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	<title>Comments on: From the files:  where in the world?</title>
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	<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/</link>
	<description>Out of the crooked timber of humanity, no straight thing was ever made</description>
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		<title>By: Mordant Espier</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296590</link>
		<dc:creator>Mordant Espier</dc:creator>
		<pubDate>Fri, 27 Nov 2009 20:49:15 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296590</guid>
		<description>One other factor, besides formal education, that influences geographic understanding is media coverage. And on this front, mainstream media sources have done an abysmal job covering the world.  

http://www.ted.com/talks/lang/eng/alisa_miller_shares_the_news_about_the_news.html</description>
		<content:encoded><![CDATA[	<p>One other factor, besides formal education, that influences geographic understanding is media coverage. And on this front, mainstream media sources have done an abysmal job covering the world.</p>

	<p><a href="http://www.ted.com/talks/lang/eng/alisa_miller_shares_the_news_about_the_news.html" rel="nofollow">http://www.ted.com/talks/lang/eng/alisa_miller_shares_the_news_about_the_news.html</a></p>
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		<title>By: andrew</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296266</link>
		<dc:creator>andrew</dc:creator>
		<pubDate>Wed, 25 Nov 2009 09:38:29 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296266</guid>
		<description>&lt;em&gt;So we sometimes fall back on our second line of argument, namely, that college students in 1964 or 1982 were every bit as ignorant as this year’s survey victims. &lt;/em&gt;

The interesting thing about geography, as opposed to pretty much any of the other standard subjects, is that the field really has shrunk in the last few decades - at least measured by number of faculty/departments. I don&#039;t know what this has meant in terms of curricula, but it has to have had an effect. Whether it&#039;s the kind of effect that can be captured on this kind of survey is another question.</description>
		<content:encoded><![CDATA[	<p><em>So we sometimes fall back on our second line of argument, namely, that college students in 1964 or 1982 were every bit as ignorant as this year&#8217;s survey victims. </em></p>

	<p>The interesting thing about geography, as opposed to pretty much any of the other standard subjects, is that the field really has shrunk in the last few decades &#8211; at least measured by number of faculty/departments. I don&#8217;t know what this has meant in terms of curricula, but it has to have had an effect. Whether it&#8217;s the kind of effect that can be captured on this kind of survey is another question.</p>
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		<title>By: Zamfir</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296265</link>
		<dc:creator>Zamfir</dc:creator>
		<pubDate>Wed, 25 Nov 2009 08:40:35 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296265</guid>
		<description>&lt;i&gt;I think you can argue that some of the map knowledge is not so much important in itself as a proxy for other kinds of knowledge and attention.&lt;/i&gt;
Sure, but there is a danger in using proxies when comparing different countries and their education systems. The correlation between topographical knowledge and other knowledge may be very different in different countries. 

In this case, I would argue that topographical knowledge of places you will never navigate to yourself is of limited importance. Map reading as a skill obviously is important, and (here I apparently disagree with our host) only more so in a GPS age where information is more likely to be cast in map form. But note that the US scores middle-of-the-roadish on those skills in the report, while the topography results are horrible.</description>
		<content:encoded><![CDATA[	<p><i>I think you can argue that some of the map knowledge is not so much important in itself as a proxy for other kinds of knowledge and attention.</i><br />
Sure, but there is a danger in using proxies when comparing different countries and their education systems. The correlation between topographical knowledge and other knowledge may be very different in different countries.</p>

	<p>In this case, I would argue that topographical knowledge of places you will never navigate to yourself is of limited importance. Map reading as a skill obviously is important, and (here I apparently disagree with our host) only more so in a <span class="caps">GPS</span> age where information is more likely to be cast in map form. But note that the US scores middle-of-the-roadish on those skills in the report, while the topography results are horrible.</p>
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		<title>By: Michael Bérubé</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296255</link>
		<dc:creator>Michael Bérubé</dc:creator>
		<pubDate>Wed, 25 Nov 2009 04:28:38 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296255</guid>
		<description>Colin @ 52:  &lt;i&gt;That does not mean, re #41, that there’s a correspondence between your understanding of the local situation and your policy views—you can just as easily make an anti-intervention argument on the basis of ideology, not knowledge of a situation. Didn’t some cultural studies perfesser just write a book that made that argument? Or would that be too weird?&lt;/i&gt;

It wouldn&#039;t be too weird -- it would simply be unpossible.  Everybody knows that cultural studies is dead.

