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Constructivist approach versus traditional mathmatics?

 
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Xapis10
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Joined: 11 Feb 2012
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PostPosted: Wed Jul 04, 2012 7:38 pm    Post subject: Constructivist approach versus traditional mathmatics? Reply with quote

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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Joined: 06 Oct 2005
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Location: Missouri, US

PostPosted: Thu Jul 12, 2012 9:04 am    Post subject: Reply with quote

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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1to1tutor
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Joined: 14 Aug 2012
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Location: Tustin, CA

PostPosted: Thu Aug 30, 2012 11:22 pm    Post subject: Reply with quote

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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PostPosted: Wed Sep 19, 2012 3:13 am    Post subject: Reply with quote

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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sgottlieb
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Joined: 07 Oct 2013
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PostPosted: Mon Oct 07, 2013 11:01 am    Post subject: Reply with quote

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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PostPosted: Mon Oct 07, 2013 7:50 pm    Post subject: Reply with quote

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