[Squeakland] the non universals

Sun Aug 19 07:05:20 PDT 2007

Hi Bob --

At 02:44 PM 8/18/2007, Robert Parks wrote:
>I've been listening with interest, and I've got a couple of 
>questions and (possible) provocations.
>
>    1. would learning calculus as a "powerful idea" (rather than 
> through the duller algebraic approach) be counted as "using 
> discovery or inquiry based learning as a substitute for hard facts"?

I don't see why it should, but there are few bounds on rhetoric and 
innuendo. I like Bruner's term "scaffolded learning" because real 
discoveries are rare -- we've learned how to teach 10 year olds a 
good and mathematical version of calculus but no child has ever 
discovered calculus without guidance (and it took 200,000 years for 
two smart adults to do it with hints). Much of the "discovery and 
inquiry learning" curricula I've seen is pretty soft.

But learning and teaching would be easy if it could be transmitted by 
words or actions. Instead, some changes have to happen in the 
learner's mind/brain through some actions on their part (which could 
involve doing something or just sitting in a chair pondering). Things 
are sometimes not obvious because they are literally invisible, or 
because the explanations fall outside of existing commonsense 
thinking patterns. Or some new set of coordinations have to be 
learned/built that were not there before.

These have many of the trappings of creativity and the having of 
ideas that are not simple increments from the ideas of the 
surrounding context. The phrase I use for this is "Learning a 
powerful idea requires a lot of the same kinds of creativity as it 
took to invent it in the first place". This is because it has to be 
invented anew by the learner.

The good news is that learners for already invented ideas almost 
never have to be as smart and unusual as the original inventors 
(calculus can be learned by pretty much everybody, but Newton and 
Leibniz were unusual). On the other side, some real work has to be 
done to "cross the barriers".

Tim Gallwey (the incredible tennis teacher) use to say: you have to 
hit thousands of balls to learn to play tennis -- my method gets you 
to hit those thousands of balls, but feeling and thinking 
differently. A good method in mathematics (like Mary Laycock's or 
Seymours) still requires you to do lots of things (to get your 
mind/brain fluent) but can be and feel mathematical for most of the 
journey rather than painful in many ways. This is what we've called 
"Hard fun", and it is a process that is shared by any set of 
arts/sports/skills that have been developed.

Another way to look at it is "If you don't read for fun, you will 
never get fluent enough to read for purpose".

The big problem with the "standard algebraic route" is not so much 
algebra, but that the standard route requires lots of work but 
doesn't deliver "real math" very well. It's not situated in 
mathematical thinking, but much more in rule learning and following. 
People have turned Logo (and other computing) into rule learning and 
following, etc. It can be done to any initially terrific subject.

>    2. What IS a "powerful idea", and how does it become 
> powerful?   I'm particularly interested in asking whether ideas get 
> their power from abstraction (finding similarity in structure), or 
> generalization (finding similarity in features) - or from both.

Seymour and I have tried to characterize "powerful ideas" 
operationally rather than by structure. Even though there are not a 
lot of powerful ideas (hundreds or so) there are enough of different 
types to make simple structural definitions difficult. For example, 
"modern science" itself is a powerful idea: it is one of the greatest 
sets of processes ever devised for getting around many of the defects 
of the human mind/brain/genetic/culture system that has been so 
confusing and dangerous over our species time on the planet. On the 
other hand, "increase-by" as we use it in Etoys is the essential 
building block of the calculus (especially for children) and it is a 
"powerful idea" because it can be used in so many different kinds of 
"change situation" and it illuminates the change processes and makes 
them easier to think about and to calculate.

These two "powerful ideas" are on different scales and in different 
domains. But operationally they have the power to greatly amplify and 
channel our thinking processes. A phrase I've used in the past is 
"Point of view equals 80 IQ points". Choosing and using a context can 
be like adding an extra brain. This is why today's scientists and 
engineers -- who are not better endowed by nature to work in their 
fields -- are so much more effective than some of the great geniuses 
in the past.

