SK> All high school and below math should teach the underlying
SK> reasons behind the algorithms. Otherwise it's just a bunch of black
SK> magic, hocus-pocus to the students. Students who understand the 
SK> reasons
SK> know better when to apply them. They also remember them better and 
SK> feel
SK> more secure using them.
    Does math _need_ to be more than "black magic" to _users_?  Most drivers 
have little or no conception of what makes their car work, but they can apply 
the "algorithm" of driving just fine.  Life is full of situations where 
_users_ need to know how to use the techniques, not the theory behind them.
    I'm also unconvinced that trying to get the _masses_ of K-12 students to 
understand theory will result in them "remember[ing] them better" after the 
course.  The prof in a freshman-math course I tutored a help session in 
agreed with me that few students passing the course with a "C" or better 
would be able to pass the exact same final if they were given it three weeks 
after the end of the course.  I majored in math, and I'm sure there are 
things from HS math I've forgotten.
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