Seminars in Bogota, Columbia, July 25, 2002
Biological Brain, Mathematical Mind and Technological Tools.
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. 

Click here to download a copy of Acrobat Reader for your computer. 
My presentations focus on the way that human beings use a biological brain to build a mathematical mind using technological tools. The group in Columbia base their work on the use of the TI92. My perception is that this provides a part of a wider scenario in which we build up conceptual structures by perception, action and reflection.I put forward the theory that these three activities produce three fundamentally different worlds of mathematics which I term the EMBODIED, SYMBOLICPROCEPTUAL and FORMAL. The embodied world underpins all our activities. It begins with our perceptions and actions on the actual world and through the use of language for internal and interpersonal communication, it builds from perceptual representations to platonic representations. The proceptual world is the world of calculation in arithmetic and symbolmanipulation in algebra and symbolic calculus. It uses very special symbols (called ‘procepts’) which can function either as a process (such as addition) or as a concept (such as sum). This special type of symbol ideally suits the human need to do mathematics by carrying out calculations and manipulations and to think about the concepts of mathematics. Later maturity in embodied and proceptual mathematics leads to our recognising many properties of the concepts we study until we are able to take these properties and use them as fundamental axioms and definitions as a basis of a coherent formal structure of theorems and proof.
The four days each focus on a different aspect of the theory, beginning with an overview on the first day, then successive days on embodied aspects (with particular application to calculus), proceptual development of symbols, and the development of formal proof.
The overheads for the seminars are downloadable for private study.
Photographs taken at the Seminar can be found here.
Workshop: from embodied to formal geometry using Cabri on the TI92.
Workshop: Visual Calculus using the TI92.
Workshop: Programming in Calculus using the TI92.
Workshop: Summarising the week’s ideas, and, if time permits, a final session on ProblemSolving and Proof.
last modified: 