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	<pubDate>Tue, 07 Jul 2009 10:28:27 +0000</pubDate>
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		<title>Revealing Mathematical Jokes</title>
		<link>http://workingmath.com/2009/05/12/revealing-mathematical-jokes/</link>
		<comments>http://workingmath.com/2009/05/12/revealing-mathematical-jokes/#comments</comments>
		<pubDate>Tue, 12 May 2009 13:48:40 +0000</pubDate>
		<dc:creator>Franz Rasch</dc:creator>
		
		<category><![CDATA[Math Articles]]></category>

		<category><![CDATA[characterisation of mathematic profession]]></category>

		<category><![CDATA[jokes]]></category>

		<category><![CDATA[mathematician jokes]]></category>

		<category><![CDATA[mathematics]]></category>

		<guid isPermaLink="false">http://workingmath.com/?p=45</guid>
		<description><![CDATA[A collection of mathematical jokes characterising the field and the profession wth links to mathematician jokes sites.]]></description>
			<content:encoded><![CDATA[<p><script type="text/javascript"><!--
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</script></p><p class="MsoNormal"><!--[if gte mso 9]&gt;    &lt;![endif]--><!--[if gte mso 9]&gt;  Normal 0 21   &lt;![endif]--><span style="font-family: Arial;" lang="EN-GB">It can safely be said that jokes and satire are often the most condensed characterisation of a person, profession or political group.</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">The same goes for mathematicians – the majority of the populace hold the belief they themselves are not particularly good at maths (or even loathe it) and that the way mathematicians think is especially hard to understand.</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">We’ll try and take the jocular approach and have tried to collect a few jokes that highlight certain features of the mathematical profession and sometimes we add a comment as to what specific epistemological issue this joke alludes to. And as with all things mathematical, there is of course <a href="http://en.wikipedia.org/wiki/Mathematical_joke"><strong>a theoretical approach to math jokes</strong></a> …</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">An astronomer, a physicist and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">&#8220;How interesting,&#8221; observed the astronomer, &#8220;all Scottish sheep are black!&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">To which the physicist responded, &#8220;No, no! Some Scottish sheep are black!&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">The mathematician gazed heavenward in supplication, and then intoned, &#8220;In Scotland there exists at least one field, containing at least one sheep, at least <em>one side of which</em> is black.<span id="more-45"></span></span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">And another nice one:</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">One day a mathematician decides that he is sick of math. So, he walks down to the fire department and announces that he wants to become a fireman.</span></p>
<p class="MsoNormal"><span lang="EN-GB">The fire chief says, &#8220;Well, you look like a good guy. I&#8217;d be glad to hire you, but first I have to give you a little test.&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">The firechief takes the mathematician to the alley behind the fire department which contains a dumpster, a spigot, and a hose. The chief then says, &#8220;OK, you&#8217;re walking in the alley and you see the dumpster here is on fire. What do you do?&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB">The mathematician replies, &#8220;Well, I hook up the hose to the spigot, turn the water on, and put out the fire.&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">The chief says, &#8220;That&#8217;s great&#8230; perfect. Now I have to ask you just one more question. What do you do if you&#8217;re walking down the alley and you see the dumpster is not on fire?&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB">The mathematician puzzles over the question for awhile and he finally says, &#8220;I light the dumpster on fire.&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB">The chief yells, &#8220;What? That&#8217;s horrible! Why would you light the dumpster on fire?&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB">The mathematician replies, &#8220;Well, that way I reduce the problem to one I&#8217;ve already solved.&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">And a nice quotation:</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different.</span></p>
<p class="MsoNormal" style="text-align: right;" align="right"><em><span lang="EN-GB">Johann Wolfgang von Goethe</span></em></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">And don’t miss this one:</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">Some say the pope is the greatest cardinal.</span></p>
<p class="MsoNormal"><span lang="EN-GB">But others insist this cannot be so, as every pope has a successor.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://www.workjoke.com/mathematicians-jokes.html"><strong>http://www.workjoke.com/mathematicians-jokes.html</strong></a></span></p>
