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		<title>Dispatches from the Learning Lab: Inauthentic Agreement</title>
		<link>http://researchinpractice.wordpress.com/2012/01/25/dispatches-from-the-learning-lab-inauthentic-agreement/</link>
		<comments>http://researchinpractice.wordpress.com/2012/01/25/dispatches-from-the-learning-lab-inauthentic-agreement/#comments</comments>
		<pubDate>Wed, 25 Jan 2012 15:57:07 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Learning Research]]></category>
		<category><![CDATA[Math Education]]></category>
		<category><![CDATA[disorientation]]></category>
		<category><![CDATA[encouragement]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=917</guid>
		<description><![CDATA[Here&#8217;s another one. It should be quick. When a student says, &#8220;Is it like this?&#8221; or the equivalent, I used to err on the side of &#8220;yes.&#8221; I.e. even if I wasn&#8217;t sure exactly what they were saying, but I thought it sounded like it might make sense. I think this was somewhat a function [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=917&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Here&#8217;s another one. It should be quick.</p>
<p>When a student says, &#8220;Is it like this?&#8221; or the equivalent, I used to err on the side of &#8220;yes.&#8221; I.e. even if I wasn&#8217;t sure exactly what they were saying, but I thought it sounded like it might make sense. I think this was somewhat a function of the fact that I adopted a generally encouraging posture (this is my personality but also a deliberate choice), but it itself was just sort of my reflexive response from within this posture (not a deliberate choice).</p>
<p>It never felt quite right, so over time I trained myself instead to say things like, &#8220;I can&#8217;t understand what you&#8217;re saying but I think you might be onto something, but I&#8217;m not sure.&#8221; I never had concrete evidence that my original response was doing something unhelpful though.</p>
<p>Now I do. In a recent conversation with one of my teachers, several times I said, &#8220;Let me explain back to you what I think you&#8217;re saying, and you tell me if it&#8217;s right&#8230;&#8221; And he said, &#8220;yes yes yes it&#8217;s like&#8230;&#8221; But I didn&#8217;t recognize my attempted explanation in what he seemed to be saying yes to. So, it&#8217;s official: this is TOTALLY UNHELPFUL. I&#8217;m disoriented; that&#8217;s why I asked the question. Unless I come away from your answer feeling sure that you understood me, your &#8220;yes&#8221; only serves to make me more disoriented.</p>
<p>Take-home lesson. Never say &#8220;yes&#8221; unless you are sure you have understood fully what the student is saying, and agree with it. As I&#8217;ve often discussed before, sometimes a &#8220;yes&#8221; is inappropriate even then; for example if there&#8217;s a danger that the student is trying to foist onto you the work of judging for her or himself. But if you have any doubt, then the &#8220;yes&#8221; is <i>definitely</i> inappropriate: the encouragement is fake, and the student is left being equally unsure as before, and now also having exhausted the resource of checking with you. Retrospectively the only student who even feels good hearing the &#8220;yes&#8221; in this situation is the one who is <a href="http://researchinpractice.wordpress.com/2009/10/24/required-reading-for-math-teachers-i/">playing a Clever Hans game</a>, and in this case it does him or her the disservice of encouraging the game.</p>
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		<slash:comments>4</slash:comments>
	
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			<media:title type="html">benblumsmith</media:title>
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		<title>Dispatches from the Learning Lab: Why I Don&#8217;t Always Ask My Question</title>
		<link>http://researchinpractice.wordpress.com/2012/01/24/dispatches-from-the-learning-lab-why-i-dont-always-ask-my-question/</link>
		<comments>http://researchinpractice.wordpress.com/2012/01/24/dispatches-from-the-learning-lab-why-i-dont-always-ask-my-question/#comments</comments>
		<pubDate>Tue, 24 Jan 2012 15:21:25 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Learning Research]]></category>
		<category><![CDATA[Math Education]]></category>
		<category><![CDATA[confusion]]></category>
		<category><![CDATA[questions]]></category>
		<category><![CDATA[reflection]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=908</guid>
		<description><![CDATA[One of the many reasons I put myself in a math PhD program is that it is an intense full-time laboratory in which for me to examine my own learning process, and my experience as a participant in math classrooms from the student side. I hope to record many lessons from this laboratory on this [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=908&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>One of the many reasons I put myself in a math PhD program is that it is an intense full-time laboratory in which for me to examine my own learning process, and my experience as a participant in math classrooms from the student side. I hope to record many lessons from this laboratory on this blog. Here is one.</p>
<p>As a teacher I have always strongly encouraged people to pipe up when they&#8217;re confused, whether working in groups or (especially) at the level of whole-class discussion. To encourage this, I do things like:</p>
<p>* I leave lots of wait time.<br />
* I respond to questions (especially those expressing confusion) with enthusiasm when they are asked, and after they are discussed I point out concrete, specific ways in which the questions advanced the conversation.<br />
* I give (very deeply felt) pep talks about the value of these questions.<br />
* Sometimes I directly solicit questions from people whose faces make it seem like they have one.</p>
<p>I am behind all of these practices. However, in every class that I have taught, whether for students or teachers, including all those of an extended enough length so that the practices would have time to shape the culture, it has always seemed to me that participants are often not asking their questions. This has puzzled me a bit. I&#8217;ve generally responded by trying harder: leaving longer wait-time, making more of a point to highlight the value of questions when they happen, giving more strident and frequent pep talks. This hasn&#8217;t resolved the matter.</p>
<p>Now I am not about to pronounce a new solution. But I have what for me is a very new insight. I imagine some readers of this blog will read it and be like, &#8220;Ben, I could have told you that.&#8221; I&#8217;m sure you could have, but this wouldn&#8217;t have helped me: retrospectively, students have told me it many, many times. But I didn&#8217;t get it till I felt it. This is the value of putting yourself in their position.</p>
