Abstract
One of the fundamental ideas of modern education is the idea of spiral curriculum, when students repeatedly revisit the same sequence of topics at the increasing levels of depth, detail, and sophistication. In this chapter, we show that under reasonable assumptions, the optimal sequence of presenting the material should indeed follow a spiral pattern.
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References
O. Kosheleva, Spiral curriculum: towards mathematical foundations, in Proceedings of the International Conference on Information Technology InTech’07, Sydney, Australia, 12–14 December 2007. pp. 152–157
H. Gardner, Jerome S. Bruner, in Fifty Modern Thinkers on Education. From Piaget to the present, ed. by J.A. Palmer (Routledge, London, 2001)
J. Bruner, The Process of Education (Harvard University Press, Cambridge, 1960)
J.S. Bruner, Toward a Theory of Instruction (Belkapp Press, Cambridge, 1966)
J.S. Bruner, The Relevance of Education (Norton, New York, 1971)
J. Bruner, Child’s Talk: Learning to Use Language (Norton, New York, 1983)
J. Bruner, Actual Minds, Possible Worlds (Harvard University Press, Cambridge, 1986)
J. Bruner, The Culture of Education (Harvard University Press, Cambridge, 1996)
J. Bruner, J. Goodnow, A. Austin, A Study of Thinking (Wiley, New York, 1956)
A. Finkelstein, O. Kosheleva, V. Kreinovich, Astrogeometry, error estimation, and other applications of set-valued analysis. ACM SIGNUM Newsl. 31(4), 3–25 (1996)
A. Finkelstein, O. Kosheleva, V. Kreinovich, Astrogeometry: towards mathematical foundations. Int. J. Theor. Phys. 36(4), 1009–1020 (1997)
S. Li, Y. Ogura, V. Kreinovich, Limit Theorems and Applications of Set Valued and Fuzzy Valued Random Variables (Kluwer Academic Publishers, Dordrecht, 2002)
R. Aló, O. M. Kosheleva, Optimization techniques under uncertain criteria, and their possible use in computerized education, in Proceedings of the 25th International Conference of the North American Fuzzy Information Processing Society NAFIPS’2006, Montreal, Quebec, Canada, IEEE Press, Piscataway, New Jersey, 3–6 June 2006
O.M. Kosheleva, R. Aló, Towards economics of education: optimization under uncertainty, in Proceedings of the Second International Conference on Fuzzy Sets and Soft Computing in Economics and Finance FSSCEF’2006, St. Petersburg, Russia, June 28– July 1, 2006, pp. 63–70
H. Busemann, The Geometry of Geodesics (Academic Press, New York, 1955)
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Kosheleva, O., Villaverde, K. (2018). Spiral Curriculum: Towards Mathematical Foundations. In: How Interval and Fuzzy Techniques Can Improve Teaching. Studies in Computational Intelligence, vol 750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55993-2_15
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DOI: https://doi.org/10.1007/978-3-662-55993-2_15
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