<p class="DefinitionTerm"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">An infinite crowd of mathematicians enters a bar.</span></p>
<p class="MsoNormal"><span lang="EN-GB">The first one orders a pint, the second one a half pint, the third one a quarter pint&#8230;</span></p>
<p class="MsoNormal"><span lang="EN-GB">&#8220;I understand&#8221;, says the bartender - and pours two pints.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">Q: When did <a href="http://www.123exp-biographies.com/t/00034114703/"><strong><span>Bourbaki</span></strong></a> stop writing books?</span></p>
<p class="MsoNormal"><span lang="EN-GB">A: When they realized that <a href="http://www.123exp-biographies.com/t/00034306668/,Serge%20Lang,Serge%20Lang"><strong><span>Serge Lang</span></strong></a> was a single person &#8230;</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">That’s a nice one: <a href="http://en.wikipedia.org/wiki/Nicolas_Bourbaki"><strong>Bourbaki</strong></a> was actually a group a academics (officially &#8220;Association des collaborateurs de Nicolas Bourbaki&#8221; at the École Normale Supérieure in Paris, while <a href="http://en.wikipedia.org/wiki/Serge_Lang"><strong>Serge Lang</strong></a> was a French-born American mathematician known for his work in number theory etc. A member of the Bourbaki group &#8220;He was a prolific writer of mathematical texts, often completing one on his summer vacation.&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><strong><span lang="EN-GB">Theorem</span></strong><span lang="EN-GB">. A cat has nine tails.</span></p>
<p class="MsoNormal"><strong><span lang="EN-GB">Proof</span></strong><span lang="EN-GB">. No cat has eight tails. Since one cat has one more tail than no cat, it must have nine tails.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://www.math.ualberta.ca/~runde/jokes.html"><strong>http://www.math.ualberta.ca/~runde/jokes.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">Old mathematicians never die; they just lose some of their functions.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">There is no logical foundation of mathematics, and Gödel proved it!</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">A statistician is someone who is good with numbers but lacks the personality to be an accountant.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">A mathematician is asked to design a table. He first designs a table with no legs. Then he designs a table with infinitely many legs. He spend the rest of his life generalizing the results for the table with N legs (where N is not necessarily a natural number).</span></p>
<p class="DefinitionTerm"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://www.math.utah.edu/~cherk/mathjokes.html"><strong>http://www.math.utah.edu/~cherk/mathjokes.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">Another great collection can be found here:</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://mathworld.wolfram.com/topics/MathematicalHumor.html"><strong>http://mathworld.wolfram.com/topics/MathematicalHumor.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">And the anthology &#8220;<a href="http://www.ams.org/notices/200501/fea-dundes.pdf"><strong>Foolproof: A Sampling of Mathematical Folk Humor</strong></a>&#8221; by Paul Renteln and Alan Dundes</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">An absent minded professor (alright, it was <a href="http://en.wikipedia.org/wiki/Norbert_Wiener"><strong><span>Norbert Wiener</span></strong></a>) was moving. His wife, knowing Norbert would forget his address, took out a sheet of paper and wrote it down for him. Later that day, Norbert had a flash of insight, and fumbling for a piece of paper, wrote down his new theorem on the paper his wife gave him. On further reflection, Norbert found a fallacy in this thinking and threw out the paper in disgust. When he came home that night, to the now empty house he moved from, he remembered he had moved, but had no idea where he had moved to. Just then he spied a little girl on the street. &#8220;Little girl,&#8221; he asked, &#8220;my name is Norbert Wiener, do you know where I live now?&#8221; &#8220;Yes daddy, mommy thought you would forget.&#8221;</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">Two Jews on a train in Russia. One asks the other, &#8220;Where are you going?&#8221; and the second one replies, &#8220;To Kiev.&#8221; Whereupon the first says, &#8220;You liar, you tell me you are going to Kiev so I would think you are going to Odessa. But I know you are going to Kiev, so why do you lie?&#8221;</span></p>
