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Topic: More on Drill and Kill, practice and learning

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Subject:   RE: More on Drill and Kill, practice and learning
Author: Mathman
Date: Jan 18 2005
On Jan 18 2005, Rudy Lopes wrote:
> In the context of baseball, the purpose of practicing the throw to
> first base is so that you can do it (the mechanics) without thinking
> about it; properly ingrained by practice, when you encounter a
> situation requiring the throw all it takes is for you to know that
> you need to do so.  As with math, the player/student that has to
> think about the situation AND the mechanics is at a big
> disadvantage.

Therefore, I suppose that while drill/practice is
> essential for creating proficiency in the mechanics of math, it is
> pointless without the coaching required to help students put the
> mechanics into a real-world context -- recognize when to use what
> skills.

You are correct, of course.  But that brings up the argument of what's the point
of teaching something unless you know the student is going to need it?  Then
which student needs what, and when?  There's the rub.  So, we teach in the hope
and general expectation that they will find a use for it ...perhaps even a
better use than is already known.   We teach at a time when they can absorb the
context, even though they have not yet a specific need.  It is also a thing in
and of itself, just "mathematics", and needs no other directive.

When do students study Complex Numbers?  When do they find a practical need?
When do they need to see the similarities between algebraic structures and
number systems, or the need for generalised coordinates, or vector geometry?
...and so on.  There is a time to learn something, and a time to use it.


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