Combinatorics and Reasoning pp 3-8 | Cite as

# The Longitudinal Study

Chapter

## 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.

## Preview

Unable to display preview. Download preview PDF.

## References

- Bruner, J. (1960).
*The process of education*. Cambridge, MA: Harvard University Press.Google Scholar - Davis, R. B. (1984).
*Learning mathematics: The cognitive science approach to mathematics education*. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar - Davis, R. B., & Maher, C. A. (Eds.). (1993).
*Schools, mathematics, and the world of reality*. Needham, MA: Allyn & Bacon.Google Scholar - 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 - 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 - 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 Unpublished doctoral dissertation, Rutgers, The State University of New Jersey, New Brunswick, NJ.Google Scholar - Landis, J. H., & Maher, C. A. (1989).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 - 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 - 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 - 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 - 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
- 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 - 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 - 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 - 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 - 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 - 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