<p class="MsoNormal" style="text-align: right;" align="right"><em><span lang="EN-GB">From <a title="Adventures of a Mathematician  by S. M. Ulam" href="http://vur.me/s/Ulam" target="_blank">Adventures of a Mathematician</a>, Stan Ulam&#8217;s autobiography (p. 143)</span></em></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://varatek.com/scott/math_jokes.html"><strong>http://varatek.com/scott/math_jokes.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">And then some:</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://camel.math.ca/Recreation/mjokes-1.html"><strong>http://camel.math.ca/Recreation/mjokes-1.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">In the bayous of Louisiana, there is a small river called the Dirac. Many wealthy people have their mansions near its mouth. One of the social leaders decided to have a grand ball. Being a cousin of the Governor, she arranged for a detachment of the state militia to serve as guards and traffic directors for the big doings. A captain was sent over with a small company; naturally he asked if there was enough room for him and his unit. The social leader replied, “But of course, Captain! It is well known that the <a href="http://en.wikipedia.org/wiki/Dirac_delta_function"><strong><span>Dirac delta function</span></strong></a> has unit area.”</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://komplexify.com/epsilon/2008/11/10/the-dirac-river/"><strong>http://komplexify.com/epsilon/2008/11/10/the-dirac-river/</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">(This is about mathematician <a href="http://en.wikipedia.org/wiki/Dirac"><strong>Paul Dirac</strong></a>.) They have a whole lot of math jokes here:</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://komplexify.com/math/humor.html"><strong>http://komplexify.com/math/humor.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">And still some more:</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://www.ahajokes.com/math_jokes.html"><strong>http://www.ahajokes.com/math_jokes.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://www.sonoma.edu/math/faculty/falbo/jokes.html"><strong>http://www.sonoma.edu/math/faculty/falbo/jokes.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><a href="http://www.sgoc.de/math.html"><strong>http://www.sgoc.de/math.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">It was mentioned on CNN that the new prime number discovered recently is four times bigger than the previous record.</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">Ha hum … <a href="http://www.juliantrubin.com/mathjokes.html"><strong>http://www.juliantrubin.com/mathjokes.html</strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">Another one concerning physicists is nice too and must be commended for its poetic form as well as the entangled wit:</span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">The Perils of Modern Living</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">Well up above the tropostrata<br />
</span><span lang="EN-GB">There is a region stark and stellar</span><span lang="EN-GB"><br />
Where, on a streak of anti-matter<br />
Lived Dr. Edward Anti-Teller.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">Remote from Fusion&#8217;s origin,<br />
</span><span lang="EN-GB">lived unguessed and unawares<br />
</span><span lang="EN-GB">With all his antikith and kin,<br />
And kept <a href="http://en.wikipedia.org/wiki/Antimacassar"><strong><span>macassars</span></strong></a> on his chairs.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">One morning, idling by the sea,<br />
</span><span lang="EN-GB">He spied a tin of monstrous girth</span><span lang="EN-GB"><br />
That bore three letters: <a href="http://en.wikipedia.org/wiki/United_States_Atomic_Energy_Commission"><strong><span>A. E. C.<br />
</span></strong></a>Out stepped a visitor from Earth.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">Then, shouting gladly o&#8217;er the sands,</span><span lang="EN-GB"><br />
Met two who in their alien ways<br />
Were like as lentils. Their right hands<br />
Clasped, and the rest was gamma rays.</span></p>
<p class="MsoNormal"><span lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span lang="EN-GB">by <a href="http://en.wikipedia.org/wiki/Harold_Furth"><strong><span>Harold P. Furth</span></strong></a></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
<p class="MsoNormal"><span style="font-family: Arial;" lang="EN-GB">Tropostrata: combination of <a href="http://en.wikipedia.org/wiki/Troposphere"><strong>troposphere</strong></a> and <a href="http://en.wikipedia.org/wiki/Stratosphere"><strong>stratosphere</strong></a>. <a href="http://en.wikipedia.org/wiki/Antimatter"><strong>Antimatter</strong></a> and <a href="http://en.wikipedia.org/wiki/Gamma_rays"><strong>gamma rays</strong></a>: &#8220;The presence of … antimatter is detectable by the gamma rays produced when <a href="http://en.wikipedia.org/wiki/Positron"><strong>positrons</strong></a> annihilate with nearby matter.&#8221;</span></p>
<p class="DefinitionTerm"><span style="font-family: Arial;" lang="EN-GB"><!--[if !supportEmptyParas]--> <!--[endif]--></span></p>
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		<title>Mathematical Thinking - How Children Learn to &#8230;</title>
		<link>http://workingmath.com/2009/04/30/mathematical-thinking-how-children-learn-to/</link>
		<comments>http://workingmath.com/2009/04/30/mathematical-thinking-how-children-learn-to/#comments</comments>
		<pubDate>Wed, 29 Apr 2009 23:17:13 +0000</pubDate>
		<dc:creator>Franz Rasch</dc:creator>
		
