<html><head><style type="text/css"></style></head><body><div style="font-family:times new roman,new york,times,serif;font-size:12pt"><div style="font-family: times new roman,new york,times,serif; font-size: 12pt;"><br><br><div style="font-family: times new roman,new york,times,serif; font-size: 12pt;">----- Original Message ----<br>From: Albert Cahalan <acahalan@gmail.com><br>To: Alan Kay <alan.nemo@yahoo.com><br>Cc: its.an.education.project@tema.lo-res.org<br>Sent: Thursday, July 17, 2008 8:57:50 AM<br>Subject: Re: [IAEP] reconstructed maths<br><br>On Thu, Jul 17, 2008 at 10:55 AM, Alan Kay <<a ymailto="mailto:alan.nemo@yahoo.com" href="mailto:alan.nemo@yahoo.com">alan.nemo@yahoo.com</a>> wrote:<br><br>>> However, where did I say anything about skipping arithmetic?<br><br>>Technically you did not. <br><br>             -- Meaning I actually didn't ...<br><br>>Can I get you to agree that all children<br>>must memorize traditional arithmetic methods long before getting<br>>any exposure to vector calculus?<br><br><div style="margin-left: 40px;">No, and for many reasons. However, as I said, I have nothing against drill and practice for certain parts of learning developed ideas. Skills are very useful. But, it happens that little beyond the concepts of adding and accumulating are needed for vector calculus (particularly in the differential geometry style). And, base 10 numerals can even be distracting<br></div><br>>Can I get you to agree that<br>>constructionism does not work for teaching math?<br><br><div style="margin-left: 40px;">No, and for many reasons. Not the least of which is that I said nothing using the C-word and intended nothing using the C-word. Again, I fear you are projecting.<br><br>I'm writing about the many things that can be done (and in many cases need to be done) to help children get fluent in real mathematics. There's no reason to assign a label and category to things that can be partially enumerated and discussed. Again, as with music, different children need different approaches but they can all learn to "speak and do" real music and real math.<br></div><br>>In case not, please note that you're up against an independently<br>>reviewed study that would cost about 3.3 billion in 2008 dollars.<br>>In this real-world test, all 5 constructionist programs failed.<br>>Personal experience, even 35 years of it, does not compare.<br><br><div style="margin-left: 40px;">Again, I'm not saying anything one way or another about a category you decided I was talking about and you introduced into the discussion.<br><br>I am saying that a few things have been learned over the years about what real math can be for children, and some of the ways they can learn to actually do real mathematical thinking.<br><br></div>Best wishes,<br><br>Alan<br></div></div></div><br> </body></html>