Constructivist approach versus traditional mathmatics?

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Xapis10
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Constructivist approach versus traditional mathmatics?

Postby Xapis10 » Wed Jul 04, 2012 7:38 pm

I'm wondering about the pros and cons of a constructivist approach to math. Any thoughts or any articles addressing this? Thanks!

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Theodore
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Postby Theodore » Thu Jul 12, 2012 9:04 am

If I'm understanding the question correctly, constructivist math seems to be about supplying students with a whole bunch of different techniques and then letting them "build" their own math skills. Only problem is, that doesn't work with math, which is very abstract and really does have a best way to do everything. Students taught through constructivist methods are at a major disadvantage vs those taught traditionally, since it takes them longer to arrive at the "right" method and they're not given the repetition necessary for the math skills to sink in. Since they can't do basic operations at any speed, they're then given more access to calculators, which further reinforces the problem.

Short version - it's ok to play with different methods and formulas, but only after you have mastered traditional math. There will be plenty of scope for creativity in Calculus.

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Postby 1to1tutor » Thu Aug 30, 2012 11:22 pm

Constructive maths may be a time taking process initially but for a long run it will save a lot of time and energy. It avoid students in memorizing the formulas and they can derive it more easily if they forgot the formulas. I think it will be the best technique for the students who are looking to build career in Mathematics.

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Theodore
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Postby Theodore » Wed Sep 19, 2012 3:13 am

The theory behind the formulas is important, yes. I'm just saying that with math, only the "best" way(s) to do each problem should be supplied - anything else is just adding confusion - and there should be a lot of focus on math drill. Being able to do math quickly in your head is every bit as important as knowing why a specific math technique works.

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Postby sgottlieb » Mon Oct 07, 2013 11:01 am

A constructivisti s a very strange mathematician. If you tell them that the light switch is NOT on they WILL NOT conclude that the light switch is off. They always think there is a 3rd option in that case. Very few mathematicians are like this and they are looked down upon by other mathematicians.
As far as knowing how to proof things ALL (pure) mathematicians will agree that this is the only way to proceed.

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Theodore
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Postby Theodore » Mon Oct 07, 2013 7:50 pm

Could be on dim or broken, though that's probably not what you meant.


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