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The Longitudinal Study

  • Carolyn A. Maher
Part of the Mathematics Education Library book series (MELI, volume 47)

Abstract

Where do new ideas come from? Our view is that building new ideas is a process; new ideas come from old ideas that are revisited, reviewed, extended, and connected(Davis, 1984; Maher & Davis, 1995). Building new ideas also involves the retrievaland modification of representations of existing ideas.

Keywords

Mathematical Idea Teacher Development Elementary Grade Problem Task Classroom Session 
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.

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References

  1. Bruner, J. (1960). The process of education. Cambridge, MA: Harvard University Press.Google Scholar
  2. Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  3. Davis, R. B., & Maher, C. A. (Eds.). (1993). Schools, mathematics, and the world of reality. Needham, MA: Allyn & Bacon.Google Scholar
  4. Davis, R. B., & Maher, C. A. (1997). How students think: The role of representations. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 93–115). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  5. Francisco, J. M., & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. Journal of Mathematical Behavior, 24(2/3), 361–372.CrossRefGoogle Scholar
  6. Landis, J. H. (1990). Teachers’ prediction and identification of children’s mathematical behaviors: Two case studies. Unpublished doctoral dissertation, Rutgers, The State University of New Jersey, New Brunswick, NJ.Google Scholar
  7. Landis, J. H., & Maher, C. A. (1989). Observations of Carrie, a fourth grade student, doing mathematics. Journal of Mathematical Behavior, 8(1), 3–12.Google Scholar
  8. Maher, C. A. (1988). The teacher as designer, implementer, and evaluator of children’s mathematical learning environments. The Journal of Mathematical Behavior, 6, 295–303.Google Scholar
  9. Maher, C. A. (2002). How students structure heir own investigations and educate us: What we have learned from a fourteen year study. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the twenty-sixth annual meeting of the International Group for the Psychology of Mathematics Education (PME26) (Vol. 1, pp. 31–46). Norwich, England: School of Education and Professional Development, University of East Anglia.Google Scholar
  10. Maher, C. A. (2005). How students structure their investigations and learn mathematics: Insights from a long-term study. Journal of Mathematical Behavior, 24(1), 1–14.CrossRefGoogle Scholar
  11. Maher, C. A. (2008). The development of mathematical reasoning: A 16-year study (Invited Senior Lecture for the 10th International Congress on Mathematics Education, published in book with electronic CD). In M. Niss (Ed.), Proceedings of ICME 10 2004. Roskilde, DK: Roskilde University, IMFUFA, Department of Science, Systems and Models.Google Scholar
  12. Maher, C. A., & Davis, R. B. (1995). Children’s explorations leading to proof. In C. Hoyles & L. Healy (Eds.), Justifying and proving in school mathematics (pp. 87–105). London: Mathematical Sciences Group, Institute of Education, University of London.Google Scholar
  13. Maher, C. A., & Martino, A. M. (1996a). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education, 27(2), 194–214.CrossRefGoogle Scholar
  14. Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. Journal of Mathematical Behavior, 18(1), 53–78.CrossRefGoogle Scholar
  15. O’Brien, M. (1994). Changing a school mathematics program: A ten-year study. Unpublished doctoral dissertation, Rutgers, the State University of New Jersey, New Brunswick, NJ.Google Scholar
  16. Sfard, A. (2001). Learning mathematics as developing a discourse. In R. Speiser, C. Maher, & C. Walter (Eds.), Proceedings of 21st conference of PME-NA (pp. 23–44). Columbus, OH: Clearing House for Science, Mathematics, and Environmental Education.Google Scholar
  17. Torkildsen, O. (2006). Mathematical archaeology on pupils’ mathematical texts. Un-earthing of mathematical structures. Unpublished doctoral dissertation, Oslo University, Oslo.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Graduate School of Education, Rutgers UniversityNew BrunswickUSA

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