Mathematics Education: Taking a Clue
From the Recent Technological Revolution
An Object Oriented Pitch
Object oriented methodology has a proven track record.
Object orientation appears congenial to human problem solving facilities.
Object-oriented ideas permeate mathematics.
In hardware industries, it found expression in the invention of integrated circuits and off-the-shelf-component architecture.
It saved software industry by enabling common programmers to produce sophisticated and reasonably reliable software. Even more importantly, it made the software maintenance task feasible.
In the automotive industry, it resulted in cost reduction by
standardizing parts between various cars. (This is an exercise. Can you
explain how the OO methodology might have played a role in the auto industry?)
Technology moves into the classroom. This may be the right time to move
there the underlying methodology as well.
Object orientation suggests a few pedagogical principles:
- Distinguish between abstract and concrete: by all means teach concrete
but learn abstract.
- Present concrete with abstract in mind.
Concrete problems must be presented so as to underscore their similarities
and differences. Do not mix different concepts in a single concrete device.
For example, counting has nothing to do with the numerals or the decimal
system.
- Start from the concept, not method for its presentation.
Manipulatives are not the end goal of education. Use them to present
concepts, if necessary.
- Grasp the difference between the abstract and the class. Class is a concrete description of the abstract. A concept that can't be represented as an object class may be too broad an abstraction to teach.
- Be consistent and honest across selection of presentation vehicles.
If using measurements is a proper way to introduce geometric concepts,
then using the Roman numerals is a good way to introduce counting.
- Emphasize relationship between concepts.
- Expand Polya's approach with
- Finding concepual context for a problem
- Developing awareness of problem attributes
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