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		<description><![CDATA[Mathematical teaching at school or in kindergarten unfortunately is mostly not oriented at how children form their mathematical constructs. Rather is is taught as an afterthought of academic study of "how mathematics would be taught if human beings were robots or computers". Unfortunately this puts many children off, it can lead to deep frustration and in the end leave them with a feeling that "mathematics is not for them" that carries over into adult life. But things could be much easier if human mathematical learning were taken into consideration. Here's how.]]></description>
			<content:encoded><![CDATA[<p>While humankind developed the faculty of speech probably hundreds of thousands of years ago, complex mathematical thinking seems to have been an afterthought of human development. It seems that the concept of numbers as discrete entities on which certain specifically arithmetical operations can be performed is not older than eight thousand years, symbolic calculus and mathematical proof (esp. in geometry) date back only about two and a half thousand years in ancient Greece, differential calculus is about 400 years old, negative numbers were consciously introduced into mathematics in the eighteenth century and abstract algebraic concepts date back less than 200 years. In other words, high school level math is on a level that maybe two hundred years ago a university professor would not have mastered while linguistic and rhetoric abilities were certainly always superior in adults of any age than in children or teenagers.<span id="more-30"></span>In his book &#8220;The Mathematical Gene&#8221; Keith Devlin tries to show how mathematical abilities must be closely linked to earlier linguistic abilities since they could hardly have evolved in the short span of 8,000 years or less. From this we may conclude two things:</p>
<ul>
<li>everyone who&#8217;s good at languages should be able to cope with mathematics and</li>
<li>if people grapple with math it might be caused by the didactical methods and not by a lack of mathematical talent.</li>
</ul>
<p>While language is picked up through the intimate communication between child and parent, there is no equally relaxed and subtle communication about math in these first formative years. Maybe there should be. Children can pick up more than one native language, some children speaking not only two but four and more fluently by the age of three or four. What if mathematics were just another language and picked up just as easily?</p>
<p>This article is to give future generations and you as parents a little hope and some pointers. We are currently developing teaching concepts for pain- and effortless mathematical education at our sister website <a title="Interactive Mathematical Teaching and Learning" href="http://www.viaregia.ch/" target="_blank">www.viaregia.ch</a> which will address exactly these issues. While we&#8217;re still in preparation phase, we want to shed a little light on what to expect from these methods soon.</p>
<p>Before we write a whole book on the subject (you will find one on the subject on <a title="Captain Mnemo - THE site for all your learning needs!" href="http://www.captainmnemo.net/" target="_blank">www.captainmnemo.net</a> in the near future) let us share some bullet points here:</p>
<p>a) (multiplication) tables are not calculated, they&#8217;re learnt by heart (and by rote in most cases, although we&#8217;re going to address that on <a title="Interactive Mathematical Teaching and Learning" href="http://www.viaregia.ch/" target="_blank">www.viaregia.ch</a> too). Giving children the impression that adults calculated confuses children. Let&#8217;s be honest with them.</p>
