoogle Scholar - Daston, L. (1988).
*Classical probability in the enlightenment*. Princeton, NJ: Princeton University Press.Google Scholar - David, F. N. (1962).
*Games, gods, and gambling*. New York: Hafner Publishing Company.Google Scholar - Davis, P. J., & Hersh, R. (1986).
*Descartes' dream: The world according to mathematics*. Sussex, England: Harvester.Google Scholar - Department of Education (2003).
*National Curriculum Statement, Grades 10–12 (General): Mathematics*. Pretoria, South Africa: Government of South Africa. (http://education.pwv.gov.za/content/documents/112.pdf)Google Scholar - Department for Education and Employment (1999).
*Mathematics: The national curriculum for England*. London: Her Majesty's Stationery Office.Google Scholar - Doumbia, S. (1989). Mathematics in traditional African games. In C. Keitel, P. Damerow, A. Bishop, & P. Gerdes (Eds.),
*Mathematics, education, and society*(pp. 174–175). Paris: UNESCO.Google Scholar - Erickson, T. (2001).
*Data in depth: Exploring mathematics with Fathom*. Emeryville, CA: Key Curriculum Press.Google Scholar - Er-sheng, D. (1999). Mathematics curriculum reform facing the new century in China. In Z. Usiskin (Ed.),
*Developments in mathematics education around the world*. (Vol. 4, pp. 58–70). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Falk, R., & Konold, C. (1992). The psychology of learning probability. In F. Gordon & S. Gordon (Eds.),
*Statistics for the twenty-first century*(pp. 151–164). Washington, DC: Mathematical Association of America.Google Scholar - Finkelstein, M. O. (1998). Teaching statistics to law students. In L. Pereira-Mendoza, L. S. Kea, T. W. Kee, & W. K. Wong (Eds.),
*Proceedings of the Fifth International Conference on Teaching Statistics*(Vol. 1, pp. 505–511). Voorburg, The Netherlands: International Statistical Institute.Google Scholar - Finkelstein, M. O. & Levin, B. (1990).
*Statistics for lawyers*. New York: Springer-Verlag.Google Scholar - Fischbein, E. (1975).
*The intuitive sources of probabilistic thinking in children*. Dordrecht, The Netherlands: Reidel.Google Scholar - Fischbein, E. (1990). Training teachers for teaching statistics. In A. Hawkins (Ed.),
*Training teachers to teach statistics: Proceedings of the International Statistical Institute round table conference, Budapest, July, 1988*(pp. 48–58). Voorburg, The Netherlands: International Statistical Institute.Google Scholar - Franklin, J. (2001).
*The science of conjecture: Evidence and probability before Pascal*. Baltimore, MD: John Hopkins University Press.Google Scholar - Freudenthal, H. (1973).
*Mathematics as an educational task*. Dordrecht, The Netherlands: Reidel.Google Scholar - Gabriel, K. (1996).
*Gambler way: Indian gaming in mythology, history, and archaeology in North America*. Boulder, CO: Johnson Books.Google Scholar - Gal, I., & Garfield, J. B. (Eds.). (1997).
*The assessment challenge in statistics education*. Amsterdam, The Netherlands: IOS Press.Google Scholar - Garber, D., & Zabell, S. (1979). On the emergence of probability.
*Archive for History of Exact Sciences*,*21*(1), 33–52.CrossRefGoogle Scholar - Garfield, J., & Chance, B. (2000). Assessment in statistics education: Issues and challenges.
*Mathematical Thinking and Learning, 1/2*, 99–126.CrossRefGoogle Scholar - Greer, B. (2001). Understanding probabilistic thinking: The legacy of Efraim Fischbein.
*Educational Studies in Mathematics, 45*, 15–33.CrossRefGoogle Scholar - Griffiths, T. L., & Tenenbaum, J. B. (2001). Randomness and coincidences: Reconciling intuition and probability theory. In J. D. Moore & K. Stenning (Eds.),
*Proceedings of the 23*^{rd}*Annual Conference of the Cognitive Science Society*, Edinburgh, Scotland (pp. 370–375). Mahwah, NJ: Erlbaum.Google Scholar - Hacking, I. (1975).
*The emergence of probability*. Cambridge: Cambridge University Press.Google Scholar - Hacking, I. (1990).
*The taming of chance*. Cambridge: Cambridge University Press.Google Scholar - Harlow, L., Mulaik, S., & Steiger, J. (Eds.) (1997)
*What if there were no significance tests?*Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar - Hawkins, A. (Ed.). (1990).
*Training teachers to teach statistics: Proceedings of the International Statistical Institute round table conference, Budapest, July, 1988*. Voorburg, The Netherlands: International Statistical Institute.Google Scholar - Hawkins, A. (1996). Myth-conceptions. In C. Batanero (Ed.),
*Proceedings of the International Association for Statistical Education roundtable on research on the role of technology in teaching and learning statistics*(pp. 11–14). Granada, Spain: University of Granada.Google Scholar - Hawkins, P., & Hawkins, A. (1998a). Lawyers' likelihood. In L. Pereira-Mendoza, L. S. Kea, T. W. Kee, & W. K. Wong (Eds.),
*Proceedings of the Fifth International Conference on Teaching Statistics*(Vol. 1, pp. 525–531). Voorburg, The Netherlands: International Statistical Institute.Google Scholar - Hawkins, P., & Hawkins, A. (1998b). Lawyers' probability misconceptions and the implications for legal education.
*Legal Studies*,*18*(3), 316–335.CrossRefGoogle Scholar - Holmes, P. (2002, July).
*Some lessons to be learned from curriculum developments in statistics*. Paper presented at Sixth International Conference on Teaching Statistics, CapeTown, South Africa.Google Scholar - Holmes, P., & Rouncefield, M. (1989).
