Modelling Both Complexity and Abstraction: A Paradox?

New ICMI Study Series

Volumn 10, Issue , 2007, Pages 233-240

  Singer, Mihaela ^a  

^a Institute for Educational Sciences   (Romania)

Author keywords

Conceptual System; Dual Relationship; Incompleteness Theorem; Representational Power; Uncertainty Principle

Indexed keywords

EID: 85067958581     PISSN: 13876872     EISSN: 22151745     Source Type: Book Series    
DOI: 10.1007/978-0-387-29822-1_24     Document Type: Chapter

References (10)

1. Abbot, E. (1884), Flatland: A Romance of Many Dimensions. Mineola, NY: Dover Thrift Editions.
2. Bar-Yam, Y. (1997). Dynamics of complex systems. Boston: Addison-Wesley Longman Inc.
3. Doerr, H., & Lesh, R. A. (2003). Beyond constructivism: Models and modelling perspectives on mathematics teaching, learning, and problem solving. New York: LEA.
4. Fischer, K.W., & Yan, Z. (2002). Always under construction: Dynamic variations in adult cognitive microdevelopment. Human Development, ^5(3), 141-160.
5. Quartz, S., & Sejnowsky, T. J. (1997). The neural basis of cognitive development: A constructivist manifesto. Behavioral and Brain Sciences 20(4), 537-596.
6. Schwartz, J. L. (1998). Models, simulations and exploratory environments: A tentative taxonomy. From http://www.gse.harvard.edu~faculty/schwartz/modeltaxonomy.
7. Singer, F. M. (Ed.). (1999). The new National Curriculum. Bucharest: Prognosis P. H.
8. Singer, F, M. (2001). Structuring the information-a new way of perceiving the content of learning. Zentralblattfur Didaktik der Mathematik IIRME 61, 204-217.
9. Singer, F. M. (2003). From cognitive science to school practice: Building the bridge. In N.A. Pateman, B.J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2f^ PME, CRDG (pp. 207-214).
10. Usiskin, Z. (2006). The arithmetic operations as mathematical models. This Volume, Chapter 3.3.5.