Re: Stitching away

On 8/6/09 11:58 PM, "Ericka Kammerer" <eek@xxxxxxxxxxxxxxx> wrote:

ellice wrote:

Just what I was going to say. Even in subjects like geometry or trig, they
can do more with a calulator. The bigger problem is the kids that don't
understand the basics of algebra, or actual arithmetic. Even when I went to
school, I had to have a slide rule in high school for calculus and AP
Physics & Chem. Don't need a calculator IMHO for algebra, geometry or trig
- but it definitely helps with trig.

Based on what my kids have used calculators for (through
geometry, at this point), it's not that they use the calculator
instead of learning to solve things the "old fashioned way."
It's true they don't use a slide rule and they don't use logarithms
much, but they also have a much heavier emphasis on real world
sorts of problems where the math doesn't work itself out nicely.
They still learn the usual methods, and work the practice problems
sans calculators, but then they go on to do more applied problems
for which they are more likely to use the calculator. I don't
have any objections to that, and actually think that it improves
the program to have them do more real world sorts of problems.
I'd say that to date, the kids have only used calculators for
maybe 10-20 percent of their math classes, but the use has seemed
quite sensible to me. Once the basic ability to solve a particular
type of problem has been mastered, the important thing is to get
a lot of practice figuring out when to apply that technique and
using it to solve a variety of problems.

The way you describe your kids usage makes sense to me. They just don't
have to spend the time doing the math, so to speak. Which, OTOH, translates
into the problem seen all over of not recognizing a wrong math solution
because that familiarity with number relations, manipulation is not gained
(the repetition, practice thing even with math). So often what ends up
missing later on is that recognition of a solution being slightly, or even
order of magnitude, off.

There are definitely kids who don't understand basic
arithmetic or algebra or whatever the topic is at hand--but
I don't think that's because they've used calculators. There
were kids who didn't master arithmetic or algebra or what
have you before calculators as well ;-) Not only are more
things being covered in these math courses, but many more
students are taking higher level math courses than previously,
which would also lead one to expect some dilution in accomplishments.
There may be some kids who aren't getting algebra all that well,
but a generation ago, they might not have even attempted algebra.
Whether that's a good thing or a bad thing can, of course, be
debated ;-)

I think the difference in how much, how far in math type education kids go
now compared to 20 or 40 years ago really depends on school systems.
Honestly, compared to my high school the average kid takes less math
nowadays. Our system required math thru Algebra II - IIRC those who were
really struggling would perhaps go to a business math class instead. I had
friends in the then Honors program who weren't heading for science careers
and much to the shock of our classmates dropped math after Algebra II (only
to later discover they had to take more math in university). Depending on
where you fell on the scale WRT Math/Science programs kids would go thru
Trig/analyt or Calculus, some with a 2nd year of calculus or some other math
development. Educational strategies are always interesting. Having close
friends that are academics in the science/engineering world we end up
talking about the math thing a lot. Even from work - it is interesting to
me that interplay between math and its applications. People doing fabulous
calculational simulations - but they don't have the right science background
to know that while their math is right the physics is off. Then the
converse, people who are certain of the physics involved, but have no
inherent feel for the numbers. I guess part of that is in some advanced
math stuff - well - the numbers don't come into it - until you're in the
real world trying to apply complex equations, and then the real part of
things kicks in. It's all pretty interesting how things change, and in some
ways remain the same.

Ellice

.

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