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Abstraction and consolidation of the limit procept by means of instrumented schemes: the complementary role of three different frameworks

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Abstract

I investigate the contributions of three theoretical frameworks to a research process and the complementary role played by each. First, I describe the essence of each theory and then follow the analysis of their specific influence on the research process. The research process is on the conceptualization of the notion of limit by means of the discrete continuous interplay. I investigate the influence of the different perspectives on the research process and realize that the different theoretical approaches intertwine. Moreover, I realize that the research study demanded the contribution of more than one theoretical approach to the research process and that the differences between the frameworks could serve as a basis for complementarities.

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Acknowledgements

A preliminary and partial version of this research was presented (Kidron 2006) in the working group on theoretical perspectives in mathematics education at CERME 4. I would like to thank the coordinator, Tommy Dreyfus, as well as the co-organizers of the working group for the fruitful discussions we had which influenced the analysis presented in this paper. I also thank the reviewers for their important remarks on the previous version of this paper.

The research was supported by Israel Science Foundation grant number 1340/05.

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  1. Department of Applied Mathematics, Jerusalem College of Technology, Havaad Haleumi Str. 21, POB 16031, Jerusalem, 91160, Israel

    Ivy Kidron

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Kidron, I. Abstraction and consolidation of the limit procept by means of instrumented schemes: the complementary role of three different frameworks. Educ Stud Math 69, 197–216 (2008). https://doi.org/10.1007/s10649-008-9132-6

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