, Volume 41, Issue 4, pp 481–492 | Cite as

Dynamic mathematics and the blending of knowledge structures in the calculus

  • David O. Tall
Original Article


This paper considers the role of dynamic aspects of mathematics specifically focusing on the calculus, including computer software that responds to physical action to produce dynamic visual effects. The development builds from dynamic human embodiment, uses arithmetic calculations in computer software to calculate ‘good enough’ values of required quantities and algebraic manipulation to develop precise symbolic values. The approach is based on a developmental framework blending human embodiment, with the symbolism of arithmetic and algebra leading to the formalism of real numbers and limits. It builds from dynamic actions on embodied objects to see the effect of those actions as a new embodiment that needs to be calculated accurately and symbolised precisely. The framework relates the growth of meaning in history to the mental conceptions of today’s students, focusing on the relationship between potentially infinite processes and their consequent embodiment as mental concepts. It broadens the strategy of process-object encapsulation by blending embodiment and symbolism.


Mathematical Thinking Solution Curve Slope Function Limit Concept Short Line Segment 
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Copyright information

© FIZ Karlsruhe 2009

Authors and Affiliations

  1. 1.Institute of EducationUniversity of WarwickCoventryUK

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