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Visit to USA September 2001

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The files here are in PDF (portable document format) which may be read using Adobe Acrobat Reader on any PC, Unix Machine, or Macintosh computer.

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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’.

Overheads for talk.

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.b. Tall, D. (2000). Biological Brain, Mathematical Mind & Computational Computers (how the computer can support mathematical thinking and learning), Proceedings of ACTM, Chang Mai, Thailand.

2.c. David Tall & Marcia Maria Fusaro Pinto (2001). ‘Following students’ development in a traditional university classroom’, PME 25.

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).

3.a. David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Yudariah Yusof (2001). Symbols and the Bifurcation between Procedural and Conceptual Thinking, Canadian Journal of Science, Mathematics and Technology Education.

3.b. David Tall, Eddie Gray (2001) Relationships between embodied objects and symbolic procepts: an explanatory theory of success and failure in mathematics, PME 25