Dynamic mathematics and the blending of knowledge structures in the calculus
 David O. Tall
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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 processobject encapsulation by blending embodiment and symbolism.
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 Title
 Dynamic mathematics and the blending of knowledge structures in the calculus
 Journal

ZDM
Volume 41, Issue 4 , pp 481492
 Cover Date
 20090801
 DOI
 10.1007/s1185800901926
 Print ISSN
 18639690
 Online ISSN
 18639704
 Publisher
 SpringerVerlag
 Additional Links
 Authors

 David O. Tall ^{(1)}
 Author Affiliations

 1. Institute of Education, University of Warwick, Coventry, CV4 7AL, UK