<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns="http://www.w3.org/TR/REC-html40"> <head> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii"> <meta name=Generator content="Microsoft Word 11 (filtered medium)">  <style>  </style> </head> <body lang=EN-AU link=blue vlink=purple> <div class=Section1> This might be of interest – “how do we learn math” by Keith Devlin –<o:p></o:p> <a href="http://www.maa.org/devlin/devlin_12_08.html" title="blocked::http://www.maa.org/devlin/devlin_12_08.html">http://www.maa.org/devlin/devlin_12_08.html</a><o:p></o:p> <o:p> </o:p> honest appraisal of the state of the research <o:p></o:p> <o:p> </o:p> “Still, over the past twenty years I've read a ton of research in [relevant] domains - enough to realize that we know far, far less about how the brain does mathematics, how it acquired that ability, and how young children learn it, than we do about the subject itself.”<o:p></o:p> <o:p> </o:p> Contrasts two views of math learning<o:p></o:p> <o:p> </o:p> He makes a case that the process of abstraction by which we initially learn number concepts, for example, is not the same as how many mathematicians tend to learn more advanced concepts ….that many often learn in a rule based way, and then deepen and generalise and link what they have learnt – like a chess player learning the rules as arbitrary rules, and only later seeing the patterns and strategies<o:p></o:p> <o:p> </o:p> Also expands on Lockhart’s lament  - which is generally arguing that a rule based approach kills the life out of most early maths education <o:p></o:p> <a href="http://www.maa.org/devlin/devlin_05_08.html" title="blocked::http://www.maa.org/devlin/devlin_05_08.html">http://www.maa.org/devlin/devlin_05_08.html</a><o:p></o:p> <o:p> </o:p> which I gather is Paperts critique – school maths is being like being fed the menu at a restaurant <o:p></o:p> <o:p> </o:p> the contrast between these positions – where and when they are appropriate –seems to be at the heart of the “maths wars”<o:p></o:p> <o:p> </o:p> more here:<o:p></o:p> <a href="http://www.maa.org/devlin/" title="blocked::http://www.maa.org/devlin/">http://www.maa.org/devlin/</a>   <o:p></o:p> <o:p> </o:p> Bill, I saw that ABC doco – love the light hearted spoof angle; and it gets you thinking<o:p></o:p> <o:p> </o:p> Like the observation that not one Roman mathematician is celebrated today, and the dark ages in Europe also co-incided with the Roman numeral number system, while India math was centuries ahead…someone quoted Whitehead to similar effect – good notation frees the mind to work on the real problems<o:p></o:p> <o:p> </o:p> <o:p> </o:p> <o:p> </o:p> <div style='border:none;border-left:solid blue 1.5pt;padding:0cm 0cm 0cm 4.0pt'> <div> <div class=MsoNormal align=center style='text-align:center'> <hr size=2 width="100%" align=center tabindex=-1> </div> From: iaep-bounces@lists.sugarlabs.org [mailto:iaep-bounces@lists.sugarlabs.org] On Behalf Of Alan Kay Sent: Monday, 5 January 2009 5:06 AM To: Bill Kerr; iaep Subject: Re: [IAEP] foundational skills in literacy and numeracy<o:p></o:p> </div> <o:p> </o:p> <div> <div> Bill -- Also check out mathematicians turned great math teachers (such as Mary Laycocke) who have spent decades learning how to get young children to learn "real math". Much of this would be called "constructionalistic" (by those who call themselves "constructionalists"). Also, I have given an account in several places of some of the wonderful teaching approaches of first grade teacher Julia Nishijima (when she was at the LA Open Magnet School). These include setting up an environment in which children construct and really do discover 1st and 2nd order growth laws as arithmetic progressions. Most of her (and Mary Laycocke's) stuff was done before computers (and doesn't need computers) but can later be enhanced by computers. The biggest limitation by far here is not the knowledge of how to do this stuff, but the fact that most elementary school teachers have essentially no sense of math, and very few of these really want to learn anything about math. Cheers, Alan<o:p></o:p> </div> <div> <o:p> </o:p> <div> <div class=MsoNormal align=center style='text-align:center'> <hr size=1 width="100%" align=center> </div> From: Bill Kerr <billkerr@gmail.com> To: iaep <iaep@lists.sugarlabs.org> Sent: Sunday, January 4, 2009 9:45:04 AM Subject: Re: [IAEP] foundational skills in literacy and numeracy<o:p></o:p> <div> <blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt; margin-left:4.8pt;margin-right:0cm'> I'm not aware of anything that Papert wrote about teaching foundational skills like number (meaning integers) or basic literacy using phonics. <o:p></o:p> </blockquote> <div> <o:p> </o:p> </div> </div> self correction: The Progressive Construction of Mind by Robert Lawler June 1980 (Logo Memo 57, MIT AI Lab) was probably supervised by Papert Naturalistic study of his two children aged 6 (Miriam) and 8 (Robby) includes plenty of observations about how the kids learnt addition, subtraction etc. I need to reread this.<o:p></o:p> </div> </div> </div> <o:p> </o:p> </div> </div> Important - This email and any attachments may be confidential. 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