Some of the most important "powerful ideas" can be drawn from 
Anthropology, Bio-behavior, Neuroethology, etc., (how History can be 
interpreted in the light of these, etc.) and have to do with insights 
about ourselves that are critical and have remained hidden for 10s of 
centuries. Our research project is ultimately about getting children 
to start learning these, but we decided that we needed to learn how 
to teach math and physical science (and what kinds of each of these) 
to children first. Jerome Bruner saw this earlier than anyone and 
pioneered one of the greatest curriculum designs for elementary 
school children in "Man A Course Of Study" (MACOS), an intellectually 
honest presentation of Anthropology to 5th graders. This was 
implemented in more than 10,000 schools in the US in the late 60s, 
was a masterpiece, and ultimately was destroyed by religious 
fundamentalists in Congress.

But it and other deep insight powerful ideas curricula need to be 
done again, better, and with more support.

Cheers,

Alan

>Bob
>
>
>>On 8/17/07, David Corking 
>><<mailto:lists at dcorking.com>lists at dcorking.com> wrote:
>> > But what if the
>> > secondary math teachers complained loudly? I don't think they are in
>> > any decision process that I can find.
>>
>>I don't know the US systems very well.  I would like to think that
>>school boards and education departments consult professionals first.
>>Are there countries where that does happen?
>>
>>
>>hi David,
>>
>>Curriculum statements have become contentious and politicised 
>>beasts because they are the main instrument of attempted control 
>>over teachers work. Many stakeholders fighting over problematic ideologies.
>>
>>As long ago as 1994 two Australian academics - rather than 
>>describing them as academics I should say two of the most notable 
>>educational maths researchers in Australia - wrote a book ('The 
>>National Curriculum Debacle' by Nerida Ellerton and Ken Clements) 
>>complaining bitterly that the leading maths educational research 
>>group in Australia had not been listened to in the development of 
>>the then national profiles. This book is really a blow by blow 
>>description of the farcical process as well as a critique of 
>>outcomes  based education
>>
>>In more recent times in Western Australia (Australian education 
>>system is a State responsibility) there has been outrage at 
>>attempts at curriculum reform. One perception has been that 
>>outcomes based education has led to a watering down and 
>>socialisation of the maths / science curriculum. To quote retired 
>>Associate Professor Steve Kessell, Science and Mathematics 
>>Education Centre, Curtin University, letter to The Sunday Times 
>>21/5/2006: "Learning about the sociology of the cosmetics industry 
>>is not real chemistry, discussing whether air bags should be 
>>mandatory is not real physics ... A 'culturally sensitive 
>>curriculum' borders on nonsense ..." This is but one small sample 
>>of a flood of complaint. See the PLATO (People Lobbying Against 
>>Teaching Outcomes) website for a lot more detail 
>><http://www.platowa.com/>http://www.platowa.com/ btw I'm not 
>>endorsing their approach just pointing out how contested this area has become
>>
>>My understanding is that this trend is world wide:
>><http://billkerr2.blogspot.com/2007/06/physics-teacher-begs-for-his-subject.html>http://billkerr2.blogspot.com/2007/06/physics-teacher-begs-for-his-subject.html
>>"Wellington Grey, a physics teachers in the UK, has written 
>><http://www.wellingtongrey.net/articles/archive/2007-06-07--open-letter-aqa.html>an 
>>open letter about the conversion of physics in his country from a 
>>science of precise measurement and calculation into "... something 
>>else, something nebulous and ill defined"
>>
>>To critique it thoroughly would require a hard look at outcomes 
>>based education.
>>
>>Summarising some of the issues:
>>- watering down, diluting, trivializing science and maths curriculum
>>- converting science / maths content into sociological content
>>- using discovery or inquiry based learning as a substitute for hard facts
>>
>>This appears to be occurring systematically in western education 
>>systems. (Not in developing countries who are serious about 
>>catching up to the west and actively promote the importance of 
>>maths, science and computing science).
>>
>>This is a big topic. Science and maths education seems to be 
>>polarising between a back to basics movement and soft sociological 
>>reform, often ineffectual "discovery learning". I believe there is 
>>a third way, that traditional science education can be reformed and 
>>still remain real science. Student designed computer simulations 
>>using software such as Etoys / Squeak could play an important role here.
>>
>>--
>>Bill Kerr
>><http://billkerr2.blogspot.com/>http://billkerr2.blogspot.com/
>>
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>
>
>
>--
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