Kenny @ 55:  &lt;i&gt;It seems somewhat ahead-of-your-time to include a paragraph about the ubiquity of GPS in 2002. Where did people keep their GPS devices in 2002? On their landline?&lt;/i&gt;

2002 is more like the present than you think.  I saw GPS in golf carts as early as 1998 (it enabled the clubhouse to keep track of slow players), and the cell phone was indeed ubiquitous by 2002.  OK, the line about GPS in watches was a stretch.

2002 was also the year I first saw flat-screen TVs in NYC convenience stores (so that you could watch CNN while buying toothpaste) and elevators.  Video feeds are now available in taxis and on refrigerators.  The result, I think, will be that by 2016 no one in the US will be able to identify anything on any map anywhere.</description>
		<content:encoded><![CDATA[	<p>Colin @ 52:  <i>That does not mean, re #41, that there&#8217;s a correspondence between your understanding of the local situation and your policy views&#8212;you can just as easily make an anti-intervention argument on the basis of ideology, not knowledge of a situation. Didn&#8217;t some cultural studies perfesser just write a book that made that argument? Or would that be too weird?</i></p>

	<p>It wouldn&#8217;t be too weird&#8212;it would simply be unpossible.  Everybody knows that cultural studies is dead.</p>

	<p>Kenny @ 55:  <i>It seems somewhat ahead-of-your-time to include a paragraph about the ubiquity of <span class="caps">GPS</span> in 2002. Where did people keep their <span class="caps">GPS</span> devices in 2002? On their landline?</i></p>

	<p>2002 is more like the present than you think.  I saw <span class="caps">GPS</span> in golf carts as early as 1998 (it enabled the clubhouse to keep track of slow players), and the cell phone was indeed ubiquitous by 2002.  OK, the line about <span class="caps">GPS</span> in watches was a stretch.</p>

	<p>2002 was also the year I first saw flat-screen TVs in <span class="caps">NYC</span> convenience stores (so that you could watch <span class="caps">CNN</span> while buying toothpaste) and elevators.  Video feeds are now available in taxis and on refrigerators.  The result, I think, will be that by 2016 no one in the US will be able to identify anything on any map anywhere.</p>
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		<title>By: Kenny Easwaran</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296233</link>
		<dc:creator>Kenny Easwaran</dc:creator>
		<pubDate>Wed, 25 Nov 2009 00:00:08 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296233</guid>
		<description>It seems somewhat ahead-of-your-time to include a paragraph about the ubiquity of GPS in 2002.  Where did people keep their GPS devices in 2002?  On their landline?

I would conjecture that the rise of google-maps-with-GPS cell phones will make more people capable of using maps.</description>
		<content:encoded><![CDATA[	<p>It seems somewhat ahead-of-your-time to include a paragraph about the ubiquity of <span class="caps">GPS</span> in 2002.  Where did people keep their <span class="caps">GPS</span> devices in 2002?  On their landline?</p>

	<p>I would conjecture that the rise of google-maps-with-GPS cell phones will make more people capable of using maps.</p>
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		<title>By: Salient</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296229</link>
		<dc:creator>Salient</dc:creator>
		<pubDate>Tue, 24 Nov 2009 23:06:06 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296229</guid>
		<description>Ok, ok, a note to stave off further piling on from other commenters infuriated or madly amused, this was not a general education thread, ok, got it. Honest, I was attempting to respond to Colin Danby, and to MB&#039;s closing statement &lt;i&gt;Every last one of us knows that we are exactly where we are right now, and so we shall remain, until our nation’s geographers and educators provide us with the Global Decentering System we so desperately need.&lt;/i&gt; It&#039;s not like being able to read a map is all that fundamentally different a skill from reading a pie chart or a histogram or a set of visual instructions for putting together a cabinet. Apparently I did not successfully comment re: educators providing a possible Global Decentering System, so I apologize for having failed in my aim.

