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The fundamental cycle of concept construction underlying various theoretical frameworks \ud

By John Pegg and David Tall

Abstract

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning. \u

Topics: QA, L1
Publisher: Springer
Year: 2005
OAI identifier: oai:wrap.warwick.ac.uk:478

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  1. (1998). A synthesis of Two Models: Interpreting Student Understanding in Geometry. In
  2. (1992). Assessing students’ understanding at the primary and secondary level in the mathematical sciences. In
  3. (2003). Assessment in Mathematics: a developmental approach.
  4. (1990). Cognitive development in real children: Levels and variations. In
  5. (1983). Conceptual Entities. In Dedre Gentner, Albert L. Stevens (Eds.), Mental Models,
  6. (2000). Consciousness: How Matter Becomes Imagination. doi
  7. (1991). Duality, Ambiguity and Flexibility in Successful Mathematical Thinking.
  8. (1994). Duality, ambiguity and flexibility: a proceptual view of simple arithmetic. doi
  9. (2004). Effect as a pivot between actions and symbols: the case of vector. Unpublished PhD thesis,
  10. (1999). Knowledge construction and diverging thinking doi
  11. (1984). Learning Mathematics: The cognitive science approach to mathematics education. doi
  12. (1991). Multimodal learning and the quality of intelligent behaviour. In
  13. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on processes and objects as different sides of the same coin, doi
  14. (1999). One theoretical perspective in undergraduate mathematics education research.
  15. (1991). Reflective Abstraction in Advanced Mathematical Thinking. doi
  16. (2001). Relationships between embodied objects and symbolic procepts: an explanatory theory of success and failure in mathematics.
  17. (1991). Situated Learning: Legitimate peripheral participation. doi
  18. (1986). Structure and Insight: a theory of mathematics education. New York: Academic Press. ___________ Authors Pegg,
  19. (1994). The Astonishing Hypothesis, doi
  20. (1977). The Essential Piaget doi
  21. (1992). The Mind’s Staircase: Exploring the conceptual underpinnings of children‘s thought and knowledge. doi
  22. (2004). Thinking through three worlds of mathematics. doi
  23. (1966). Towards a Theory of Instruction, doi

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