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	<title>Comments on: On multiple choice questions in mathematics</title>
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	<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/</link>
	<description>Updates on my research and expository papers, discussion of open problems, and other maths-related topics.  By Terence Tao</description>
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		<title>By: Rex</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-129629</link>
		<dc:creator><![CDATA[Rex]]></dc:creator>
		<pubDate>Tue, 21 Feb 2012 13:15:34 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-129629</guid>
		<description><![CDATA[The link to the &quot;Princess Bride&quot; video is defunct.

&lt;i&gt;[Updated, thanks - T.]&lt;/i&gt;]]></description>
		<content:encoded><![CDATA[<p>The link to the &#8220;Princess Bride&#8221; video is defunct.</p>
<p><i>[Updated, thanks - T.]</i></p>
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		<title>By: Interesting and Must Read Papers and Articles in Mathematics &#124; MY DIGITAL NOTEBOOK</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-118716</link>
		<dc:creator><![CDATA[Interesting and Must Read Papers and Articles in Mathematics &#124; MY DIGITAL NOTEBOOK]]></dc:creator>
		<pubDate>Tue, 27 Dec 2011 03:41:27 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-118716</guid>
		<description><![CDATA[[...] Multiple Choice Questions in Mathematics http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/ Terence [...]]]></description>
		<content:encoded><![CDATA[<p>[...] Multiple Choice Questions in Mathematics <a href="http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/" rel="nofollow">http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/</a> Terence [...]</p>
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		<title>By: PETER MWALIMU MWENDWA</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-113441</link>
		<dc:creator><![CDATA[PETER MWALIMU MWENDWA]]></dc:creator>
		<pubDate>Wed, 07 Dec 2011 08:38:41 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-113441</guid>
		<description><![CDATA[Rarely will you find life challenges well packaged into two, three or five sets of choices from which to pick one&#039;s option. In the same vein, if mathematics is to be effectively used to enable persons to make useful decisions in life, then assessment should not be a package of choices for every problem posed. It should be a spark to ignite one&#039;s variety of views to the problem with minimal restriction or distraction to sway ones creativity away from the norm. Multiple choice tests in mathematics may effectively discourage originality and advancement of theories by lingering around the established norms ( Pythagoras theory, Eulers theory, ....) and not allowing creative follow up and meaningful advancement or critique of the said norms. 

When will mathematics be viewed as it should: a very cognitively nourishing  spectrum of opportunities and a way to overcome many life puzzles? This cannot be the view if one is bound by perhaps faulty imaginations of another   party in the name of the examiner. Mathematics should be a liberating rather than an enslaving and thought restricting discipline. It should be a bedrock of scientific disciplines as well as arts by setting the mind free to manipulate ideas and prove results. This encourages innovation and adventure and is a recipe for industrial revolution in any economy.

Whereas options may crop up in life, certainly not in all instances and when they do, first the liberal mind is the best to get the most appropriate option. Assessment should therefore encourage independence of thought in consideration of other people&#039;s findings and not bind the learner in the perhaps shallow confines of the one or few persons&#039; setting the questions and devising the possible options. It should spark or rather elicit a rich response or opinion of the learner allowing him/her to believe in oneself and defend one&#039;s stand point.