I had figured there wouldn&#039;t be a whole lot of community good coming from Chris&#039; post, with commenters unsatisfied by somebody&#039;s points referencing the list as an imputation, whether sardonically or with open hostility. But I hadn&#039;t expected both within 48 hours, directed at me. I am sorry for having done what I did to provoke this. Forgiveness for those who attempt to be a type-10 commenter but fail would be... I don&#039;t know. A nice thing, a good thing. Maybe give people at least a couple posts on a thread before lambasting them for hijacking or failure to uphold the new &lt;strike&gt;fifteen&lt;/strike&gt; ten commandments of CT expectations, you know?</description>
		<content:encoded><![CDATA[	<p>Ok, ok, a note to stave off further piling on from other commenters infuriated or madly amused, this was not a general education thread, ok, got it. Honest, I was attempting to respond to Colin Danby, and to MB&#8217;s closing statement <i>Every last one of us knows that we are exactly where we are right now, and so we shall remain, until our nation&#8217;s geographers and educators provide us with the Global Decentering System we so desperately need.</i> It&#8217;s not like being able to read a map is all that fundamentally different a skill from reading a pie chart or a histogram or a set of visual instructions for putting together a cabinet. Apparently I did not successfully comment re: educators providing a possible Global Decentering System, so I apologize for having failed in my aim.</p>

	<p>I had figured there wouldn&#8217;t be a whole lot of community good coming from Chris&#8217; post, with commenters unsatisfied by somebody&#8217;s points referencing the list as an imputation, whether sardonically or with open hostility. But I hadn&#8217;t expected both within 48 hours, directed at me. I am sorry for having done what I did to provoke this. Forgiveness for those who attempt to be a type-10 commenter but fail would be&#8230; I don&#8217;t know. A nice thing, a good thing. Maybe give people at least a couple posts on a thread before lambasting them for hijacking or failure to uphold the new <strike>fifteen</strike> ten commandments of CT expectations, you know?</p>
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		<title>By: bianca steele</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296217</link>
		<dc:creator>bianca steele</dc:creator>
		<pubDate>Tue, 24 Nov 2009 21:14:49 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296217</guid>
		<description>No consolation necessary, Salient.  There are probably lots of readers of this blog who read your post and realized that their knowledge of mathematics is weak because they didn&#039;t go to the kind of school that teaches the answer to &quot;what is information?&quot; (which fact they never even realized until today).  Maybe they can devote the rest of their political lives to supporting your cause.</description>
		<content:encoded><![CDATA[	<p>No consolation necessary, Salient.  There are probably lots of readers of this blog who read your post and realized that their knowledge of mathematics is weak because they didn&#8217;t go to the kind of school that teaches the answer to &#8220;what is information?&#8221; (which fact they never even realized until today).  Maybe they can devote the rest of their political lives to supporting your cause.</p>
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		<title>By: Colin Danby</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296211</link>
		<dc:creator>Colin Danby</dc:creator>
		<pubDate>Tue, 24 Nov 2009 20:30:58 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296211</guid>
		<description>Re #33, I think you can argue that some of the map knowledge is not so much important in itself as a proxy for other kinds of knowledge and attention.  Anyone who has thought through arguments about intervention in Iraq or Afghanistan has to have thought about location and borders.  That does not mean, re #41, that there&#039;s a  correspondence between your understanding of the local situation and your policy views -- you can just as easily make an anti-intervention argument on the basis of ideology, not knowledge of a situation.  Didn&#039;t some cultural studies perfesser just write a book that made that argument?  Or would that be too weird?</description>
		<content:encoded><![CDATA[	<p>Re #33, I think you can argue that some of the map knowledge is not so much important in itself as a proxy for other kinds of knowledge and attention.  Anyone who has thought through arguments about intervention in Iraq or Afghanistan has to have thought about location and borders.  That does not mean, re #41, that there&#8217;s a  correspondence between your understanding of the local situation and your policy views&#8212;you can just as easily make an anti-intervention argument on the basis of ideology, not knowledge of a situation.  Didn&#8217;t some cultural studies perfesser just write a book that made that argument?  Or would that be too weird?</p>
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		<title>By: dsquared</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-2/#comment-296202</link>
		<dc:creator>dsquared</dc:creator>
		<pubDate>Tue, 24 Nov 2009 19:16:35 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296202</guid>
		<description>&lt;i&gt;See, this is why the tired leftist slogan “U.S. out of Nicaragua” makes no sense&lt;/i&gt;

