In real life, children do sometimes have epiphanies about why math
works the way it does while dealing with a concrete situation. I never
really got fractions until I used them in cooking (halving and
doubling recipes). Similarly, my son taught himself to divide by
figuring out how many pancakes each person in our family would get on
Sunday morning (if there was a remainder of three, he'd add one to
each child's quota, if a remainder of two, he'd add to the adults'
quota, if one or four, he'd say "and one person gets ..." whatever the
different amount was).
I think people tend to extrapolate from that kind of thing to assume
that math problems involving such real-life examples will be more
vivid for the child. Unfortunately, it doesn't necessarily work that
way -- it's the whole fact that the child CHOSE that concrete activity
and NEEDED the math that made the learning easier to them. To me, the
made-up examples always seemed much *more* abstract and boring than
working with real numbers. Part of the problem was that I was not
taught systematic ways of reading the problems and figuring out what
was being asked for. Once I got to algebra and was taught openly that
I was translating from English into math, I got the point (that may of
course have been my own greater maturity).
Right now, the schools often seem to be trying to do the holistic
learning in the classroom in big groups, and sending home the
drill-'n'-kill. I think it ought to be the other way around, if
anything -- much of the more formal, abstract stuff that really is the
same for everyone should be done at school in groups, and most of the
seize-the-moment enrichment at home.
--Helen
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