TITLE:

TEN MIRANDEAN PRINCIPLES FOR TEACHING, LEARNING, AND CREATING MATH

DATE:

Monday, April 28th, 2008

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Guillermo Miranda, Universidad Central de Venezuela

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 Castillo

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