&lt;a href=&quot;http://www.we7.com/#/track/USA-Out-OF-NYC-!trackId=1650820&quot; rel=&quot;nofollow&quot;&gt;USA out of NYC!&lt;/a&gt;</description>
		<content:encoded><![CDATA[	<p><i>See, this is why the tired leftist slogan &#8220;U.S. out of Nicaragua&#8221; makes no sense</i></p>

	<p><a href="http://www.we7.com/#/track/USA-Out-OF-NYC-!trackId=1650820" rel="nofollow"><span class="caps">USA</span> out of <span class="caps">NYC</span>!</a></p>
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		<title>By: Michael Bérubé</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-1/#comment-296201</link>
		<dc:creator>Michael Bérubé</dc:creator>
		<pubDate>Tue, 24 Nov 2009 19:06:13 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296201</guid>
		<description>J. Fisher @ 44 and blah @ 46:  didn&#039;t I already address this important matter @ 40, in response to Veblen?

Shane in Utah:  &lt;i&gt;Michael, I’m confused about what group you’re talking about. College graduates? Current college students? “College-age Americans”?&lt;/i&gt;

Check the National Geographic survey.  18-to-24 year-olds in nine countries, plus 25-34 year-olds in the US.</description>
		<content:encoded><![CDATA[	<p>J. Fisher @ 44 and blah @ 46:  didn&#8217;t I already address this important matter @ 40, in response to Veblen?</p>

	<p>Shane in Utah:  <i>Michael, I&#8217;m confused about what group you&#8217;re talking about. College graduates? Current college students? &#8220;College-age Americans&#8221;?</i></p>

	<p>Check the National Geographic survey.  18-to-24 year-olds in nine countries, plus 25-34 year-olds in the US.</p>
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		<title>By: Salient</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-1/#comment-296198</link>
		<dc:creator>Salient</dc:creator>
		<pubDate>Tue, 24 Nov 2009 18:55:00 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296198</guid>
		<description>&lt;i&gt;I do question the idea that the way you seem to be going about rebuilding the curriculum from the ground up is the best way to gradually broaden the distribution of knowledge about math.&lt;/i&gt;

If it&#039;s any consolation or reassurance, I spend a nontrivial amount of time every day questioning that idea, and I spend lots of time questioning other people about it, and ultimately the advocacy work I do is for substantially tamped-down and moderated approaches to the kinds of ideas that I share with quite radical emphasis on blogs.

But enough from me about mathematics, this was about geography. I&#039;ll be radical blog-commenter me and assert that &quot;geography&quot; qua geography is nearly so appropriate a topic of study as, say, world cultural studies &amp; world history &amp; etc. It&#039;s not just a trade-off: I would explicitly argue that any time spent explicitly on the acquisition of geographic facts is time that rather should have been spent learning to cook and sow. (This is meant to be literal, and is very much not a degradation of cooking and sowing, but rather the exact opposite: I assert that developing these particularly useful skills ought to be considered more important than the memorization of names of geographic entities and their locations. These skills ought to be valuated, and the kind of geographic knowledge discussed above ought to be correspondingly devaluated, and this ought to be reflected in curriculum decisions.)

