Visit to USA September 2001
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This page has downloadable files related to talks given at Penn State, University of Massachusetts at Dartmouth, University of Illinois at Chicago, and planned, but cancelled after the crisis of September 11th, for the RUMEC conference at Chicago, and Arizona State at Pheonix. Papers relate to three main headings, Technology and Calculus, Visualization and Proof in Calculus and Mathematical Analysis, The Theory of Procepts.
This is the draft chapter for the book on Research in the use of Technology in the Teaching and Learning of Mathematics. It is to be discussed at Penn State, and then completed for publication.
1.a. Tall, D, Smith, D, and Piez C. (in preparation). A draft of ‘Technology and Calculus’.
This seminar is a reflection on research into the contrasting effects of visualisation and proof in Calculus and Analysis. It is based on ideas from four main sources: A review of research on using technology in calculus (2.a); the value of the computer in mathematical thinking, particularly that part of the paper on conceptual ideas on visual calculus (2.b); different ways of approaching proof in mathematics (natural/visual and formal) (2.c); how a natural/visual approach can lead to a natural formalist approach that underpins logic with visual thought experiments (2.d). The papers concerned are:
2.a. Tall, D, Smith, D, and Piez C. (in preparation). A draft of ‘Technology and Calculus’ (as above).
2.d. David Tall (2001), Natural and Formal Infinities, Educational Studies in Mathematics.
Many symbols in mathematics operate flexibly and ambiguously as both process and concept. These are termed ‘procepts’. These occur throughout arithmetic, algebra, calculus. The presentation will focus on two papers, the first a broad discussion of the development of procepts in mathematics (3.a); the second a new theoretical development relating procepts to visual imagery (3.b).
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