It isn't only in math that this situation exists.
In that final years of my teaching science I was constantly faced with
administrators who wanted the "hands-on-approach" used to teach science.
I watched as teachers struggled to try to have students come up with the law
of levers, (usually they guessed the correct simple relationship of two
weights on sides of the fulcrum but it took large amounts of time), the
inclinded plane (using a rolling car down an incline, with undiscovered and
unknown friction being involved in each trial), the law of floating objects,
etc. Some, very few and I mean VERY few students, ever 'discovered' the
rules for themselves. All that happened was that students became bored,
frustrated, turned-off to science, and generally confused. Of course, it did
give them a good amount of time to talk with others (social interaction),
fool around (leisure activity utilization), and generally allow the brighter
or more industrious students to do the work (apportionment of talent).
I guess I just didn't have Bohr, Edison, Heisenburg, Ampere, Volta, Curie,
Galileo, or Einstein in any of my classes.
Having to 'rediscover' everything that has been discovered before, seems to
be quite a waste of time. I'm not sure that the 'discovery' of the theory of
Pythagoras, makes it any more meaningful, more easily remembered or useful.
I tend to think that the only triangle that most individuals remember when
doing this kind of 'find it for yourself' activity is the 3-4-5 right
triangle. Those taught in the 'traditional' way, come to understand that
3-4-5 is only 1 of a series of this type of triangle.
Just my two cents worth.
Enjoy the Holiday Season
Dr. Robert C. Knodt
4949 Samish Way, #31
Bellingham, WA 98226
[EMAIL PROTECTED]
