<html><head><style type="text/css"></style></head><body><div style="font-family:times new roman,new york,times,serif;font-size:12pt"><div>Well, much of the version of calculus that is used in the physical sciences is adapted from Gauss' differential geometry of vectors, and that is the math that Seymour adapted for Logo (in part because DGofV uses the same "from where I am" coordinate system that children have built in).<br><br>So the real problem is to convince school folks (most of whom are innocent of mathematics) that Logo is actually more like the real deal than what they have gotten into the habit of teaching. This "innocence" was (I believe) one of the main factors for Logo not catching on in the early 80s (or now).<br><br>And, by the way, the circle as the limit of a polygon whose side count gets unboundedly larger with the side lengths approaching zero is the way Archimedes thought of circles, and the way he was able to get the first really good approximation to pi.<br><br>I.e. don't worry about Logo, let's worry about the school systems ... <br><br>Cheers,<br><br>Alan<br></div><div style="font-family: times new roman,new york,times,serif; font-size: 12pt;"><br><div style="font-family: times new roman,new york,times,serif; font-size: 12pt;"><font size="2" face="Tahoma"><hr size="1"><b><span style="font-weight: bold;">From:</span></b> Bill Kerr <billkerr@gmail.com><br><b><span style="font-weight: bold;">To:</span></b> Maria Droujkova <droujkova@gmail.com><br><b><span style="font-weight: bold;">Cc:</span></b> iaep <iaep@lists.sugarlabs.org><br><b><span style="font-weight: bold;">Sent:</span></b> Friday, September 4, 2009 4:27:26 PM<br><b><span style="font-weight: bold;">Subject:</span></b> Re: [IAEP] 40 maths shapes challenges<br></font><br> <div class="gmail_quote">On Sat, Sep 5, 2009 at 2:12 AM, Maria Droujkova <span dir="ltr"><<a rel="nofollow" ymailto="mailto:droujkova@gmail.com" target="_blank" href="mailto:droujkova@gmail.com">droujkova@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> Circle is one of the hardest in Scratch. Unless I am missing a command.<br></blockquote><div><br>move a little turn a little lots of times<br><br>repeat 360 [move 1 turn 1]<br><br>that is a classic discussion arising from Papert<br> does this prepare students for calculus?<br>an honest child's version of sophisticated maths?<br>or are the conventions of calculus so different from body syntonic logo maths that the learning does not transfer?<br>good one to discuss<br> <br><br> </div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"><br clear="all">Cheers,<br>Maria Droujkova<br><span><a target="_blank" href="http://www.naturalmath.com">http://www.naturalmath.com</a></span><br> <br>Make math your own, to make your own math.<br> <br> <br> <br><br><div class="gmail_quote"><div class="im">On Mon, Aug 31, 2009 at 7:19 AM, Bill Kerr <span dir="ltr"><<a rel="nofollow" ymailto="mailto:billkerr@gmail.com" target="_blank" href="mailto:billkerr@gmail.com">billkerr@gmail.com</a>></span> wrote:<br></div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> <div><div></div><div class="h5"> Image attached <div><br></div><div><span style="font-family: Georgia; color: rgb(51, 51, 51); line-height: 20px;">Forty shapes to make in <a rel="nofollow" target="_blank" href="http://scratch.mit.edu/" style="color: rgb(153, 153, 153); text-decoration: none;">Scratch</a> or some other version of logo, such as <a rel="nofollow" target="_blank" href="http://wiki.sugarlabs.org/go/Activities/Turtle_Art" style="color: rgb(153, 153, 153); text-decoration: none;">Turtle Art</a>. It's hard to see the thumbnail but click on it for a larger view.<br> <br>This is one of the best sheets ever for teaching maths (designed by Barry Newell):<br><ul><li>the logo turtle or scratch cat acts as a transitional object between the concrete maths shape and the abstraction of the script that makes the shape</li> <li>the sheet includes both simple and complex shapes, increasing in order of complexity, there is a challenge there for everyone</li><li>many of the more complex shapes are made up of combinations of the simpler shapes</li> </ul><div><span style="font-weight: bold;">Source</span>: Barry Newell's <span style="font-style: italic;">Turtle Confusion</span> (1988)</div></span></div> <br></div></div><div class="im">_______________________________________________<br> IAEP -- It's An Education Project (not a laptop project!)<br> <a rel="nofollow" ymailto="mailto:IAEP@lists.sugarlabs.org" target="_blank" href="mailto:IAEP@lists.sugarlabs.org">IAEP@lists.sugarlabs.org</a><br><span> <a target="_blank" href="http://lists.sugarlabs.org/listinfo/iaep">http://lists.sugarlabs.org/listinfo/iaep</a></span><br></div></blockquote></div><br> </blockquote></div><br><br> </div></div></div><br> </body></html>