<p>What I&#8217;ve realized since beginning graduate school is that I had an incomplete understanding of why students don&#8217;t ask questions. <b>I believed that the <i>only</i> reason not to ask a question is the fear of looking dumb.</b> My approach has been entirely aimed at ameliorating this fear and replacing it with the sense that questions are honored and their contribution is valued.</p>
<p>Now one of the great advantages of going to grad school as an adult, rather than going fresh out of college, is that I have very, very little fear of looking dumb. (In the immortal words of my friend <a href="http://gritsnsoysauce.tumblr.com/">Kiku Polk</a>, you get your &#8220;f*ck you&#8221; at 30.) To all my early-20&#8242;s people: your 20&#8242;s will be wonderful but if you make sure you keep growing, your 30&#8242;s will be better.</p>
<p>And one of the great advantages of going to grad school after over a decade as a teacher, is that I have a strong commitment to asking my questions, stemming from the value that I know they have both for myself and the class.</p>
<p>Perhaps as a consequence, I found that in all four of my classes last semester, I asked more questions than anyone else in the room.</p>
<p>Be that as it may, I frequently didn&#8217;t ask my questions.</p>
<p>What&#8217;s up?</p>
<p>As it turns out (and now, okay, maybe this is Captain Obvious talking, but a propos of all of the above, somehow I&#8217;ve been overlooking it for a decade), <b>not wanting to hold up class is its own reason not to ask questions!</b> Maybe it&#8217;s a basic piece of our social programming. If things are going one way in a room of 20 or 30 people, it feels sort of painful to contemplate forcing them in another direction on your account. Especially if you&#8217;ve already done it once or twice, but even if not. And more so the further your question seems to be from what the people around you (esp. the teacher) look like they want to talk about. All this is intensified if you&#8217;re not sure your question is going to come out perfectly articulate &#8211; not (necessarily or only) because of how this will make you look, but because you know that your interruption is going to take up more mental and social space if it has to start with a whole period of everybody just getting clear on what you&#8217;re even asking.</p>
<p>There is an added layer that it is often perceptible that the teacher <i>desires</i> for everyone to understand and appreciate what was just said as clearly as she or he understands and appreciates it. Last night I was in a lecture in which I was hyperaware of not always asking my questions, and part of the dynamic in that case was actually the professor&#8217;s enthusiasm about what he was saying! I did ask a number of questions, but one reason I didn&#8217;t ask more is that I sort of felt like I was crashing his party! My warm feelings toward this professor actually heightened this effect: messing up someone else&#8217;s flow is worse when it&#8217;s someone you <i>like</i>.</p>
<p>As I mentioned above, students have been trying to tell me this for years. I never got it, because on some level I always believed that the <i>real</i> problem was that they were afraid to look dumb. I remember a conversation with a particular student who was my advisee as well as my math student. When I pressed her on asking more questions in class, she said something to the effect of, &#8220;you know, you&#8217;re doing your thing up there, and I don&#8217;t want to get in the way.&#8221; I literally remember the voice in my head reinterpreting this as a lack of belief in herself. Now I think that that was part of it as well; but my response was all aimed at that, and so didn&#8217;t address the whole issue.</p>
<p>Now my process of figuring out how to operationalize this new insight in terms of teaching practice has only just begun, and one reason I am writing about this here is to invite you into this process. I am certainly NOT telling you to withhold your enthusiasm on the grounds that it might make kids not want to interrupt you with questions. Furthermore, evidently when I describe experiences from my graduate classes, I am describing a situation in which the measures you and I have been taking for years to encourage question-asking are mostly absent. I doubt most of my professors have even <i>heard</i> of wait time. Nonetheless, I am sure that this new point of view is fruitful in terms of actual practice. Below are my preliminary thoughts. Please comment.</p>
<p>If I want to really encourage question asking, what I have been doing (aimed at building a <i>culture</i> of question-asking) is necessary, but insufficient. It is also necessary to think about lesson <i>structure</i> with an eye to: how do I design the flow of this lesson so that (at least during significant parts where questions are likely to arise in students&#8217; minds) <i>asking their questions does not feel like an interruption?</i> One model, which is valuable in other ways as well, is to have students&#8217; questions be <i>the desired product</i> of a certain segment of class. For example, when the lesson arrives at a key idea, definition, or conclusion, ask students to turn to their neighbors and discuss the key idea and try to produce a question about it. Then have the pairs or groups report their questions.  This way, the questions cannot be interruptions because they are explicitly the very thing that is supposed to be going on right then.</p>
<p>I like this idea but it has limited scope because it requires the point in the lesson at which the questions arise to be planned, and of course this can never contain all the questions I would want to have asked. Another thing to think about is the matter of momentum. I think my discussion of enthusiasm above really revolves around momentum. Enthusiasm generates momentum, but momentum is actually the thing that it hurts to get in the way of. Therefore I submit a second idea: the question of <i>managing my/your own and the class&#8217;s momentum</i>. Having forward momentum is obviously a big part of class being engaging, but perhaps it also suppresses spontaneous questions? Or under certain conditions it does?</p>
<p>(In a way this reminds me of the tension &#8211; one I am much more confident is an essential one of our profession &#8211; between <a href="http://blog.mrmeyer.com/?p=10285">storytelling</a> and <a href="http://www.blog.republicofmath.com/archives/4708">avoidance of theft</a> &#8211; I discussed a particular case of this tension in the fourth paragraph <a href="http://researchinpractice.wordpress.com/2011/05/23/the-inconvenient-truth-behind-waiting-for-superman-and-other-stories/">here</a>. Momentum is aligned with storytelling: a good story generates momentum. Avoiding theft is aligned with inviting questions.)</p>
