Harvey Becker writes: > >Gary...I guess what I meant was....how can you find the volume of the >following rectangular solid (having w=3, l=4, h=5.3) if you don't first know >how to multiply? I'm sure most of us agree that in the second grade we were >taught the multiplication tables before any need to know such knowledge was >ever introduced. Later....applications were developed to show us why we >needed to know multiplication (as in the volume of a solid etc). I like to >teach my trigonometry kids what the definition of sine is BEFORE I ask them >to find the sine of 30 degrees and certainly prior to asking them to solve >any triangular problems involving sun's shadows and heights of trees etc....
This struck me as kind of strange. For example, if kids in first grade are sitting around taking twelve unifix cubes and rearranging them into three groups of 4 and four groups of 3 and so on, the notions of multiplication and division arise quite naturally. The notion of a sine can arise quite naturally too as, say, the hand of a clock sweeps out a circle and students make certain measurements.
Why do we seem to think that mathematics must be justified in terms of practical immediate problems, most of which kids don't care about anyway? No other subject suffers from such a lack of belief in its intrinsic relevance.
==================================== Judy Roitman, Mathematics Department Univ. of Kansas, Lawrence, KS 66049 firstname.lastname@example.org =====================================