Advertisement

Principles of Instructional Design for Supporting the Development of Students’ Statistical Reasoning

  • Paul Cobb
  • Kay McClain

Keywords

Design Principle Instructional Design Statistical Reasoning Exploratory Data Analysis Data Generation Process 
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.

Unable to display preview. Download preview PDF.

References

  1. Biehler, R. (1993). Software tools and mathematics education: The case of statistics. In C. Keitel & K. Ruthven (Eds.), Learning from computers: Mathematics education and technology (pp. 68–100). Berlin: Springer.Google Scholar
  2. Biehler, R., & Steinbring, H. (1991). Entdeckende Statistik, Strenget-und-Blatter, Boxplots: Konzepte, Begrundungen und Enfahrungen eines Unterrichtsversuches [Explorations in statistics, stem-and-leaf, boxplots: Concepts, justifications, and experience in a teaching experiment]. Der Mathematikunterricht, 37(6), 5–32.Google Scholar
  3. Bransford, J., Brown, A. L., & Cocking, R. R. (Eds.) (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.Google Scholar
  4. Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104, 801–823.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Cobb, P. (1999). Individual and collective mathematical learning: The case of statistical data analysis. Mathematical Thinking and Learning, 1, 5–44.CrossRefGoogle Scholar
  6. Cobb, P., McClain, K., & Gravemeijer, K. P. E. (2003). Learning about statistical covariation. Cognition and Instruction, 21, 1–78.CrossRefGoogle Scholar
  7. Cobb, P., & Tzou, C. (2000). Learning about data creation. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.Google Scholar
  8. de Lange, J., van Reeuwijk, M., Burrill, G., & Romberg, T. (1993). Learning and testing mathematics in context. The case: Data visualization. Madison: University of Wisconsin, National Center for Research in Mathematical Sciences Education.Google Scholar
  9. Dewey, J. (1981). Experience and nature. In J. A. Boydston (Ed.), John Dewey: The later works, 1925–1953 (Vol. 1). Carbondale: Southern Illinois University Press.Google Scholar
  10. Dorfler, W. (1993). Computer use and views of the mind. In C. Keitel & K. Ruthven (Eds.), Learning from computers: Mathematics education and technology (pp. 159–186). Berlin: Springer-Verlag.Google Scholar
  11. Gravemeijer, K. E. P. (1994) Developing realistic mathematics education. Utrecht, The Netherlands: CD-B Press.Google Scholar
  12. Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic inquiry with data: Critical barriers to classroom implementation. Educational Psychologist, 27, 337–364.CrossRefGoogle Scholar
  13. Kaput, J. J. (1991). Notations and representations as mediators of constructive processes. In E. von Glasersfeld (Ed.), Constructivism in mathematics education (pp. 53–74). Dordrecht, The Netherlands: Kluwer.CrossRefGoogle Scholar
  14. Konold, C., & Higgins, T. (in press). Working with Data. In S. J. Russell & D. Schifter & V. Bastable (Eds.), Developing Mathematical Ideas: Collecting, Representing, and Analyzing Data. Parsippany, NJ: Seymour.Google Scholar
  15. Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (1996, July). Students’ analyzing data: Research of critical barriers. Paper presented the Roundtable Conference of the International Association for Statistics Education, Granada, Spain.Google Scholar
  16. Latour, B. (1987). Science in action. Cambridge, MA: Harvard University Press.Google Scholar
  17. Lehrer, R., & Romberg, T. (1996). Exploring children’s data modeling. Cognition and Instruction, 14, 69–108.CrossRefGoogle Scholar
  18. McClain, K. (2002). Teacher’s and students’ understanding: The role of tools and inscriptions in supporting effective communication. Journal of the Learning Sciences, 11, 216–241.CrossRefGoogle Scholar
  19. McClain, K., Cobb, P., & Gravemeijer, K. (2000). Supporting students’ ways of reasoning about data. In M. Burke (Ed.), Learning mathematics for a new century (2001 Yearbook of the National Council of Teachers of Mathematics, pp. 174–187). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  20. McGatha, M. (2000). Instructional design in the context of classroom-based research: Documenting the learning of a research team as it engaged in a mathematics design experiment. Unpublished dissertation, Vanderbilt University, Nashville, TN.Google Scholar
  21. McGatha, M., Cobb, P., & McClain K. (1999, April). An analysis of student’s initial statistical understandings. Paper presented at the annual meeting of the American Educational Research Association, Montreal.Google Scholar
  22. Meira, L. (1998). Making sense of instructional devices: The emergence of transparency in mathematical activity. Journal for Research in Mathematics Education, 29, 121–142.CrossRefGoogle Scholar
  23. Noss, R., Pozzi, S., & Hoyles, C. (1999). Touching epistemologies: Statistics in practice. Educational Studies in Mathematics, 40, 25–51.CrossRefGoogle Scholar
  24. Pea, R. D. (1993). Practices of distributed intelligence and designs for education. In G. Salomon (Ed.), Distributed cognitions (pp. 47–87). New York: Cambridge University Press.Google Scholar
  25. Roth, W. M. (1997). Where is the context in contextual word problems? Mathematical practices and products in grade 8 students’ answers to story problems. Cognition and Instruction, 14, 487–527.CrossRefGoogle Scholar
  26. Saldanha, L. A., & Thompson, P. W. (2001). Students’ reasoning about sampling distributions and statistical inference. In R. Speiser & C. Maher (Eds.), Proceedings of the Twenty Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (vol. 1, pp. 449–454), Snowbird, Utah. ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH.Google Scholar
  27. Shaughnessey, J. M., Garfield, J., & Greer, B. (1996). Data handling. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (part 1, pp. 205–237). Dordrecht, The Netherlands: Kluwer.Google Scholar
  28. Wiggins, G., & McTighe, J. (1998). Understanding by design. Alexandria, VA: Association for Curriculum and Supervision.Google Scholar
  29. Wilensky, U. (1997). What is normal anyway? Therapy for epistemological anxiety. Educational Studies in Mathematics, 33, 171–202.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Paul Cobb
    • 1
  • Kay McClain
    • 1
  1. 1.Vanderbilt UniversityUSA

Personalised recommendations