<p>A last thought is that in a class of 20 or 30, having the class engage every question that pops into any student&#8217;s head at any time is obviously not a desirable situation. You might think I thought it was desirable based on the above. But the question is how to empower students to ask questions when we want them. I know that I for one have often <i>known</i> I wanted some questions so I could be responsive to them, and they weren&#8217;t forthcoming. The question is about how to change this. Part of the answer is about the culture, valuing the questions, encouraging the risks, and making everyone feel safe; but it&#8217;s the other part &#8211; how to <i>structurally</i> support the questions &#8211; that&#8217;s the new inquiry for me. As I said above, please comment.</p>
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		<slash:comments>7</slash:comments>
	
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			<media:title type="html">benblumsmith</media:title>
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		<title>Take the Tests, Decisionmakers!</title>
		<link>http://researchinpractice.wordpress.com/2011/12/08/take-the-tests-decisionmakers/</link>
		<comments>http://researchinpractice.wordpress.com/2011/12/08/take-the-tests-decisionmakers/#comments</comments>
		<pubDate>Thu, 08 Dec 2011 17:35:45 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Education Policy]]></category>
		<category><![CDATA[Social Justice]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=893</guid>
		<description><![CDATA[In case any of you missed this at f(t): A school board member in Orange County, FL had the guts to sit for his state&#8217;s high-stakes test, the type of test a lot of decisionmakers are all in such a rush to have students&#8217; futures and teachers&#8217; livelihoods resting on. Kate is asking her readers [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=893&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>In case any of you missed this at <a href="http://function-of-time.blogspot.com/2011/12/ft-is-having-moment.html">f(t)</a>:</p>
<p>A school board member in Orange County, FL had the guts to <a href="http://www.washingtonpost.com/blogs/answer-sheet/post/when-an-adult-took-standardized-tests-forced-on-kids/2011/12/05/gIQApTDuUO_blog.html?fb_ref=NetworkNews">sit for his state&#8217;s high-stakes test</a>, the type of test a lot of decisionmakers are all in such a rush to have students&#8217; futures and teachers&#8217; livelihoods resting on.</p>
<p><a href="http://function-of-time.blogspot.com">Kate</a> is asking her readers to call on NY Governor Cuomo to do the same thing.</p>
<p>This is effing brilliant. I say we take it up a notch. If you live in the US, pick an elected or appointed government official or purveyor of &#8220;education reform&#8221; who is rushing to rest more and more human futures on the results of a test, and <b>call on them to take the test</b>. I am not trying to be an organizer right now; I suppose it would be smart to make some strategic choices about whom to contact and via what medium (Kate: <a href="http://twitter.com/#!/k8nowak/status/144230404914814976">Cuomo / Twitter</a>), but that&#8217;s not my style. I do have some nominations:</p>
<p>Arne Duncan<br />
Bill Gates</p>
<p>Because these folks are operating at the national level, it&#8217;s not obvious which test to tell them to take. I want to say <b>all of them</b>, but maybe that&#8217;s just cuz I&#8217;m <i>pissed off</i>.  Abnegating my role as organizer I&#8217;ll let you call it. Here&#8217;s one that&#8217;s easy:</p>
<p>NYC Mayor Michael Bloomberg</p>
<p>Take the NY Regents, mayor, and make the results public. I don&#8217;t care how you do, but I want you to know what you&#8217;re talking about when you make policy, and I want you to be willing to be scrutinized as you are insisting that students, teachers, and schools be.</p>
<p>*****</p>
<p>Here&#8217;s what I love about this.</p>
<p>The last few years have felt to me like American schools are riding on top of a malfunctioning robot that is careening inexorably toward more and more insane school policy.  The robot is being driven by an inflated sense of the importance and automatic legitimacy of numerical data. For a decade, a chorus of voices (many of people directly involved in the practice of education) have been crying out that this is madness,<sup>[<a name="id1" href="#ftn.id1">1</a>]</sup> but the robot has only sped up.</p>
<p>&lt;Interlude&gt;</p>
<p>During the same decade, and especially in the last few years before this fall, the language used by national political figures advocating for justice and progressive change has felt more and more tepid to me. The clearest instance of this is the way that Democrats and even some progressive advocacy groups have latched onto the phrase &#8220;middle class.&#8221; Y&#8217;all are giving up the fight, guys. If you feel you are not allowed to advocate for <i>working people</i> or (God forbid) <i>poor people</i>, that in order to be a legitimate public interest your cause has to be sanded down and shellacked with a patina of educated white-collarness, then the folks who are only looking out for the interests of <i>rich people</i> have already prevailed.</p>
<p>My mood in relation to this language was not unlike my mood when beholding current debates about education: the feeling that justice and sanity are speaking, but being ignored; and they cannot find the language that will make the powerful listen.</p>
<p>So, imagine my thrill when this fall a new language took over: the 99%. Whatever you think of the Occupy Wall Street movement, you have to give it credit for a complete reshaping of the vocabulary available to discuss economic inequality. It seemed like everywhere I went this fall, somebody was talking about either &#8220;the 99%&#8221; or &#8220;the 1%&#8221; or both. This is just what I was missing: a way of talking about economic justice that feels <i>powerful</i> and <i>relevant</i>. That interrupts the inexorable slide into tepid lameness that characterized the national discourse till now.</p>
<p>&lt;/Interlude&gt;</p>
<p>What I&#8217;m getting at here is that we need ideas to interrupt the inexorable careening of the malfunctioning education reform robot, and Kate may just have found one. In the words of Rick Roach, the Orange County school board member who took the Florida tests,</p>
<blockquote><p>
“I can’t escape the conclusion that decisions about the FCAT in particular and standardized tests in general are being made by individuals who lack perspective and aren’t really accountable.”
