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*To*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Subject*: Re: [xmca] a minus times a plus*From*: Andy Blunden <ablunden@mira.net>*Date*: Mon, 20 Jul 2009 23:10:08 +1000*Delivered-to*: xmca@weber.ucsd.edu*In-reply-to*: <D322A7F4-2366-4A92-8484-D876BDB272BF@ucsd.edu>*List-archive*: <http://dss.ucsd.edu/mailman/private/xmca>*List-help*: <mailto:xmca-request@weber.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca.weber.ucsd.edu>*List-post*: <mailto:xmca@weber.ucsd.edu>*List-subscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=subscribe>*List-unsubscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=unsubscribe>*References*: <00dd01c9fefa$6dc53690$8b55d383@w2k3.fi.uu.nl><2C7F9BCA-5807-42F9-8AB7-CC1F7EE9F9FE@umich.edu><4A553223.8020809@mira.net> <30364f990907082057i3af7ecf4w93fc2bcc8b99cb8c@mail.gmail.com> <000601ca0631$0bd038c0$0202a8c0@youre6f02835ae> <D322A7F4-2366-4A92-8484-D876BDB272BF@ucsd.edu>*Reply-to*: ablunden@mira.net, "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Sender*: xmca-bounces@weber.ucsd.edu*User-agent*: Thunderbird 2.0.0.14 (Windows/20080421)

Andy Jerry Balzano wrote:

Hi Mike, from across UCSD campus ... actually from across the countrysince I'm currently in NY ...by my count, this topic has accumulated 147 emails since your originalApril 27 posting (this one would be #148) ... quite a fecund topic, andnot bad on the longevity meter either! (nearly 3 months)I just this morning ran across another remarkable connection to thetopic that I had to tell you and everyone else about as I was in googlebookland, pursuing cross refs to -- of all things -- WIttgenstein'sLectures on the Foundations of Mathematics. It's a rather fascinatingbook called Negative Math, by Alberto A. Martínez, and the online "bookoverview" starts off, believe it or not, just like this:A student in class asks the math teacher: "Shouldn't minus times minusmake minus?"There's a chapter in the book with the seemingly heretical title, "Mathis Rather Flexible", and as if to demonstrate this via a kind of tour deforce with an exceptional resonance for our discussion, Martinez asks"can we construct a system in which, say, -4 x -4 = -16? Actually, yeswe can."This raises the question: Is such a book good for students or bad forstudents? It seems terribly subversive, doesn't it? I can imagine morethan one math teacher applauding it "in principle" but panning it inpractice for fear that it "might confuse" a student who was "havingenough trouble learning the (correct) rules". But (on the other hand)perhaps if we had a more playful, less rigid attitude about "the rules",we would engender a less fearful attitude in students about them.Perhaps books in the spirit of Martinez' Negative Math would be a properantidote to such (apparently!) unproductive approaches to thinking aboutteaching and learning mathematics?The book is in our library at UCSD, and I'd be more than happy to "playwith it" with you when I return (beginning of August), if you like. Inthe meantime, the Google Books link is here.Jerry B ------- On Jul 16, 2009, at 9:18 AM, Esther Goody wrote:Dear Mike, Hope you have caught up with sleep since Alaska! Until now I have not looked at the "a minus times a plus" topic in XMCA,supposing it would be about word games or something. Now I see it isabout'How and What to teach in school maths'? This is something I stumbledintoin my northern Ghana classrooms. The first Spencer Foundation grant wasabout differences in learning literacy skills in L1 and L2 in high andlowauthority classrooms. However a large section of the middle yearreport wasabout reasons why kids were not learning school maths in the upperprimarygrades in village schools....... . . . . . . . . . . _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca

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**Follow-Ups**:**Re: [xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

**References**:**RE: [xmca] a minus times a plus***From:*"A.Bakker" <A.Bakker@fi.uu.nl>

**Re: [xmca] a minus times a plus***From:*Jay Lemke <jaylemke@umich.edu>

**Re: [xmca] a minus times a plus***From:*Andy Blunden <ablunden@mira.net>

**Re: [xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

**RE: [xmca] a minus times a plus***From:*"Esther Goody" <eg100@hermes.cam.ac.uk>

**Re: [xmca] a minus times a plus***From:*Jerry Balzano <gjbalzano@ucsd.edu>

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