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Colloquia Archive
Untitled Document
| DATE: |
Monday, April 28th, 2008 |
| TITLE: |
TEN MIRANDEAN PRINCIPLES FOR TEACHING, LEARNING, AND CREATING
MATH |
| TIME: |
3:30 PM |
| LOCATION: |
GMCS 214 |
| SPEAKER: |
Guillermo Miranda
Universidad Central de Venezuela
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| ABSTRACT: |
A long teaching and research experience has
led the author to synthetize into 10 simple guiding rules, called "Mirandean
Principles", the ways used by mathematicians (often unconsciously)
to formulate definitions, theories and problems, as well as to motivate
the how to solve the questions posed.
In this talk, a number of elementary mathematical questions are illuminated
from this point of view, exemplifying the use of one or several of these
10 principles.Even humanistically minded persons can get a true understanding
of theorems or procedures, which, otherwise, would remain either abstruse
or mechanically memorized.
The 10 Principles are:
1) Interpret Definitions and Theorems as a "stage play"
2) Change of Plane or Dimension
3) Creation by "baptizing"
4) Change everything so that everything stays the same
5) Change point of view and look for the most convenient perspective
6) "Walk around" obstructions or difficulties
7) The totality is the sum (or union) of the parts
8) Search for the new unknown at the old known or in the boundaries (or
limit) of the old known
9) Analysis and Synthesis (Motivation for the defining integrals, fluxes,
etc)
10) Use curved mirrors to illustrate isomorphisms between mathematical structures
apparently different. (For example, different matrix representations of
a single linear transformation, or positive real numbers under multiplication
and real numbers under addition via Logarithms).
Systematic use of these tools starting with kids and also in the first semesters
for undergraduates would enhance their mathematical ability as well as their
performance where math is used, as in physics or chemistry. |
| HOST: |
Jose E. Castillo |
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Computational Science Research Center :: 5500 Campanile Drive :: San Diego, CA 92182-1245 :: (619) 594-3430
©2007 Computational Science Research Center, SDSU - All rights
reserved.
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Last
updated:
May 6, 2008 10:11 AM
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