</p></blockquote>
<p>You know <a href="http://researchinpractice.wordpress.com/2011/05/02/why-we-need-a-better-word-than-accountability/">I don&#8217;t love the word &#8220;accountable,&#8221;</a> the way it is thrown around these days. But these are the folks who do love it. So if they love it so much, <b>let&#8217;s make them accountable.</b> What I really mean is this: the public defamation of public schools and teachers, and the concomitant policy initiatives, have been based on numerical data from tests whose contents are public, but this is the only public thing about them. Most critically, their development is opaque, the way the data is used is opaque, and the way that decisions get made about how the data is used is therefore not subject to legitimate public scrutiny, or even, in all probability, based on any real understanding of the tests. The decisionmakers don&#8217;t even know what taking the tests is like!</p>
<p>So, decisionmakers, take the tests! You are willing to force students to take them, to scrutinize the results, and to make important decisions about students, teachers, and schools on their basis. Finding out what you&#8217;re actually forcing on them, and opening yourself up to the same scrutiny, is the least you could do.</p>
<div class="footnote"></div>
<p>
<sup>[<a name="ftn.id1" href="#id1">1</a>]</sup>One of these voices was the television show <a href="http://en.wikipedia.org/wiki/The_Wire">The Wire</a>, which aired well before the latest and most intense phase of this insanity, but which in spite of this develops a beautifully articulated critique of numbers-driven accountability in municipal institutions. Schools are included, but the brunt of the criticism is aimed at the police department and the city government. However, the essential problem is the same in all cases: when you demand numbers from people who are supposed to be doing a job requiring creative problem-solving and perseverance, you divert their attention from their actual work to the problem of giving you what you&#8217;re asking for. If you&#8217;ve never seen the show, you can get the whole thing from Netflix. You won&#8217;t be sorry. If you think I shouldn&#8217;t be citing a fictional television show regarding public policy, let me quote <a href="http://en.wikipedia.org/wiki/Mathnet">Mathnet</a>: the names are made up but the problems are real. Not convinced? <a href="http://www.villagevoice.com/2010-05-04/news/the-nypd-tapes-inside-bed-stuy-s-81st-precinct/1">Read this.</a></p>
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		<title>Never Be Wobbly</title>
		<link>http://researchinpractice.wordpress.com/2011/09/16/never-be-wobbly/</link>
		<comments>http://researchinpractice.wordpress.com/2011/09/16/never-be-wobbly/#comments</comments>
		<pubDate>Sat, 17 Sep 2011 03:31:57 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Math Education]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[schools]]></category>
		<category><![CDATA[shout outs]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=882</guid>
		<description><![CDATA[I spent at least 9 hours today thinking about squishing baloon-shaped surfaces into other shapes. This is what a PhD program in math is doing to me.[1] Having learning as a full-time job is really, really delicious. But tonight when I stopped mathing and engaged the edublogosphere it felt like a relief to read about [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=882&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>I spent at least 9 hours today thinking about squishing baloon-shaped surfaces into other shapes. This is what a PhD program in math is doing to me.<sup>[<a name="id1" href="#ftn.id1"></a>1]</sup></p>
<p>Having learning as a full-time job is really, really delicious. But tonight when I stopped mathing and engaged the edublogosphere it felt like a relief to read about <em>classrooms</em>, populated by <em>humans</em>. (To my fellow humans: I love the differentiable manifolds but I love you more.) Thanks <a href="http://mathbebrave.blogspot.com/2011/09/yantra-in-math-class.html">Jesse Johnson</a>, <a href="http://dangoldner.wordpress.com/2011/09/15/if-then/">Dan Goldner</a>, and <a href="http://function-of-time.blogspot.com/2011/09/geometry-points-lines-and-planes.html">Kate No Wackness</a><sup>[<a name="id2" href="#ftn.id2"></a>2]</sup> for your continuing dedication to learning (your kids&#8217;, yours and ours).</p>
<blockquote><p><a href="http://function-of-time.blogspot.com/2011/09/geometry-points-lines-and-planes.html">Holy Crap, a Three-Legged Table Can Never Be Wobbly.</a></p></blockquote>
<p>This is my favorite thing <em>ever</em>.</p>
<p><sup>[<a name="ftn.id1" href="#id1"></a>1]</sup>The particular thought that was driving me crazy at least from 7pm to 10pm, not that you care, was: if <img src='http://s0.wp.com/latex.php?latex=f%3AX+%5Crightarrow+Y&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='f:X &#92;rightarrow Y' title='f:X &#92;rightarrow Y' class='latex' /> is any surjective continuous function between topological spaces that maps open sets to open sets, then I can prove that the inverse image of a compact set is compact. I studied a converse if <img src='http://s0.wp.com/latex.php?latex=X&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='X' title='X' class='latex' /> and <img src='http://s0.wp.com/latex.php?latex=Y&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='Y' title='Y' class='latex' /> happen to be <a href="http://en.wikipedia.org/wiki/Differentiable_manifold">smooth manifolds</a> and <img src='http://s0.wp.com/latex.php?latex=f&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='f' title='f' class='latex' /> happens to be an <a href="http://en.wikipedia.org/wiki/Injective">injective</a> <a href="http://en.wikipedia.org/wiki/Immersion_%28mathematics%29">immersion</a>. But these are very very strong assumptions. How much can they be weakened?</p>
<p><sup>[<a name="ftn.id2" href="#id2"></a>2]</sup>Kate, this is <a href="http://researchinpractice.wordpress.com/2010/04/14/creativity/">A&#8217;s</a> name for you. (An homage to your no bullsh*t approach.)</p>
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		<title>What can you do with this?</title>
		<link>http://researchinpractice.wordpress.com/2011/07/16/what-can-you-do-with-this/</link>
		<comments>http://researchinpractice.wordpress.com/2011/07/16/what-can-you-do-with-this/#comments</comments>