Exhibit A: &lt;a href=&quot;http://janeaustensworld.wordpress.com/2009/05/14/early-toys-the-jigsaw-or-dissected-puzzle/&quot; rel=&quot;nofollow&quot;&gt;Fanny Price&lt;/a&gt;, who is a hero to me.</description>
		<content:encoded><![CDATA[	<p><i>I do question the idea that the way you seem to be going about rebuilding the curriculum from the ground up is the best way to gradually broaden the distribution of knowledge about math.</i></p>

	<p>If it&#8217;s any consolation or reassurance, I spend a nontrivial amount of time every day questioning that idea, and I spend lots of time questioning other people about it, and ultimately the advocacy work I do is for substantially tamped-down and moderated approaches to the kinds of ideas that I share with quite radical emphasis on blogs.</p>

	<p>But enough from me about mathematics, this was about geography. I&#8217;ll be radical blog-commenter me and assert that &#8220;geography&#8221; qua geography is nearly so appropriate a topic of study as, say, world cultural studies &#038; world history &#038; etc. It&#8217;s not just a trade-off: I would explicitly argue that any time spent explicitly on the acquisition of geographic facts is time that rather should have been spent learning to cook and sow. (This is meant to be literal, and is very much not a degradation of cooking and sowing, but rather the exact opposite: I assert that developing these particularly useful skills ought to be considered more important than the memorization of names of geographic entities and their locations. These skills ought to be valuated, and the kind of geographic knowledge discussed above ought to be correspondingly devaluated, and this ought to be reflected in curriculum decisions.)</p>

	<p>Exhibit A: <a href="http://janeaustensworld.wordpress.com/2009/05/14/early-toys-the-jigsaw-or-dissected-puzzle/" rel="nofollow">Fanny Price</a>, who is a hero to me.</p>
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		<title>By: blah</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-1/#comment-296194</link>
		<dc:creator>blah</dc:creator>
		<pubDate>Tue, 24 Nov 2009 17:51:57 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296194</guid>
		<description>&lt;i&gt;You keep former graduate students in your file cabinets? You never cease to amaze, Michael.&lt;/i&gt;

What else is he supposed to do with them?  Most of them can&#039;t find jobs anyway.</description>
		<content:encoded><![CDATA[	<p><i>You keep former graduate students in your file cabinets? You never cease to amaze, Michael.</i></p>

	<p>What else is he supposed to do with them?  Most of them can&#8217;t find jobs anyway.</p>
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		<title>By: marcel</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-1/#comment-296192</link>
		<dc:creator>marcel</dc:creator>
		<pubDate>Tue, 24 Nov 2009 17:45:09 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296192</guid>
		<description>&lt;a href=&#039;http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-1/#comment-296175&#039; rel=&quot;nofollow&quot;&gt;Salient&lt;/a&gt;: 

That has to be just about the funniest use of bold-face I&#039;ve seen on the intertubes.  I tried skimming your post, and if anything, the boldface just got in the way - it makes your comment more like the fold-up back cover that I recall from Mad Magazine when I was a wee tyke.  It seems to me that your comment not only falls under at least one of the classifications in &lt;a href=&quot;http://crookedtimber.org/2009/11/22/a-vaguely-passive-aggressive-post-on-commenters/&quot; rel=&quot;nofollow&quot;&gt;CB&#039;s post&lt;/a&gt; the other day, (as does this comment BTW), but cries out for the development of several new ones not even mentioned in the comments to that post (e.g., &lt;a href=&#039;http://crookedtimber.org/2009/11/22/a-vaguely-passive-aggressive-post-on-commenters/#comment-295850&#039; rel=&quot;nofollow&quot;&gt;here&lt;/a&gt;, or  &lt;a href=&#039;http://crookedtimber.org/2009/11/22/a-vaguely-passive-aggressive-post-on-commenters/#comment-296014&#039; rel=&quot;nofollow&quot;&gt;here&lt;/a&gt;).</description>
		<content:encoded><![CDATA[	<p><a href='http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-1/#comment-296175' rel="nofollow">Salient</a>:</p>

