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Topic: [math-learn] Some GeoGebra applets
Replies: 6   Last Post: Jul 15, 2012 10:06 PM

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Ed Wall

Posts: 837
Registered: 12/3/04
Re: [math-learn] Re: Some GeoGebra applets
Posted: Jul 7, 2012 3:20 PM
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Thanks. I also took a look at the others. I will need to think about the last a bit more as I'm not sure from your directions what do do (and I gain from the expression on the wizard's face, that I am consistently wrong - smile). I plan get around to doing some 'corrections' for you, but it may not be until the end of the summer

A few comments about what I see here and these are not a criticisms as what you (and others) have done is nice. What I see largely here is what I might call decoding. You decod the fraction so as to place it on the number or decode its position so as to name it. This clearly needs to happen; however, what I'm thinking about is something somewhat different. I'll try to give you a description of how it might work and that may make what I'm thinking about somewhat clearer.

You have a number line with 1, 0, and 1/2 marked (pershaps also outside the unit interval, but this is sufficient to indicated what I'm thinking). You are given a fraction and need to point to that open segment which contains the fraction. This is not a matter of accuracy (i.e. decoding to some degree is assumed), the computer does the correct placing. You are given another fraction and again need to pick the correct open segment containig the fraction and so forth. This seems to me a different form of task - a sort of a number sense or comparative task - than decoding and seems to call for something beyond 'decoding.' While decoding is a problem, I have been finding for a number of years that students (and teachers) are mystified by operations with fractions as they have no feel for relative magnitudes and this is not alleviated all the way through the grades and through college.

I'm not aguing, by the way, that you can't solve this by marking up the interval or doing cross products, but, quite often, it is just a matter of 'understanding' fractions as, one might say, numbers. Oddly perhaps, I consider this as part of being fluent. For example, I think (smile) one should reasonable immediately know that 23/45 is bigger than 1/2 and 13/14 is smaller than 15/16.


On Jul 5, 2012, at 9:27 AM, Antonija wrote:

> --- In math-learn@yahoogroups.com, Ed Wall <ewall@...> wrote:
>> Antonija
>> Nice to hear your voice, Thanks for this.
>> Somewhat lately I and some others have been thinking about helping children gaining some sense of fractions on the number line as without this much of the further work on operations with fractions deteriorates into gibberish (this, by the way, is reflected in past work by Nancy Mack). Any applets or thoughts in this direction?
>> Ed

> Here you can find one my The Geometer's Sketchpad file.
> http://www.antonija-horvatek.from.hr/materials-English/Fractions/Fractions_on_number_line.zip
> It is possible to use it with projector when explain how to put fractions and mixed numbers on a number line. It is translated into English.
> It is allowed to use it in teaching. And, of course, it's allowed to correct all my mistakes in English before using. Thanks in advance if you send mi corrected version. :-)
> Second, here is one GGB applet in Croatian (not mine),
> http://apleti.normala.hr:8180/xwiki/bin/view/Razlomci/BrojevniPravac .
> You should put the red circle to the right position (see the given fraction). After taht, click the 'Povuci' check box (Eng. 'Drag') and then you will know if you put it to the right position. If so, you cached a fish. :-)
> Then click the 'Nova to&#269;ka' ckeck box (Eng. 'New point') to get new fraction and solve new problem.
> Third, here is another one GGB applet,
> http://apleti.normala.hr:8180/xwiki/bin/view/KoordinatniSustav/Poga%C4%91anje+to%C4%8Dke+zadane+razlomkom ,
> in Croatian again.
> You have some point, e.g. T=(1/4,-5/4).
> First, you should use the white slider to adjust division in the coordinate system,
> and then you should put the blue circle to the right position.
> Then click 'provjeri' check box (Eng. 'check').
> If you solved it correctly, the wizard will find his diamond. :-)
> I hope this helps.
> Best wishes,
> Antonija
> ------------------------------------
> Yahoo! Groups Links

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