<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:st1="urn:schemas-microsoft-com:office:smarttags" 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)"> <o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="City"/> <o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="country-region"/> <o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="place"/>  <style>  </style> </head> <body lang=EN-AU link=blue vlink=blue> <div class=Section1> We’ve had some of this discussion before : Alan has mentioned the arch metaphor before–as a key insight in building / architecture, that is distinct from mere brick laying, and so is never reached through repetition of laying however many bricks  - as an analogy for a type of learning or mathematics that is not reached by mere repetition of lower order skills <o:p></o:p> <o:p> </o:p> Also used a related metaphor that the real test of learning is the ability to do the ‘real thing’ at some level, not just reciting learning ‘about’ a topic (or switching to a music analogy he has also used, can the student do more than play scales? as useful as that may skill and drill may be… <o:p></o:p> <o:p> </o:p> (and also do more than the air guitar version which might get smuggled in (or even advocated) as a watered down version of the topic that is easier to ‘teach’ and ‘learn’)<o:p></o:p> <o:p> </o:p> Anyway, re-reading some of the previous discussions, I find we have all generally been in agreement that there is a place for “skill and drill” <o:p></o:p> <o:p> </o:p> So an argument that perhaps needs to be put to rest, as one that no educators seem to actually hold, as far as I can tell, is the suggestion that there is no role for direct instruction <o:p></o:p> <o:p> </o:p> My own observation is that while it is indeed possible to structure curriculum in a way that is more self directed and still has enough structured scaffolds (such as well sequenced materials that can accessed on demand, and mixes in some project driven enquiries) , in most cases a strong thread of direct instruction can be justified and is often needed<o:p></o:p> <o:p> </o:p> However a curriculum that does not go beyond this, that does not encourage performance or real competence as a test of learning, is, in these terms, the equivalent of only ever playing scales or brick laying, - ie it does not reach the ‘arch’ of understanding which gives new meaning and beauty to the brick laying exercise, or allow students to reach an authentic performance with some musical feel –<o:p></o:p> <o:p> </o:p> <o:p> </o:p> Idit Harel : “even "successful" pupils within this approach are often left with a kind of knowledge which some have called "inert", mathematical knowledge which may suffice for passing tests but which is not useful or available outside the classroom context in which it was originally learned.<o:p></o:p> (Educational Studies in Mathematics 24: 319-327, 1993)  <o:p></o:p> <o:p> </o:p> Some feel it’s the state of teachers that leads to this –- others hope that new and innovative software will transform the field<o:p></o:p> <o:p> </o:p> So this sense that state of traditional education  is selling us short on real learning, or at least under doing the potential  - is what I suspect informs many here at some level, in an attempt to better resource education.  And yes, education has often swung too hard and simplistically from one position to another …which is where some of us want to try to understand and contribute<o:p></o:p> <o:p> </o:p> Rereading a previous round of this (archives June 2008 on ‘reconstructing maths- http://lists.sugarlabs.org/archive/iaep/2008-July/001303.html’) <o:p></o:p> <o:p> </o:p> has got me going to back to a Papert article on possible math educations  …  <a href="http://www.papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html">http://www.papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html</a><o:p></o:p> <o:p> </o:p> and following a provocative paragraph <o:p></o:p> “A particularly clean example is an apparent paradox in the report by Sfard and Leron (in press). They ask which of the following two problems is harder: <o:p></o:p> P1: Given three points, (2,3), (-1,4), and (0,-1), in the plane, find the center and the radius of the circle through them. P2: Write a computer program that accepts any three points in the plane (given by their coordinates) and returns the center and the radius of the circle through them. <o:p></o:p> Since P2 asks for more than P1, one could argue that tautologically it must be harder. But Sfard and Leron report that more than half of their students failed at P1 and nearly all succeeded at P2. Why? It is not any magic of the computer except the fact that working at the computer transforms the stance of the students from "solving a problem" to "pursuing a project."  <o:p></o:p> <st1:place w:st="on"><st1:City w:st="on">Reading</st1:City></st1:place> through some of the work of these authors and colleagues in Journals – some via uni library – but some is also open online  <o:p></o:p> http://symbolicspecies.com/?The_2006_conference:Speakers_and_abstracts_2006:Uri_Leron<o:p></o:p> http://edu.technion.ac.il/Faculty/uril/papers/JRME_Actions_vs_Functions.pdf<o:p></o:p> <o:p> </o:p> leads further to the interesting idea of mathematics is built on more homely metaphors<o:p></o:p> <o:p> </o:p> http://www.cogsci.ucsd.edu/~nunez/web/PME24_Plenary.pdf<o:p></o:p> <o:p> </o:p> this is seemingly very non practical – as the logical discipline of mathematics itself can appear to be - but for some educators such as myself its all valuable learning, - we share a role in engaging in better IT mediated learning experiences (of math and other areas), so I at least find this compelling research, even in a parallel universe where software is not necessarily ‘free’- <o:p></o:p> <o:p> </o:p> [eg someone mentioned the need a while ago to do the ‘unsexy work of uploading and mapping n curriculum against x activities’ – that’s been exactly my role for the last 4 months in that parallel world – I wrote some tools to help  – I often see the same general issues coming up all over the place – [ie what philosophy of learning? What system structure? Do developers really need to bother with this? ] it clarifies my thinking to see the issues in other contexts – helps try to find the superstructure that these issues are derived from] … I think there are common concerns about learning, and developing systems that are more readily and deeply accessible to students as learning tools<o:p></o:p> <o:p> </o:p> So the reflective thinking / debate about IT and learning has been worth hanging around for – risking these questions might lead to better answers for those who are gripped by the questions, in whatever context  <o:p></o:p> <o:p> </o:p> [I had hoped to run a school sugar trial and may still do so if I can ..but either way all this is learning that will underpin some kids learning]. <o:p></o:p> <o:p> </o:p> cheers<o:p></o:p> <o:p> </o:p> rob <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 Bill Kerr Sent: Friday, 8 May 2009 6:37 PM To: Martin Langhoff Cc: iaep; Sugar-dev Devel Subject: Re: [IAEP] [Sugar-devel] versus, not<o:p></o:p> </div> <o:p> </o:p> I'm not sure what is meant by a "big tent" Why do some people want a big tent for learning theory but not a big tent which accepts both FOSS and proprietary software? Phrasing it that way is intended to encourage people to think about what sort of thing is learning and hopefully will not be interpreted as just being provocative for its own sake. you can have a big tent where people don't discuss learning theory because it's too hard to reach agreement you can have a big tent where people passionately argue about learning theory but actually listen to what each is saying and argue rationally when I look at minsky's theory of mind I see that he supports multiple models of thinking but also argues against models of thinking that he thinks are incorrect or which emphasise only one way of doing things, eg. although he helped create connectionism he now thinks it has too much influence that suggests another version of a big tent which I favour - cherry picking the best parts out of different learning theories / activities based on criteria (not stated here) that are substantial I don't believe that thinking people are agnostic about how people learn it seems to me that alan kay has presented a possibly strategic view of progress on these questions (that learning about bricks will not automatically lead to building arches, that we need more than just focusing on building blocks) - but that for various reasons we are not in a position to implement the learning materials based on that view in practice in the activities for me to sit in the big tent holding a strategic view feels different to "too hard basket", agnosticism or a tower of babble - teaching with an underlying strategic view is very different to just going along with the tide that would mean work to understand and implement that strategic view but also accept that we are not there yet (it will take some time) and so it is perfectably understandable and desirable that people will use and develop whatever is at hand or which they think important to develop - no one can stop that anyway accept by successful arguing someone out of a POV Does the "big tent" phrase add clarity to this conversation? <o:p></o:p> <div> On Tue, May 5, 2009 at 4:59 PM, Martin Langhoff <<a href="mailto:martin.langhoff@gmail.com">martin.langhoff@gmail.com</a>> wrote:<o:p></o:p> <div> On Tue, May 5, 2009 at 3:03 AM, Walter Bender <<a href="mailto:walter.bender@gmail.com">walter.bender@gmail.com</a>> wrote: > Fair enough. I agree that *most* people on the list agree that there > is not just one right way. And to use a metaphor that has been > oft-spoken in the <st1:country-region w:st="on"><st1:place w:st="on">US</st1:place></st1:country-region> news of late, Sugar Labs has to have a "big > tent." > > Sugar itself has affordances that can be used in support of many > educational approaches and virtually any content area.<o:p></o:p> </div> Completely for the big tent, and wide ranging use models. It also means I have to swallow hard when people use things I build in ways that I consider... not particularly good. You might hear me mention that "that's a practise that I don't emphasize" ;-) cheers, m --  <a href="mailto:martin.langhoff@gmail.com">martin.langhoff@gmail.com</a>  <a href="mailto:martin@laptop.org">martin@laptop.org</a> -- School Server Architect  - ask interesting questions  - don't get distracted with shiny stuff  - working code first  - <a href="http://wiki.laptop.org/go/User:Martinlanghoff" target="_blank">http://wiki.laptop.org/go/User:Martinlanghoff</a><o:p></o:p> </div> <o:p> </o:p> </div> </div> Important - This email and any attachments may be confidential. If received in error, please contact us and delete all copies. Before opening or using attachments check them for viruses and defects. Regardless of any loss, damage or consequence, whether caused by the negligence of the sender or not, resulting directly or indirectly from the use of any attached files our liability is limited to resupplying any affected attachments. 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