<p>b) Mathematics itself has much to do with pattern recognition and analysis, in geometry it&#8217;s obvious, but it is equally true for set theory, number theory, topology and all other areas of mathematics.</p>
<p>c) To be able to think mathematically you need to think logically; the formal logic underlying speech analysis and discourse is much the same as is used in mathematics.</p>
<p>d) Even babies have an idea of numbers or otherwise they would not be able to recognise if something was missing from or added to a group of identical items, e.g. building blocks. In the very first days after birth babies can already distinguish between the cardinal number two and three.</p>
<p>e) But when it comes to sets greater than three, a different mechanism seems to operate in the human brain. Up to three items are recognised immediately, if the number increases, the recognition time increases too, suggestion that now a counting mechanism is employed.</p>
<p>f) If you look at calculation tables from 1 to 100 then you need not remember 100 facts but just 18 (!), since 3*7 is the same as 7*3, bringing it down to fifty, then allowing for the first row being from 1 to 10, so you can deduct that, equally 1*10 to 10*10 etc. 18 items to learn by heart and still children and even many adults struggle here while as a six-year-old they already knew up to 100,000 words in their native language (when counting &#8220;go&#8221; and &#8220;went&#8221; as separate words). Amazing. This points to some obstacle that is on one hand rather obstinate while suggesting that it on the other hand should be quite easy to overcome once analysed properly. This is what workingmath.com is all about &#8230;</p>
<p>One reason for this seems to be that mathematics is a type of language but that mathematical entities, esp. numbers are expressed both in the language of mathematics as well as in normal speech. It&#8217;s as if you tried to force a bilingual child to always listen in one and answer in the other language. And indeed, children whose native language mimics the mathematical number constructs more closely also learn their tables etc. much easier and earlier, e.g. Japanese and Chinese. While English speakers need to figure out that twelve means ten and two, while twenty-three means two tens and three, the Chinese know this to be ten-two (12) and two-tens and three (23) etc. that&#8217;s probably the main reason why Chinese children at age four can count to forty, while US-American children just master fifteen at that age.</p>
<p>All readers will hopefully agree that Chinese and US or English toddlers are born equal and that there&#8217;s no room for ideas about racial supremacy. If that is so, then we need to rethink how math, and arithmetic for starters, is taught at school, in fact, how the foundations should be laid in pre-school so that mathematical thinking for children becomes as effortless as the grasp of their native language at that age normally is. Stay tuned, we will shed more light on exactly this problem and some possible solutions in this blog.</p>
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		<title>About Workingmath.com</title>
		<link>http://workingmath.com/2009/04/12/about-workingmathcom/</link>
		<comments>http://workingmath.com/2009/04/12/about-workingmathcom/#comments</comments>
		<pubDate>Sun, 12 Apr 2009 13:10:19 +0000</pubDate>
		<dc:creator>Franz Rasch</dc:creator>
		
