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	<title>Comments on: Guess the Number of Gumballs, Then Do a Differential Equation</title>
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	<link>http://blogs.discovermagazine.com/80beats/2008/09/08/guess-the-number-of-gumballs-then-do-a-differential-equation/</link>
	<description>80beats is DISCOVER&#039;s news aggregator, weaving together the choicest tidbits from the best articles covering the day\&#039;s most compelling topics.</description>
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		<title>By: Everett Williams</title>
		<link>http://blogs.discovermagazine.com/80beats/2008/09/08/guess-the-number-of-gumballs-then-do-a-differential-equation/comment-page-1/#comment-22194</link>
		<dc:creator>Everett Williams</dc:creator>
		<pubDate>Sun, 29 Mar 2009 18:46:27 +0000</pubDate>
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		<description>Gentlemen, 

There is nothing new about this type of research. In the early work with children who had hemispherectomies, it was thought that they would need special intervention to be able to perform normally. This turned out not to be the case, but some of the techniques used to train these children produced interesting results. As part of their curriculum, flash cards were used with various numbers of randomly placed symbols. Over time, it was discovered that these children could glance at a group of people or a field full of animals and tell you how many, with great accuracy. Since hemispherectomies are seldom done in this day in time, there is no longer a cohort to test, but it would be interesting to examine the adults to see what their overall mathematical abilities test out to.</description>
		<content:encoded><![CDATA[<p>Gentlemen, </p>
<p>There is nothing new about this type of research. In the early work with children who had hemispherectomies, it was thought that they would need special intervention to be able to perform normally. This turned out not to be the case, but some of the techniques used to train these children produced interesting results. As part of their curriculum, flash cards were used with various numbers of randomly placed symbols. Over time, it was discovered that these children could glance at a group of people or a field full of animals and tell you how many, with great accuracy. Since hemispherectomies are seldom done in this day in time, there is no longer a cohort to test, but it would be interesting to examine the adults to see what their overall mathematical abilities test out to.</p>
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		<title>By: DAW</title>
		<link>http://blogs.discovermagazine.com/80beats/2008/09/08/guess-the-number-of-gumballs-then-do-a-differential-equation/comment-page-1/#comment-7609</link>
		<dc:creator>DAW</dc:creator>
		<pubDate>Thu, 18 Sep 2008 21:40:27 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/80beats/2008/09/08/guess-the-number-of-gumballs-then-do-a-differential-equation/#comment-7609</guid>
		<description>That&#039;s a crazy comment, Hank Campbell. The writers of the articles were very careful to say that &quot;an intuitive understanding of numbers that closely correlates with their aptitude for complex math&quot;, and the phrase, &quot;are related to&quot; includes correlational relationships. 

There initial premise before starting the study was that the correlation coefficient between the two things was zero - in other words, that they are uncorrelated. But next, they were found to be correlated, and that is a very important step. The next steps in such studies involve looking for stronger connections. Perhaps a causal connection will be found someday - or a term you&#039;ve probably never heard of, one of them could be &quot;mean-square predictable&quot; from the other, which is a much stronger relationship than merely correlated. 

So, now is not the time to make gripes and complaints. These things progress in a step-by-step matter - just like putting men in orbit is a step towards putting men on the Moon. 

DAW</description>
		<content:encoded><![CDATA[<p>That&#8217;s a crazy comment, Hank Campbell. The writers of the articles were very careful to say that &#8220;an intuitive understanding of numbers that closely correlates with their aptitude for complex math&#8221;, and the phrase, &#8220;are related to&#8221; includes correlational relationships. </p>
<p>There initial premise before starting the study was that the correlation coefficient between the two things was zero &#8211; in other words, that they are uncorrelated. But next, they were found to be correlated, and that is a very important step. The next steps in such studies involve looking for stronger connections. Perhaps a causal connection will be found someday &#8211; or a term you&#8217;ve probably never heard of, one of them could be &#8220;mean-square predictable&#8221; from the other, which is a much stronger relationship than merely correlated. </p>
<p>So, now is not the time to make gripes and complaints. These things progress in a step-by-step matter &#8211; just like putting men in orbit is a step towards putting men on the Moon. </p>
<p>DAW</p>
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		<title>By: Hank Campbell</title>
		<link>http://blogs.discovermagazine.com/80beats/2008/09/08/guess-the-number-of-gumballs-then-do-a-differential-equation/comment-page-1/#comment-7344</link>
		<dc:creator>Hank Campbell</dc:creator>
		<pubDate>Mon, 08 Sep 2008 21:08:48 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/80beats/2008/09/08/guess-the-number-of-gumballs-then-do-a-differential-equation/#comment-7344</guid>
		<description>Not to rain on the correlation/causation parade but sentences like &quot;individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense&quot; in that study are almost meaningless.

This study could also mean that kids who are better at math just guess better about the number of objects.  A good mechanic also has a better chance of guessing at the problem in my car by the sound than a bad one.  That does not make it an &#039;ancient&#039; biological ability.</description>
		<content:encoded><![CDATA[<p>Not to rain on the correlation/causation parade but sentences like &#8220;individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense&#8221; in that study are almost meaningless.</p>
<p>This study could also mean that kids who are better at math just guess better about the number of objects.  A good mechanic also has a better chance of guessing at the problem in my car by the sound than a bad one.  That does not make it an &#8216;ancient&#8217; biological ability.</p>
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