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Re: Re: Re: Mathematica for gifted elementary

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98988] Re: [mg98919] Re: [mg98902] Re: Mathematica for gifted elementary
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 23 Apr 2009 06:43:55 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <gsivc0$995$1@smc.vnet.net> <200904210910.FAA24543@smc.vnet.net> <200904220908.FAA13207@smc.vnet.net> <DDB181079E074D53AD497F47F62A949D@dahl1>
  • Reply-to: murray at math.umass.edu

I have no doubt as to the efficacy of some such demos for learning some 
things about some mathematical concepts. Indeed, many math concepts that 
are otherwise procedural or symbolic as ordinarily taught become clearer 
or more transparent with proper manipulable graphical representations.

Ingolf Dahl wrote:
> Maybe the demonstration site cannot teach him to DO mathematics, but it
> could teach to LEARN mathematical concepts, THINK in terms of them, TALK
> about mathematics and see mathematics put into contexts. There are a lot of
> educational and funny software for teaching basic math (the digits and
> addition up to 100 or so), and small children books where Barbapapa shows
> different shapes and colors, but the young man mentioned in the letter
> evidently has passed that stage. At the level just above the most basic it
> is very difficult to find something good and interesting. Some other kids
> learns everything worth to learn about different kinds of dinosaurs. He has
> probably already learnt about triangles and rectangles. Then, if there is
> something like a video game, telling him about dodecahedra, icosahedra,
> convex hulls, diagrams, coordinate systems, RGB colors, musical sounds, you
> name it, why should he as a six years old investigator not use it? Then his
> father and mother can see what catches his interest, and guide him further.
> It might be a bit complicated to modify the demonstrations, but it might be
> possible to find the relevant related commands, and use the examples in the
> help system to do simple experiments. Then he could get into Mathematica
> programming quite easy, if he is interested. But that is the point of the
> demonstrations - they might be a way to get him and keep him interested. And
> that is the most important point.
> 
> Another thing is that good images might go straight into your mind, creating
> strong visual memories and silent knowledge. If you see a square of 4 times
> 4 dots (or two standard Lego pieces side by side) do you need a conscious
> multiplication to know that there are 16 dots (or knobs)? There you might
> have silent knowledge, and that could be of great value. The demonstrations
> are full of good images.
> 
> And what is "doing computations"? Consider these cases:
> 1) Our young genius open Mathematica and evaluates Sqrt[2]
> 2) He opens the Travelling Salesman demonstration and enters a number of
> points interactively, and looks at the result.
> Is he doing computations himself in any of the cases?
> 
> Best regards
> 
> Ingolf Dahl
> 
>> -----Original Message-----
>> From: Murray Eisenberg [mailto:murray at math.umass.edu] 
>> Sent: den 22 april 2009 11:08
>> To: mathgroup at smc.vnet.net
>> Subject: [mg98919] Re: [mg98902] Re: Mathematica for gifted 
>> elementary school children
>>
>> But interacting with the demonstrations, while it can be 
>> educational, is not really being very creative or being 
>> engaged in learning Mathematica (unless one studies the code 
>> -- which tends to be rather more sophisticated than a rank 
>> beginner would want to see).
>>
>> Doing computations oneself, building graphic images oneself 
>> -- those things can be educational and creative and 
>> contribute toward learning Mathematica and learning how to 
>> learn Mathematica.
>>
>> Sort of the difference between playing a video game and 
>> creating a video game.
>>
>> Bob F wrote:
>>> On Apr 20, 5:09 pm, Beliavsky <beliav... at aol.com> wrote:
>>>> My son, almost 6, is good at math and inquisitive. Is there a math 
>>>> curriculum for elementary school children that uses 
>> Mathematica? He 
>>>> understands the four arithemetic operations and the 
>> concept of powers.
>>>> I have Mathematica installed on my home PC and could teach 
>> him myself.
>>>> I have written computer programs in Fortran in front of him to 
>>>> demonstrate concepts such as cubes and cube roots. We had 
>> fun, but I 
>>>> don't want to explain right now why 1000000000**3 gives 
>> -402653184 or
>>>> 1/2 gives 0.
>>>>
>>>> He is interested in the number "centillion" (10^303) and 
>> thought it 
>>>> was cool to see the 101 zeros when we asked Mathematica to compute 
>>>> centillion^(1/3).
>>>>
>>>> I see there are some math courseware 
>>>> athttp://library.wolfram.com/infocenter/Courseware/Mathematics/
>>>> , but those topics are too advanced for him at present. Maybe I 
>>>> should give him Wolfram's huge book and let him play when he wants.
>>> Try looking thru the demonstrations web site (at 
>>> http://demonstrations.wolfram.com ). There are some really 
>> nice things 
>>> and some are very well illustrated and fun to play with. 
>> There is even a "Kids and Fun"
>>> section at http://demonstrations.wolfram.com/topics.html#10
>>>
>>> Enjoy...
>>>
>>> -Bob
>>>
>> -- 
>> Murray Eisenberg                     murray at math.umass.edu
>> Mathematics & Statistics Dept.
>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>> University of Massachusetts                413 545-2859 (W)
>> 710 North Pleasant Street            fax   413 545-1801
>> Amherst, MA 01003-9305
>>
>>
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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