		<pubDate>Sat, 16 Jul 2011 18:01:52 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Lessons]]></category>
		<category><![CDATA[Math Education]]></category>
		<category><![CDATA[questions without words]]></category>
		<category><![CDATA[WCYDWT]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=863</guid>
		<description><![CDATA[We interrupt our regularly scheduled long patch of radio silence to share with you an arresting, mathematically rich visual: [source] Thanks to Josh Kershenbaum for the tip. UPDATE 7/17: To clarify something: this image was originally created as an answer to a question, but I didn&#8217;t create a WCYDWT tag for that angle on it. [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=863&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>We interrupt our regularly scheduled long patch of radio silence to share with you an arresting, mathematically rich visual:</p>
<p><a href="http://researchinpractice.files.wordpress.com/2011/07/global-water-volume-large.jpg"><img src="http://researchinpractice.files.wordpress.com/2011/07/global-water-volume-large.jpg?w=500&#038;h=479" alt="" title="global-water-volume-large" width="500" height="479" class="aligncenter size-full wp-image-865" /></a></p>
<p>[<a href="http://ga.water.usgs.gov/edu/2010/gallery/global-water-volume.html">source</a>]</p>
<p>Thanks to Josh Kershenbaum for the tip.</p>
<p>UPDATE 7/17:</p>
<p>To clarify something: this image was originally created as <i>an answer to a question</i>, but I didn&#8217;t create a WCYDWT tag for that angle on it. To me, the image lands as (a) very beautiful; relatedly, (b) <i>haunting</i>, hard to get out of my head; therefore, (c) incipiently highly narrative &#8211; it is asking us to surround it with story, whether the original story conceived by the maker of the image or some other; and, lastly, (d) unavoidably mathematical. I don&#8217;t have a clear sense of the next move, but I do think this image opens a rich vein of <i>something</i> for a math teacher to use. The question &#8220;What can you do with this?&#8221; isn&#8217;t rhetorical: what&#8217;s <i>your</i> next move?</p>
<p>(See exchange with Dan Meyer below.)</p>
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		<title>The Inconvenient Truth Behind Waiting for Superman and other stories</title>
		<link>http://researchinpractice.wordpress.com/2011/05/23/the-inconvenient-truth-behind-waiting-for-superman-and-other-stories/</link>
		<comments>http://researchinpractice.wordpress.com/2011/05/23/the-inconvenient-truth-behind-waiting-for-superman-and-other-stories/#comments</comments>
		<pubDate>Mon, 23 May 2011 15:13:16 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Education Policy]]></category>
		<category><![CDATA[Lessons]]></category>
		<category><![CDATA[Math Education]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=859</guid>
		<description><![CDATA[I just recently learned of an organization in NYC called the Grassroots Education Movement, which last Thursday premiered a documentary film with the awesome title The Inconvenient Truth Behind Waiting for Superman. They will apparently send you a copy for free; I just ordered mine. Meanwhile, the city of New York continues to besiege its [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=859&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>I just recently learned of an organization in NYC called the <a href="http://gemnyc.org/">Grassroots Education Movement</a>, which last Thursday premiered a documentary film with the awesome title <a href="http://www.waitingforsupermantruth.org/"><i>The Inconvenient Truth Behind Waiting for Superman</i></a>.  They will apparently send you a copy for free; I just ordered mine.</p>
<p>Meanwhile, the city of New York continues to besiege its own public schools with budget cuts, looming layoffs, and a multi-year hiring freeze.  (Having spent the year training 12 new teachers, let me not even get started on the hiring freeze.)  Another thing that happened on Thursday was that <a href="http://www.eschs.org/">East Side Community High School</a>, a wonderful school on the Lower East Side where I used to teach and where the math teaching is strong enough that we placed four student teachers there this quarter, had its first fund-raiser.  Like, big event, speakers, performances by students, pay to get in, as though it were a non-profit, carrying out its own civic mission and in need of private funding to do it,  rather than a <i>public school</i>, charged with a civic mission by the <i>state</i>, which no longer sees fit to pay for it.</p>
<p>I missed both the documentary premiere and ESCHS&#8217;s fund-raiser because I was teaching the final class of a 3-session minicourse at <a href="http://www.mathforamerica.org/">Math for America</a> on the <a href="http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic">fundamental theorem of arithmetic</a>.  Let me do a little reflecting on the execution:</p>
<p>At the end of the 2nd session, I gave participants about a half-hour to try to figure out something quite difficult.  I attempted to scaffold this with some unobtrusive PCMI-style tricks in a previous problem set: sequences of problems with the same answer for a mathematically significant reason.  It turned out not to be enough.  There was high engagement the whole time, but no one seemed to be headed in my intended direction after that half-hour.  On the other hand, that half-hour had made the group into a legit mathematical research community.  What was afoot was a live process of trying things out, questioning, pressing on others&#8217; logic, and generally behaving like research mathematicians.  I was left with a dilemma.  I had one session remaining.  I wanted to protect that process, meaning I did not want to <a href="http://www.blog.republicofmath.com/archives/4708">steal from them</a> any of the deliciousness (or pain &#8211; also delicious) of the process they were in the middle of by offering them too much direction.  But at the same time I felt I needed to guarantee that we would reach resolution.  (<a href="http://blog.mrmeyer.com/?p=10285">Storytelling</a> purposes.)</p>