Multiple choice tests should rarely be used in summative evaluation unless in a very minimal extent.]]></description>
		<content:encoded><![CDATA[<p>Rarely will you find life challenges well packaged into two, three or five sets of choices from which to pick one&#8217;s option. In the same vein, if mathematics is to be effectively used to enable persons to make useful decisions in life, then assessment should not be a package of choices for every problem posed. It should be a spark to ignite one&#8217;s variety of views to the problem with minimal restriction or distraction to sway ones creativity away from the norm. Multiple choice tests in mathematics may effectively discourage originality and advancement of theories by lingering around the established norms ( Pythagoras theory, Eulers theory, &#8230;.) and not allowing creative follow up and meaningful advancement or critique of the said norms. </p>
<p>When will mathematics be viewed as it should: a very cognitively nourishing  spectrum of opportunities and a way to overcome many life puzzles? This cannot be the view if one is bound by perhaps faulty imaginations of another   party in the name of the examiner. Mathematics should be a liberating rather than an enslaving and thought restricting discipline. It should be a bedrock of scientific disciplines as well as arts by setting the mind free to manipulate ideas and prove results. This encourages innovation and adventure and is a recipe for industrial revolution in any economy.</p>
<p>Whereas options may crop up in life, certainly not in all instances and when they do, first the liberal mind is the best to get the most appropriate option. Assessment should therefore encourage independence of thought in consideration of other people&#8217;s findings and not bind the learner in the perhaps shallow confines of the one or few persons&#8217; setting the questions and devising the possible options. It should spark or rather elicit a rich response or opinion of the learner allowing him/her to believe in oneself and defend one&#8217;s stand point.</p>
<p>Multiple choice tests should rarely be used in summative evaluation unless in a very minimal extent.</p>
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		<title>By: vishnu kumar</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-68242</link>
		<dc:creator><![CDATA[vishnu kumar]]></dc:creator>
		<pubDate>Thu, 18 Aug 2011 11:27:08 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-68242</guid>
		<description><![CDATA[i  wants to more examples]]></description>
		<content:encoded><![CDATA[<p>i  wants to more examples</p>
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		<title>By: Manoj Srinivasan</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-46789</link>
		<dc:creator><![CDATA[Manoj Srinivasan]]></dc:creator>
		<pubDate>Sat, 04 Sep 2010 23:29:26 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-46789</guid>
		<description><![CDATA[Gerard:

Your &quot;source-of-sound&quot; question, and especially what you call the correct answer, sounds a bit fishy to me.

You say every source of sound is a net emitter of sound. 

Take some big machine (like a computer, say), that eats a LOT of energy (that is, work is performed on it), and produces a TINY little bit of sound. Such a machine would be emitting sound, but will be a net absorber of energy. So not all sound emitters are &#039;net&#039; emitters of energy.

In fact, THE quintessential emitter of sound -- a speaker -- typically has about 1% efficiency. That is, 99% of electrical power input gets converted to heat. Now if you carefully heat-insulate the speaker, the speaker would be a very good net absorber of energy.

Anyway, I think one should carefully define what &quot;a source of sound&quot; means, before asking/answering this question.]]></description>
		<content:encoded><![CDATA[<p>Gerard:</p>
<p>Your &#8220;source-of-sound&#8221; question, and especially what you call the correct answer, sounds a bit fishy to me.</p>
<p>You say every source of sound is a net emitter of sound. </p>
<p>Take some big machine (like a computer, say), that eats a LOT of energy (that is, work is performed on it), and produces a TINY little bit of sound. Such a machine would be emitting sound, but will be a net absorber of energy. So not all sound emitters are &#8216;net&#8217; emitters of energy.</p>
<p>In fact, THE quintessential emitter of sound &#8212; a speaker &#8212; typically has about 1% efficiency. That is, 99% of electrical power input gets converted to heat. Now if you carefully heat-insulate the speaker, the speaker would be a very good net absorber of energy.</p>
<p>Anyway, I think one should carefully define what &#8220;a source of sound&#8221; means, before asking/answering this question.</p>
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		<title>By: Gérard P. Michon</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-39793</link>
		<dc:creator><![CDATA[Gérard P. Michon]]></dc:creator>
		<pubDate>Mon, 29 Jun 2009 15:42:44 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-39793</guid>
		<description><![CDATA[Not all multiple-choice questions are bad.  However, students who have been routinely rewarded for speed with little or no &quot;penalty for guessing&quot; often miss the point of well-designed questions, like this superbly crafted example (not mine ;-) where actual thinking IS required and rewarded:

The source of every sound is something that is
A) undergoing simple harmonic motion.
B) accelerating.
C) a net emitter of energy.
D) moving.
E) vibrating.

http://answers.yahoo.com/question/index?qid=20080809103803AApEWeK
Apparently, fewer than 20% of &quot;guessers&quot; pick the ONLY correct choice (C) because most or all wrong answers may look better, or more &quot;plausible&quot; at first.

Questions of that quality being so rare, it&#039;s still safe to say that multiple-choice exams are a disgrace (except, possibly, in quick self-evaluations).

Also, let&#039;s not forget that exams graded by a teacher are a rare opportunity for students to assert themselves in a creative sense.  That opportunity is denied to them if they are only asked to check boxes...

