Now, adults needing to perform calculations quickly and accurately have electronic tools that are both more accurate and more efficient than those procedures.
Why is that constructivist are only concerned about efficiency when it relates to calculators?
Why are they so anti-efficiency when it comes to pencil and paper computation?
Catherine speaking: Good question.
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and from Steve H
Used properly, calculators should make math more difficult, not less. Instead of focusing on data sets that have only 5 numbers, they can ask the students to find the average of 50 numbers. They are so concerned about real-world examples, but they don't have the kids work with lots of numbers.
This is what happened for me when calculators took over sliderules in college. The techniques we learned became much more complicated and required many more calculations. However, in lower schools, calculators are used to avoid work.
When you get to algebra, one can use a graphing calculator. It may be a nice tool to quickly see shape changes in varying lines, parabolas and ellipses, but they are avoiding the development of symbolic algebraic manipulation skills. What happens if the calculator (black box program) can't do the job?
This is math for students who won't have a technical career when they grow up. The problem is that using this approach in the early grades guarantees that the students won't have a technical career.
The Dartmouth admissions officer lit up when our superintendent asked him about calculators in grade school.
ReplyDeleteHe said that in B-school they'd had B-school calculators.
He had no idea what the different calculations meant, and he'd always wished he did.
I'm sure that someone thought that having calculators in grade school was a good idea. Unfortunately, they wrote entire curriculums that assumed calculators would be used without ever testing the idea. Then the math professors stepped back into their ivory towers.
ReplyDeleteWhat actually happens is that students don't get used to working with numbers.
Here's a comparison to playing soccer: it's like teaching the players how to kick the ball and then having them always play games. They don't necessarily learn the proper technique. And techniques that work when you are 9 and quick, doesn't necessarily work at 15 when the game gets very physical. Meanwhile, the players who have practiced proper technique have passed you by (Kumon anyone?) and you can't catch up.
Invented multiplication algorithims that work fine in 3rd grade will hold you back when you have to add (non standard) fractions in middle school.
No one has the courage to admit that having elementary school students use calculators just doesn't get them where they need to be.
Anne Dwyer
it's like teaching the players how to kick the ball and then having them always play games.
ReplyDeleteAbsolutely.
That's Martin Brooks' direct advice.
Always teach wholes - have the kid figure out the parts.
Education, for Brooks, is 13 years of kids engaged in reverse engineering.
Guaranteed to hold their attention.
ReplyDelete