<p>The solution I went with: I had them pick up in the final session where they left off, but I brought in a sequence of hints on little cut-up slips of paper.  I tried to call them &#8220;idea-starters&#8221; as opposed to &#8220;hints&#8221; to emphasize that the game was you thinking on your own, and this is just to get you moving if you&#8217;re stuck, rather than I have a particular idea and I want you to figure out what it is, but I don&#8217;t think I was consistent with this, and I think they pretty much all called them &#8220;hints,&#8221; and I don&#8217;t think it really mattered.  They were in an order from least-obtrusive to most-directive.  None of them were very directive.  Most importantly, I told the participants that if they wanted to get one, they needed to decide this as a table.  (There were 6 tables with 3-4 folks each.)</p>
<p>How this went: a) it preserved the sense of mathematical community.  I do not think there was much of a cost to participant ownership of what they found out.  b) People were actually pretty hesitant to use the &#8220;idea-starters.&#8221;  Most of them went untouched.  This would probably be different with a different audience.  (High schoolers instead of teachers?)  c) The &#8220;idea-starters&#8221; worked great, but very slowly.  I planned to spend 45 min letting them work in this arrangement, but after 45 min, most of the groups were still deep in the middle of something.  After over an hour, I asked two groups to present what they had, however incomplete, for the sake of a change of pace and the opportunity for cross-pollination of ideas between the tables.  I had actually meant to do a lot more of this but had forgot to mention it at the beginning.  I let everybody work for another 10-15 min while these groups laid out their presentations.  By the time they presented, I realized that there wasn&#8217;t enough time left for everyone to really get back to work afterward, but in any case their ideas had gotten more fully developed in that 10 min. so they actually had pretty much figured out everything I had wanted them to.  I presented the final link in the logical chain, just to fill in the picture, in the last 5 minutes.  It was pretty satisfying to me to watch the presentations, except that it happened so late in the session.  This for two reasons.  One was that I would have ideally liked to have time to encourage the participants to interrogate the presenters more, but there wasn&#8217;t time for that.  The other was that I had intended to spend the last half-hour with the participants consolidating their understanding of the argument by applying it to a new situation in which they didn&#8217;t know the outcome and it would tell them; but we didn&#8217;t have time for that either.  I really feel a loss about that.</p>
<p>If I were to repeat it I think I would interrupt much earlier to have people present partial work.  The cross-pollination of ideas might or might not accelerate the figuring-out process.  Either way I think the change of pace would have been good for concentration.  Also, I could have put some of the questions I used as &#8220;idea-starters&#8221; into the Session 2 problem sets, trying to move some of the combustion I got in session 3 into session 2.  But these would both be experiments as well.  I hope I get a chance to try them.</p>
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		<title>Induction</title>
		<link>http://researchinpractice.wordpress.com/2011/05/09/induction/</link>
		<comments>http://researchinpractice.wordpress.com/2011/05/09/induction/#comments</comments>
		<pubDate>Tue, 10 May 2011 00:44:58 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=854</guid>
		<description><![CDATA[(N is studying calculus. She has just completed an induction proof of the power rule for negative exponents based on the quotient rule.) N: Induction feels like cheating. Me: I know, right?? You only prove 2 things, and then you&#8217;ve proved an infinite number of things. N: It&#8217;s not just that, it&#8217;s that you already [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=854&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>(N is studying calculus.  She has just completed an induction proof of the power rule for negative exponents based on the quotient rule.)</p>
<p>N: Induction feels like cheating.</p>
<p>Me: I know, right??  You only prove 2 things, and then you&#8217;ve proved an infinite number of things.</p>
<p>N: It&#8217;s not just that, it&#8217;s that you already assume you&#8217;re right.  It&#8217;s like you&#8217;re borrowing against your own rightness.</p>
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			<media:title type="html">benblumsmith</media:title>
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		<title>Why We Need a Better Word than &#8220;Accountability&#8221;</title>
		<link>http://researchinpractice.wordpress.com/2011/05/02/why-we-need-a-better-word-than-accountability/</link>
		<comments>http://researchinpractice.wordpress.com/2011/05/02/why-we-need-a-better-word-than-accountability/#comments</comments>
		<pubDate>Mon, 02 May 2011 20:55:39 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Education Policy]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=845</guid>
		<description><![CDATA[Everybody needs to chill for a second with the word &#8220;accountability.&#8221; It is not doing schools any good. There is a very simple reason. It totally collapses two distinct concepts. As it is deployed (by schools, bureaucratic structures in charge of schools, politicans, education reformers, etc.), it simultaneously means 1) Making what you&#8217;re doing public, [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=845&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Everybody needs to chill for a second with the word &#8220;accountability.&#8221;  It is not doing schools any good.</p>
<p>There is a very simple reason.  It totally collapses two distinct concepts.  As it is deployed (by schools, bureaucratic structures in charge of schools, politicans, education reformers, etc.), it simultaneously means</p>
<p><b>1) Making what you&#8217;re doing public, i.e. investing others in what you&#8217;re doing</b></p>
<p>on the one hand; and</p>
<p><b>2) Judging you with an eye to making decisions about you</b></p>
<p>on the other.</p>
<p>THESE ARE NOT THE SAME.</p>
<p><b>Public stake vs. high-stakes judgement</b></p>
<p>At a school where I used to teach, I had a colleague who taught a self-contained special education class.  This was well before the recent accountability fervor, and my colleague was frustrated by the <i>lack</i> of accountability to which he was subject.  He read in it a lack of concern for the education of his kids on the part of the administration.  &#8220;If I felt like it I could breakdance in class all year and nobody would say anything to me.&#8221;  It <i>bugged</i> him.</p>