The Big Picture: Education consists in passing civilization and knowledge from one generation to the next.  Ultimately, some students ought to be able to write better questions than their elders, or else the whole exercise is pointless and/or doomed... Checking boxes in front of existing questions does not help at all in that process.]]></description>
		<content:encoded><![CDATA[<p>Not all multiple-choice questions are bad.  However, students who have been routinely rewarded for speed with little or no &#8220;penalty for guessing&#8221; often miss the point of well-designed questions, like this superbly crafted example (not mine ;-) where actual thinking IS required and rewarded:</p>
<p>The source of every sound is something that is<br />
A) undergoing simple harmonic motion.<br />
B) accelerating.<br />
C) a net emitter of energy.<br />
D) moving.<br />
E) vibrating.</p>
<p><a href="http://answers.yahoo.com/question/index?qid=20080809103803AApEWeK" rel="nofollow">http://answers.yahoo.com/question/index?qid=20080809103803AApEWeK</a><br />
Apparently, fewer than 20% of &#8220;guessers&#8221; pick the ONLY correct choice (C) because most or all wrong answers may look better, or more &#8220;plausible&#8221; at first.</p>
<p>Questions of that quality being so rare, it&#8217;s still safe to say that multiple-choice exams are a disgrace (except, possibly, in quick self-evaluations).</p>
<p>Also, let&#8217;s not forget that exams graded by a teacher are a rare opportunity for students to assert themselves in a creative sense.  That opportunity is denied to them if they are only asked to check boxes&#8230;</p>
<p>The Big Picture: Education consists in passing civilization and knowledge from one generation to the next.  Ultimately, some students ought to be able to write better questions than their elders, or else the whole exercise is pointless and/or doomed&#8230; Checking boxes in front of existing questions does not help at all in that process.</p>
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		<title>By: Anonymous</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-39400</link>
		<dc:creator><![CDATA[Anonymous]]></dc:creator>
		<pubDate>Sat, 13 Jun 2009 06:13:45 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-39400</guid>
		<description><![CDATA[Do you think you could turn off the annoying &quot;snap shots&quot; on this blog?  I finally found instructions on how to do it:

http://www.blork.org/blorkblog/2008/03/31/how-to-disable-snap-shots-on-blogs/

&lt;i&gt;[Snap shots has been disabled for about a month or so here.  If others are still finding it activated, please notify me.  -T.]&lt;/i&gt;]]></description>
		<content:encoded><![CDATA[<p>Do you think you could turn off the annoying &#8220;snap shots&#8221; on this blog?  I finally found instructions on how to do it:</p>
<p><a href="http://www.blork.org/blorkblog/2008/03/31/how-to-disable-snap-shots-on-blogs/" rel="nofollow">http://www.blork.org/blorkblog/2008/03/31/how-to-disable-snap-shots-on-blogs/</a></p>
<p><i>[Snap shots has been disabled for about a month or so here.  If others are still finding it activated, please notify me.  -T.]</i></p>
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		<title>By: salman abbas</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-37817</link>
		<dc:creator><![CDATA[salman abbas]]></dc:creator>
		<pubDate>Fri, 03 Apr 2009 12:39:53 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-37817</guid>
		<description><![CDATA[I want to take exam as soon as possible]]></description>
		<content:encoded><![CDATA[<p>I want to take exam as soon as possible</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: TAYEM</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-36142</link>
		<dc:creator><![CDATA[TAYEM]]></dc:creator>
		<pubDate>Tue, 24 Feb 2009 19:38:58 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-36142</guid>
		<description><![CDATA[I  LOVE SUCH EFFORTS TO ENABLE STUDENTS TO STUDY EASILLY ONLINE.PLEASE I&#039;LL LOVE TO GET SOME EXERCISES FROM HERE.]]></description>
		<content:encoded><![CDATA[<p>I  LOVE SUCH EFFORTS TO ENABLE STUDENTS TO STUDY EASILLY ONLINE.PLEASE I&#8217;LL LOVE TO GET SOME EXERCISES FROM HERE.</p>
]]></content:encoded>
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		<title>By: AISHA</title>
		<link>http://terrytao.wordpress.com/2008/12/14/on-multiple-choice-questions-in-mathematics/#comment-35419</link>
		<dc:creator><![CDATA[AISHA]]></dc:creator>
		<pubDate>Mon, 02 Feb 2009 17:05:05 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1178#comment-35419</guid>
		<description><![CDATA[YA IT IS GOOD. I AM READY FOR TEST..............................]]></description>
		<content:encoded><![CDATA[<p>YA IT IS GOOD. I AM READY FOR TEST&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;</p>
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