*From co-operation to co-ordination*. Sheffield, England: Centre for Statistical Education.Google Scholar - Howson, A. G. (1991).
*National curricula in mathematics*. Leicester, England: The Mathematical Association.Google Scholar - Ismael, A. (2001).
*An ethnomathematical study of Tchadji: About a Mancala type boardgame played in Mozambique and possibilities for its use in mathematics education*. Unpublished doctoral dissertation, University of the Witwatersrand, Johannesburg, South Africa.Google Scholar - Kaput, J. J., & Shaffer, D. W. (2002). On the development of human representational competence from an evolutionary point of view. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.),
*Symbolizing, modeling and tool use in mathematics education*(pp. 277–293). Dordrecht, The Netherlands: Kluwer.Google Scholar - Kline, M. (1972).
*Mathematical thought from ancient to modern times*. New York: Oxford University Press.Google Scholar - Kriiger, L., Daston, L. J., & Heidelberger, M. (1987).
*The probabilistic revolution*. Cambridge, MA: MIT Press.Google Scholar - Lamprianou, I., & Afantiti Lamprianou, T. (2002). The nature of students' probabilistic thinking in primary schools in Cyprus. In A. D. Cockburn & E. Nardi (Eds.),
*Proceedings of the 26*^{th}*Conference of the International Group for the Psychology of Mathematics Education*(Vol 3. pp. 273–280). Norwich, England: University of East Anglia.Google Scholar - Metz, K. E. (1997). Dimensions in the assessment of students' understanding and application of chance. In I. Gal & J. B. Garfield (Eds.),
*The assessment challenge in statistics education*(pp. 223–238). Amsterdam, The Netherlands: IOS Press.Google Scholar - Metz, K. E. (1998). Emergent ideas of chance and probability in primary-grade children. In S. P. Lajoie (Ed.),
*Reflections on statistics: Learning, teaching, and assessment in grades K-12*(pp. 149–174). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar - Moore, D. S. (1997). Probability and statistics in the core curriculum. In J. Dossey (Ed.),
*Confronting the core curriculum*(pp. 93–98). Washington, DC: Mathematical Association of America.Google Scholar - National Council of Teachers of Mathematics (2000).
*Principles and standards for school mathematics*. Reston, VA: Author.Google Scholar - Nemetz, T. (1997). State of the art of teaching probability at secondary level. In B. Phillips (Ed.),
*Papers on statistical education presented at ICME-8, Seville, Spain, July 14–21, 1996*(pp. 75–86). Hawthorn, Australia: Swinburne University of Technology.Google Scholar - Nobre, S. R. (1989). The ethnomathematics of the most popular lottery in Brazil: The “Animal Lottery”. In C. Keitel, P. Damerow, A. Bishop, & P. Gerdes (Eds.),
*Mathematics, education, and society*(pp. 175–177). Paris: UNESCO.Google Scholar - Parzysz, B. (2003, August).
*From frequency to probability: Some questions posed by the new French senior high school curricula*. Invited paper at 54^{th}Conference of the International Statistics Institute, Berlin.Google Scholar - Paulos, J. A. (1996).
*A mathematician reads the newspaper*. New York: Anchor Books.Google Scholar - Piaget, J., & Inhelder, B. (1975).
*The origin of the idea of chance in children*(L. Leake, Jr., P. Burrell, & H. D. Fischbein, Trans.). London: Routledge and Kegan Paul. (Original work published in 1951)Google Scholar - Polaki, M. V. (2002). Using instruction to identify key features of Basotho elementary students' growth in probabilistic thinking.
*Mathematical Thinking and Learning*,*4*(4), 285–313.CrossRefGoogle Scholar - Selin, H. (Ed.). (2000).
*Mathematics across cultures: The history of non-Western mathematics*. Dordrecht, The Netherlands: Kluwer.Google Scholar - Shaughnessy, J. M. (1992). Research in probability and statistics: Reflection and directions. In D. Grouws (Ed.),
*Handbook of research on mathematics teaching and learning*(pp. 465–494). New York/ Reston, VA: Macmillan/ National Council of Teachers of Mathematics.Google Scholar - Shaughnessy, J. M. (2003). Research on students' understandings of probability. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.),
*A research companion to “Principles and standards for school mathematics”*(pp. 216–226). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Skovsmose, O. (2000). Aporism and critical mathematics education.
*For the Learning of Mathematics*,*20*(1), 2–8.Google Scholar - Stewart, I. (1989).
*Does Godplay dice?*London: Penguin.Google Scholar - Truran, J. (2001).
*The teaching and learning of probability, with special reference to South Australian schools from 1959–1994*. Doctoral thesis, Adelaide University, Australia. [Online:http://thesis.library.adelaide.edu.au/public/adt-SUA20020902.154115/]Google Scholar - Van Dooren, W. (2003, November). Personal communication.Google Scholar
- Varga, T. (1983). Statistics in the curriculum for everyone–how young children and their teachers react. In D. R. Grey, P. Holmes, V. Barnett, & G. M. Constable (Eds.),
*Proceedings of the First International Conference on Teaching Statistics*(pp. 71–80). Sheffield, England: Statistics Teaching Trust.Google Scholar - Yager, R. R., Ovchinnikov, S., Tong, R. M., & Nguyen, H. T. (1987).
*Fuzzy sets and applications: Selected papers by L. A. Zadeh*. New York: Wiley.Google Scholar - Zaslavsky, C. (1973).
*Africa counts: Number and patterns in African culture*. Boston: Prindle, Weber, and Schmidt.Google Scholar

## Copyright information

© Springer Science+Business Media, Inc. 2005