<p>Really what he was frustrated by was the lack of public stake in what he was doing.  What he wanted was to feel that the administration of the school was invested in his students and their learning in his class.  He wanted his teaching to be part of a conversation and a striving bigger than himself.</p>
<p>I believe that the desire for this is what makes all the recent talk about increasing the accountability of schools compelling to well-meaning people.  We want the education of our children to be treated as a matter of public interest.  We want society as a whole to care about it.  We don&#8217;t like the idea that it&#8217;s going on behind closed doors and nobody is checking up on what&#8217;s happening.</p>
<p>The problem is that the only name for &#8220;public stake in the job you&#8217;re doing&#8221; that anybody seems to know right now is &#8220;accountability.&#8221;  And &#8220;accountability&#8221; is equally well a name for &#8220;let me judge what you&#8217;re doing so I can give you high 5 if it&#8217;s awesome and kick your *ss if it&#8217;s not.&#8221;</p>
<p>I hope you see what this adds up to.  Really I hope a lot of people who probably aren&#8217;t reading this will see what it adds up to.  Because your classroom practice being the subject of a public stake &#8211; the energy, thought, discussion, problem-solving, and passion behind what you do spreading through and beyond you to your whole community &#8211; this is gonna help your kids.  In fact even the knowledge that your work is gonna be visible to lots of folks who care about it is an inspiration.  But your practice being the subject of high-stakes judgement &#8211; the energy, thought, etc. that would have been squarely on the educational problems you&#8217;re working on now diverted to your stress, your fear, and the work-intensive processes of making sure your *ss is covered and trying to hide the areas where you think you don&#8217;t look good &#8211; this is not gonna help your kids.  You are filled with a desire to reach a state of &#8220;success&#8221; for the sake of survival, but not for the sake of inspiration, and in any case your stress works against your thinking clearly through the problem of how you will get there.</p>
<p>My answer: we need to express a public stake in education in ways that don&#8217;t look like high-stakes judgement.  There are already existing models: serious mentoring and coaching programs; critical friends groups (observation-based, video-based, student work-based&#8230;); Japanese lesson study; and more.  There are still more to be found.  But the central point is this: we need to be in this together, working together, looking at what each other are doing, not afraid to be critical, not afraid to expose ourselves to the thoughts and analyses of others.  This should be the norm and the expectation in the profession.  But this DOES NOT mean we need to judge and be judged.</p>
<p>To make all this concrete.  Have a look at <a href="http://www.washingtonpost.com/local/education/evaluating-teachers-is-a-delicate-conversation/2011/03/09/ABpPILn_print.html">this journalistic account of a meeting</a> between teacher and evaluator in DC.  Here&#8217;s what kills me about this.  The evaluator thinks this is so great because the evaluation rubric provides a uniform language for talking about instruction and improving it systematically.  He thinks he is here to help teachers grow.  Meanwhile, the teacher he is evaluating walks away from the meeting feeling judged, misunderstood and demoralized.</p>
<blockquote><p>Bethel gave him the final score, which was low. If the trend continued, Harris realized, he could lose his job.</p>
<p>“It’s just — I don’t feel that I’m putting in ‘minimally effective’ effort at all,” he said.</p>
<p>For Bethel, this was most excruciating part of the job. He began shutting off his computer.</p>
<p>“This does not measure your effort,” he said, packing his bag. “But I do see your effort, Mr. Harris.”</p>
<p>“So — what is this measuring?” Harris asked.</p>
<p>“It’s measuring the effectiveness of that effort,” Bethel said. “This is not a reflection of your passion for education, your love for students. Not at all.”</p>
<p>Which for Harris was precisely the problem and for Bethel was part of a difficult, painful solution.</p>
<p>As he left, Bethel offered to help Harris with lesson planning, a gesture that would not count on Bethel’s own evaluation. Harris leaned back in the little chair. He pursed his lips.</p>
<p>“I don’t think you’re being personally unfair, it’s just — ” he paused. “I’m going to look over it again. I know where I could improve. So. Yeah. It was nice talking to you.”</p></blockquote>
<p>The bit that landed hardest for me was when the evaluator offered to help the teacher with lesson planning.  In the context of just having given a bad evaluation, this gesture plays as maybe above and beyond the call of duty (as the journalist stressed) but also as condescending, and more importantly half-*ssed and hollow: if you really wanted to help me, you would listen to my explanation of my choices, and you sure as f*ck wouldn&#8217;t jeopardize my job.  Is Harris going to change his practice because of this evaluation?  Probably not in a positive direction, in my view &#8211; he&#8217;s being told to do something but not given the tools to take it on for real.  Maybe he&#8217;ll stick more closely to his lesson plan next time; but he&#8217;ll be doing it out of fear, and with resentment.  If you want a formula for removing passion from his practice, this is it.</p>
<p>Now just for a second imagine how this conversation would have gone if the evaluator were a coach instead, there to help, not judge.  <i>To express the community&#8217;s stake in the job at hand without fear or threat.</i>  Just imagine.</p>
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			<media:title type="html">benblumsmith</media:title>
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		<title>Technology Advice Request</title>
		<link>http://researchinpractice.wordpress.com/2011/04/19/technology-advice-request/</link>
		<comments>http://researchinpractice.wordpress.com/2011/04/19/technology-advice-request/#comments</comments>
		<pubDate>Tue, 19 Apr 2011 21:01:00 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[advice request]]></category>
		<category><![CDATA[technology]]></category>