	<p>That has to be just about the funniest use of bold-face I&#8217;ve seen on the intertubes.  I tried skimming your post, and if anything, the boldface just got in the way &#8211; it makes your comment more like the fold-up back cover that I recall from Mad Magazine when I was a wee tyke.  It seems to me that your comment not only falls under at least one of the classifications in <a href="http://crookedtimber.org/2009/11/22/a-vaguely-passive-aggressive-post-on-commenters/" rel="nofollow">CB&#8217;s post</a> the other day, (as does this comment <span class="caps">BTW</span>), but cries out for the development of several new ones not even mentioned in the comments to that post (e.g., <a href='http://crookedtimber.org/2009/11/22/a-vaguely-passive-aggressive-post-on-commenters/#comment-295850' rel="nofollow">here</a>, or  <a href='http://crookedtimber.org/2009/11/22/a-vaguely-passive-aggressive-post-on-commenters/#comment-296014' rel="nofollow">here</a>).</p>
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		<title>By: J. Fisher</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-1/#comment-296191</link>
		<dc:creator>J. Fisher</dc:creator>
		<pubDate>Tue, 24 Nov 2009 17:24:21 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296191</guid>
		<description>&lt;i&gt;I have three five-drawer file cabinets in my office, full to bursting with the records of class preparations, former graduate students, essays assigned in faculty reading groups, tenure and promotion reviews, offprints and copies of old essays, book contracts, and so forth. &lt;/i&gt;

You keep former graduate students in your file cabinets?  You never cease to amaze, Michael.</description>
		<content:encoded><![CDATA[	<p><i>I have three five-drawer file cabinets in my office, full to bursting with the records of class preparations, former graduate students, essays assigned in faculty reading groups, tenure and promotion reviews, offprints and copies of old essays, book contracts, and so forth. </i></p>

	<p>You keep former graduate students in your file cabinets?  You never cease to amaze, Michael.</p>
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		<title>By: bianca steele</title>
		<link>http://crookedtimber.org/2009/11/23/from-the-files-where-in-the-world/comment-page-1/#comment-296190</link>
		<dc:creator>bianca steele</dc:creator>
		<pubDate>Tue, 24 Nov 2009 17:19:44 +0000</pubDate>
		<guid isPermaLink="false">http://crookedtimber.org/?p=13880#comment-296190</guid>
		<description>@38: Well put.  But I think it&#039;s important that the proportion of any population that is really good at mathematics--doing manipulations, remembering and understanding the application of new notations, simply understanding abstraction itself (what an abstraction is) as well as commutation, etc., etc.--is pretty small.  Those are the students who are able to answer your introductory questions.  I agree that increasing real understanding is important.  I do question the idea that the way you seem to be going about rebuilding the curriculum from the ground up is the best way to gradually broaden the distribution of knowledge about math.

This seems like a hijacking, sorry.  Geography and even map reading aren&#039;t much like mathematics (not at at the college level), and different models are appropriate to different subject matters.  It truly is impressive how many randomly selected Italians can identify Cuba on an unmarked map, but I think most people will get by just fine even if they can&#039;t tell which is Cuba and which Puerto Rico, or the latter from Hispaniola.</description>
		<content:encoded><![CDATA[	<p>@38: Well put.  But I think it&#8217;s important that the proportion of any population that is really good at mathematics&#8212;doing manipulations, remembering and understanding the application of new notations, simply understanding abstraction itself (what an abstraction is) as well as commutation, etc., etc.&#8212;is pretty small.  Those are the students who are able to answer your introductory questions.  I agree that increasing real understanding is important.  I do question the idea that the way you seem to be going about rebuilding the curriculum from the ground up is the best way to gradually broaden the distribution of knowledge about math.</p>

	<p>This seems like a hijacking, sorry.  Geography and even map reading aren&#8217;t much like mathematics (not at at the college level), and different models are appropriate to different subject matters.  It truly is impressive how many randomly selected Italians can identify Cuba on an unmarked map, but I think most people will get by just fine even if they can&#8217;t tell which is Cuba and which Puerto Rico, or the latter from Hispaniola.</p>
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