		<category><![CDATA[Math Articles]]></category>

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		<guid isPermaLink="false">http://workingmath.com/?p=10</guid>
		<description><![CDATA[This site will bring to you information on the training of children (or adults who like our methods) in arithmetics and from there on mathematics in general. Learning to count, then to calculate and later to grasp more complex mathematical constructs takes time. To some children it seems to come just naturally, but many others [...]]]></description>
			<content:encoded><![CDATA[<p>This site will bring to you information on the training of children (or adults who like our methods) in arithmetics and from there on mathematics in general. Learning to count, then to calculate and later to grasp more complex mathematical constructs takes time. To some children it seems to come just naturally, but many others abhor the whole subject of mathematics for the rest of their lives.  This need not be.  Mathematics can be great fun and it is this fun we want to bring back to you should you somehow lost it or make sure your child never loses while it still has a chance.</p>
<p>Watch future posts on this blog regarding all aspects of mathematics that we&#8217;ll eventually cover. For today, just consider this:</p>
<p>About 75% of all arithmetic you need later in life is simple additions, maybe 20% subtractions, then very little multiplications while the times you need to really divide any larger numbers is negligible in comparison. This leads to two simultaneous conclusions: you should be a good adder <img src='http://workingmath.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' /> to master everyday mathematical requirements but you also ought to master those calculations that you rarely need.  It&#8217;s like when you&#8217;re driving: you need to know about the accelerator, the steering wheel etc., in short you need to be able to at least navigate your car. But from time to time you need to check the oil, the brake fluid etc., even if you normally let someone else check on these. You most certainly should know that mixing the two up could be life-threatening or at least damage your engine. Certainly you need to be able to refill the windscreen washer system by yourself if necessary or check the tyres and be able to (re)inflate them. And you need to be able to sense if something&#8217;s awry even if you&#8217;re not able to finally diagnose it, much less repair it, right?<span id="more-10"></span>It&#8217;s very much the same with basic mathematics: you need at least to be able to understand if someone else who does calculations affecting you (like your bank calculating your mortgage, your insurance broker or a real-estate agent) are on the right track at all. I&#8217;ve seen bankers getting 30 year mortgages all wrong, and many people think that if something increases 7% per year then after 10 years that means to look at 170% - while actually any capital that bears 7% interest annually would effectively double in ten years time.</p>
<p>You need to be able to add and multiply to work out these or it could cost you dearly.</p>
<p>Now, while we all know that in later life we need very, very little of the mathematics e.g. taught at high school, we do know that no kid can get away without it while there or else they won&#8217;t move on to college or even any decent job if they don&#8217;t get some respectable grades. It acts more as a filter rather than anything else and all parents want their kids to squeeze past these.</p>
<p>Unfortunately, if there are gaps in your or your children&#8217;s mathematical understanding, you will never get a real grasp of the subject matter, although anyone with a brain can master at least high school mathematics!</p>
<p>So we designed a course that will let everyone start at the proficiency level they really have and end at where they want to get to. You see, if you go to a restaurant that looks run-down, the food is served cold and arranged so that it turns you off you won&#8217;t eat much or nothing at all and you won&#8217;t return. Maybe they can force you to return, but they can&#8217;t make you eat or at least they can&#8217;t make you enjoy it, can they? If, likewise, at school you feel uneasy about a subject then they may be able to force you back there five days a week but you and they find you won&#8217;t really learn much, right? Did you draw the conclusion, from visiting a scrubby restaurant, that eating is not for you? Well, you may have been lucky and indeed have tasted some delicious food somewhere else before you visited. That made you quite immune to the thought that eating isn&#8217;t for you, probably. And so, if you visit that scrubby restaurant, it will only have been twice: the first and last time (nice math pun &#8230;). Unfortunately, the first time you or your kids were confronted with mathematics in earnest it might just not have tasted right and from then on you and calculus were at loggerheads. However, with the way schools operate you were barred from taking your custom elsewhere resp. you knew that the math restaurant next door wasn&#8217;t any better.</p>
<p>In comes workingmath.com where we try to cover all the subjects that might interest you around mathematics and its sister sites viaregia.ch where soon our computer-based training courses will begin while on CaptainMnemo.Net you are taken through actually the whole syllabus, not only math, by Captain Mnemo in his miraculous submarine cum spaceship exploring the wonders of nature while finding mathematical structures in the spiralling snail shell as well as in outer space when approaching black holes and spiralling galaxies. Start watching this spot, subscribe to our newsletters and RSS feeds and we&#8217;ll keep you posted, to show you how to climb the path to brilliance!</p>
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		<title>New Math Site &#8220;ViaRegia Math&#8221;</title>
		<link>http://workingmath.com/2009/04/05/new-math-site-viaregia-math/</link>
		<comments>http://workingmath.com/2009/04/05/new-math-site-viaregia-math/#comments</comments>
		<pubDate>Sun, 05 Apr 2009 15:34:22 +0000</pubDate>
		<dc:creator>admin</dc:creator>
		
		<category><![CDATA[Math Sites]]></category>

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		<guid isPermaLink="false">http://workingmath.com/?p=4</guid>
		<description><![CDATA[ViaRegia Math is a interactive math learn page where beginners can practice simple arithmetics.
]]></description>
			<content:encoded><![CDATA[<p>ViaRegia Math is a interactive math learn page where beginners can practice simple arithmetics.<img class="size-medium wp-image-5 alignleft" title="Screenshot: Start page" src="http://workingmath.com/wp-content/uploads/2009/04/003-300x185.png" alt="Screenshot: Start page" width="300" height="185" /></p>
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