		<guid isPermaLink="false">http://researchinpractice.wordpress.com/?p=829</guid>
		<description><![CDATA[So I am going to begin a PhD in math at NYU&#8217;s Courant Institute of Mathematical Sciences in the fall. (Congratulations me! EXCITED.) Do not for a second think this means I am abandoning Team Teacher. K-12 education 4eva. More on this another time. Anyway, for a math teacher blogger I am sort of a [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=829&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>So I am going to begin a PhD in math at NYU&#8217;s Courant Institute of Mathematical Sciences in the fall.</p>
<p>(Congratulations me!  EXCITED.)</p>
<p>Do not for a second think this means I am abandoning Team Teacher.  K-12 education 4eva.  More on this another time.</p>
<p>Anyway, for a math teacher blogger I am sort of a luddite so I could use some internet advice.</p>
<p>I&#8217;m trying to start a study group for my cohort at NYU.  (We have to pass a written exam during the first year of study; a lot of folks e.g. me want to get it done in the fall.)  So far nobody who&#8217;s written back is going to be in New York over the summer, so an online study group seems indicated.  Question: what&#8217;s a good platform for an online study group?</p>
<p>We need to be able to ask, answer, and reason through stuff.  We need to be able to write stuff.  My thoughts so far:</p>
<p>Idea A: a group-authored WordPress blog.  I have never done anything group-authored on WordPress so I don&#8217;t know how to think this through, but it supports LaTeX so we can typeset stuff.  Somebody can post on a question or problem they&#8217;re struggling with and other folks can answer in the comments.  Drawbacks: everybody needs a WordPress account, right?  And writing a post is not the most user-friendly thing compared to commenting.  And we&#8217;d need to be deliberate about how to make it easily navigable.</p>
<p>Idea B: somehow get our hands on the platform used for <a href="http://mathoverflow.net/">MathOverflow</a> and <a href="http://stackexchange.com/">Stack Exchange</a>.  It&#8217;s already set up for questions and answers and also has full LaTeX support.  Drawbacks: how will we get our hands on the platform?  Also, the &#8220;reputation&#8221; part would be bad for our purpose &#8211; can we omit it?</p>
<p>Idea C: One of my classmates suggested a Facebook group.  I&#8217;ve never used a Facebook group for anything and somehow the idea seems lame to me, but I don&#8217;t have a valid basis for that.  Do you have experience with them?  What are they good for?</p>
<p>Okay, do you have other ideas for me?  Do you have any additional thoughts/advice about these ideas?</p>
<p>Thanks for real.</p>
<p>UPDATE 4/20:</p>
<p>To clarify what I think we need (although if you have experience with online study collaboration, I want to hear what you think we need too) &#8211; </p>
<p>We need to be able to ask, answer and discuss math problems.  I think that means we need to be able to typeset math, so LaTeX support is a plus; we need to be able to have back-and-forth discussions, so support of comment threads or the like is a necessity; and we need to be able to participate in multiple conversations at once, so some sort of easy-to-navigate organizational structure would be nice.  (The last of these is the primary drawback of a WordPress blog as I see it.)  Also, the ability for multiple people to contribute content in a user-friendly way would be nice.</p>
<p>UPDATE 5/2: </p>
<p>When I sensed this turning into a much bigger project than I intended, I went with WordPress.  I got lots of great suggestions that I&#8217;m looking forward to learning more about when I have the time.</p>
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		<title>Bob Moses in NYC</title>
		<link>http://researchinpractice.wordpress.com/2011/04/07/bob-moses-in-nyc/</link>
		<comments>http://researchinpractice.wordpress.com/2011/04/07/bob-moses-in-nyc/#comments</comments>
		<pubDate>Thu, 07 Apr 2011 14:34:14 +0000</pubDate>
		<dc:creator>Ben Blum-Smith</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

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		<description><![CDATA[I just found out that one of my heroes, Bob Moses, founder of The Algebra Project, and an important leader in the civil rights movement (specif. the SNCC voter registration movement), will be speaking at NYU this afternoon, and I can&#8217;t go. GRRR. Maybe you can. The title of the talk is: Working the Demand [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=researchinpractice.wordpress.com&amp;blog=9760012&amp;post=824&amp;subd=researchinpractice&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>I just found out that one of my heroes, Bob Moses, founder of <a href="http://algebra.org/">The Algebra Project</a>, and an important leader in the civil rights movement (specif. the <a href="http://en.wikipedia.org/wiki/Student_Nonviolent_Coordinating_Committee#Voting_rights">SNCC voter registration movement</a>), will be speaking at NYU this afternoon, <b>and I can&#8217;t go</b>.  <b>GRRR.</b>  Maybe you can.</p>
<p>The title of the talk is:</p>
<p><b>Working the Demand Side: Mississippi, SNCC and the &#8217;60s struggle for the Right to Vote. The Algebra Project, the Young People&#8217;s Project and the current struggle for a Quality Public School Education as a Constitutional Right.</b></p>
<p>The info:</p>
<p>Thursday April 7, 4:00-5:30pm<br />
King Juan Carlos Center Auditorium (NYU)<br />
53 Washington Square South, 1st floor</p>
<p>The talk is sponsored by The DOE History in the Classroom Project and NYU&#8217;s Department of Teaching and Learning.  Bob will have a book signing afterward for his two books <a href="http://www.amazon.com/Radical-Equations-Mississippi-Algebra-Project/dp/0807031275/ref=sr_1_1?ie=UTF8&amp;qid=1302186549&amp;sr=8-1">Radical Equations</a> and <a href="http://www.amazon.com/Quality-Education-Constitutional-Right-Grassroots/dp/0807032824/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1302186586&amp;sr=8-1">Quality Education as a Constitutional Right</a>.</p>
<p>I don&#8217;t have time at this second to properly introduce you to Bob Moses&#8217; work if you aren&#8217;t already familiar with it but let me at least say that if you are interested in the relationship between math education and democracy, there isn&#8217;t a deeper thinker on the subject anywhere.</p>
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