Thank you. <div><br></div><div>In your book (Davis chapter) you write:</div><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><div>The following anecdote captures the root of the problem. A teacher who had taken part in a workshop on "discovery learning" came back almost in tears complaining that the students had "discovered it wrong." Bob Davis himself and his virtuoso disciples could work with a class of children, sensitively guiding the discovery process. In particular, they could pick out the germs of good insight in what the less understanding teacher saw as simply "wrong." The problem is deep: People brought up with a view of mathematics as discrete facts to be mastered do not easily discard this view. The reformer is faced with the problem:</div>
</div><div><div>We cannot tell teachers all they need to know about teaching—we must choose. Indeed, we must choose not merely content, but also the kind of content, and in fact even the media by which and form in which this "knowledge" is presented.</div>
</div><div><div>The problem is compounded by what happens in the next year with "untrained" teachers.</div></div></blockquote><div><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div>
<div>Do you know where I can find copies of the scripts Bob Davis used as part of the Madison project? </div><div><font class="Apple-style-span" face="verdana, sans-serif"><meta charset="utf-8"><span class="Apple-style-span" style="font-family: arial; "><div>
<font class="Apple-style-span" face="verdana, sans-serif">So what is the way out of this problem (that scales)? </font></div><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div><div><font class="Apple-style-span" face="verdana, sans-serif"><br>
</font></div></span></font></div><div><font class="Apple-style-span" face="verdana, sans-serif"><div>Also in your book (Papert chapter) you write:</div></font></div></div><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;">
<div><meta charset="utf-8"><div><font class="Apple-style-span" face="verdana, sans-serif">Papert pursues such questions as, </font></div><div><font class="Apple-style-span" face="verdana, sans-serif"><i>(1)</i> What experiences and knowledge lead children to change their theories, </font><span class="Apple-style-span" style="font-family: verdana, sans-serif; ">and </span></div>
<div><span class="Apple-style-span" style="font-family: verdana, sans-serif; "><i>(2)</i> why do they learn some things without formal instruction and not learn other things despite formal instruction?</span></div></div></blockquote>
<div><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div><div><font class="Apple-style-span" face="verdana, sans-serif">I also struggle with the first question a lot. In my experience the answer depends a good deal on knowing what theories the child holds, so I guess my main question is are there any proven techniques to help the child </font></div>
</div><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><div><font class="Apple-style-span" face="verdana, sans-serif">a) see the hole/problem with their current theories (which to them make perfect logical sense)</font></div>
</div></blockquote><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;"><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;">
<div><font class="Apple-style-span" face="verdana, sans-serif">I usually attempt to cause "cognitive dissonance" by finding questions and examples that do not fit their model as I perceive it, or more easily as they verbalized it. That can work, but does not scale, also in an OLPC model where there may be no teacher or no teacher with subject matter expertise, what do you do?</font></div>
</blockquote></blockquote><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><font class="Apple-style-span" face="verdana, sans-serif">b) what does research say about proven techniques to help kids change their mental models once they see the "holes"?</font></div>
<div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div></blockquote><font class="Apple-style-span" face="verdana, sans-serif">Regarding the 2nd question I would add: "Why do they learn some things despite formal instruction?"<br>
</font><div><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div></div><div><font class="Apple-style-span" face="verdana, sans-serif"><meta charset="utf-8">Also in your book (Papert chapter) you write:</font></div>
<blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><div><font class="Apple-style-span" face="verdana, sans-serif"><div>the process of doing elementary school mathematics so that it draws on children's intuition and everyday commonsense thinking.</div>
</font></div></div><div><div><font class="Apple-style-span" face="verdana, sans-serif"><div>How Papert differs from Suppes, Davis, and Dwyer might be summed up in what I call the Papert principle: If you want to teach arithmetic to children, arithmetic might not be the best route into these ideas for an easy understanding of the topic. What is needed is a way of mathematizing the child; thereafter particular mathematical topics become easy.</div>
</font></div></div></blockquote><div><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div><div><font class="Apple-style-span" face="verdana, sans-serif">This reminds me of something I heard from Keith Devlin either <a href="http://www.youtube.com/watch?v=3pRM4v0O29o&feature=player_embedded">here</a> or in his <a href="http://mathfuture.wikispaces.com/KeithDevlin">Natural Math talk</a>, which was: </font></div>
</div><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><div>It comes down to finding new representations of mathematics.</div></div><div><br></div></blockquote>So does anyone have any good examples of new representations?<div>
<br></div><div><br></div><div>Lastly, one of the great things from the Madison project is what I call it "<a href="http://mrstevesscience.blogspot.com/search/label/Robert%20B.%20Davis">Taking Tic-Tac-Toe to the next level</a>", where the key rule of the game is you can't tell anyone the rules. Kids play the game and have to figure out the rules by playing. Kids can learn about cartesian coordinates, positive and negative numbers and practice "a number is all the ways you can name it" all without being told what to do or how to do it.</div>
<div><div><div><font class="Apple-style-span" face="verdana, sans-serif"></font></div><meta charset="utf-8"><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div><div><font class="Apple-style-span" face="verdana, sans-serif">Stephen</font></div>
<div><font class="Apple-style-span" face="verdana, sans-serif"><div>If you give a child an answer,</div><div>you solve a problem for the day.</div><div>Teach a child to find the answers,</div><div>you prepare her for a life.</div>
<div> - Mr. Steve's Science</div><div><br></div></font></div><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div><div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div>
<div><font class="Apple-style-span" face="verdana, sans-serif"><br></font></div><div><br><div class="gmail_quote">On Mon, Apr 25, 2011 at 6:38 AM, Cynthia Solomon <span dir="ltr"><<a href="mailto:cynthia@media.mit.edu">cynthia@media.mit.edu</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">I just posted my book, Computer Environments for Children: A Reflection on Theories of Learning and Education. <a href="http://computerenvironments.wikispaces.com" target="_blank">http://computerenvironments.wikispaces.com</a><br>
<font color="#888888"><br>--Cynthia<br>
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