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the non universals

Bill Kerr
Alan Kay has a couple of slides in his Europython 2006 keynote, illustrating Universals and Non Universals

It's right at the start of this video:
http://mrtopf.blip.tv/file/51972

From anthropological research of over 3000 human cultures, he presented two lists, the first were universals, the things that all human cultures have in common. This list included things like:
  • language
  • communication
  • fantasies
  • stories
  • tools and art
  • superstition
  • religion and magic
  • play and games
  • differences over similarities (?)
  • quick reactions to patterns
  • vendetta, and more
He then presented a list of non universals, the things that humans find harder to learn. This list was shorter and included:
  • reading and writing
  • deductive abstract mathematics
  • model based science
  • equal rights
  • democracy
  • perspective drawing
  • theory of harmony (?)
  • similarities over differences (?)
  • slow deep thinking
  • agriculture
  • legal systems

These lists are really important I think as a guide to what our formal education system ought to be teaching - at least a starting point to a discourse on powerful ideas, as distinct from the dumbing down and smothering effect of generalised curriculum statements

I'm curious as to where alan got his list of "non universals" from and would like more details about them. I put a question mark after a couple I didn't understand but which sounded interesting.

When I google "non universals" anthropology not much comes up but the search universals anthropology was more successful:

http://www.amazon.com/Human-Universals-Donald-E-Brown/dp/007008209X
or
http://tinyurl.com/28n7vv

--
Bill Kerr
http://billkerr2.blogspot.com/


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Re: the non universals

Alan Kay
Hi Bill --

There are various sources for "universals" on the net and off. Quite a bit more has been found out about these since the days of Lorenz and Tinbergen. One of the several fields that studies these as scientifically as possible is called "NeuroEthology" and there are a number of good books on the subject. T.G.R. Bower was one of the first to study very young humans specifically. An ancillarly field that has appeared in the last few decades is called "bio-behavior", and there also a number of illuminating books there.

I picked some of the "non-universals" that I thought were important (and some particularly to contrast items in the universal list).

To answer your question marks ...

"Theory of Harmony" is kind of like "Deductive Abstract Mathematics" in that most traditional cultures have some form of counting, adding and subtracting -- and some make music with multiple pitches at once (as did Western Culture before 1600). But the notion of harmony before 1600 was essentially as a byproduct of melodies and voice leading rather than a thing in itself in which chords have the same first class status as melodic lines. How and why this appeared is fascinating and is well known in music history.

Some of the most interesting composers in the Baroque period (especially Bach) tried to make both the old and the new schemes work completely together. Bach's harmonic language in particular was an amazing blend of harmonies and bass lines with voice leading and other contrapuntal techniques (quite a bit of his vocabulary is revealed in his harmonized chorales (some 371 or 372 of them)). That these two worlds are very different ways of looking at things is attested to by a wonderful piece by Purcell "The Contest Between Melodie and Harmonie".

As with "Greek Math", history doesn't seem to have any record of a separate and as rich invention of a harmonic theory. So it is really rare.

"Similarities over Differences" was to contrast with the standard processes of most nervous systems of most species to be more interested in "differences over similarities" (which is listed on the universal side). At most levels from reflexes to quite a bit of cognition, most similarities are accommodated and normalized while differences to the normalizations have a heightened significance (of "danger" or "pay attention").

Paying attention to differences is good for simple survival but makes it hard to think in many ways because it leads to so many cases, categories and distinctions -- and because some of the most important things may have disappeared into "normal" (in particular, things about oneself and one's own culture). So we unfortunately are much more interested in even superficial differences between humans and cultures and have a very hard time thinking of "the other" as being in the same value space as we are....

Part of the invention of modern math by the Greeks was their desire to get rid of the huge codexes of cases for geometry and arithmetic. This led to many useful abstractions which could be used as lenses to see things which looked different to normal minds as actually the same. For example, the Greek idea that there is only one triangle of each shape (because you can divide the two short sides by the long one to make a standard triangle of a given shape). This gets rid of lots of confusion and leaves room to start thinking more powerful thoughts. (The Greeks accomplished the interesting and amazing feat of using normalization to separate similarities and differences but paid attention to the similarities.) Calculus is a more subtle and tremendously useful example of separating similarities and differences. Convolution theory is yet more subtle ...

One way to think of my chart is that a lot of things we correlate with "enlightenment" and "civilization" are rather un-natural and rare inventions whose skills require us to learn how to go against many of our built in thought patterns. I think this is one of the main reasons to have an organized education (to learn the skills of being better thinkers than our nervous systems are directly set up for).

History suggests that we not lose these powerful ideas. They are not easy to get back.

The non-built-in nature of the powerful ideas on the right hand list implies they are generally more difficult to learn -- and this seems to be the case. This difficulty makes educational reform very hard because a very large number of the gatekeepers in education do not realize these simple ideas and tend to perceive and react (not think) using the universal left hand list .....

Cheers,

Alan


At 09:11 AM 8/13/2007, Bill Kerr wrote:
Alan Kay has a couple of slides in his Europython 2006 keynote, illustrating Universals and Non Universals

It's right at the start of this video:
http://mrtopf.blip.tv/file/51972

From anthropological research of over 3000 human cultures, he presented two lists, the first were universals, the things that all human cultures have in common. This list included things like:
  • language
  • communication
  • fantasies
  • stories
  • tools and art
  • superstition
  • religion and magic
  • play and games
  • differences over similarities (?)
  • quick reactions to patterns
  • vendetta, and more
He then presented a list of non universals, the things that humans find harder to learn. This list was shorter and included:
  • reading and writing
  • deductive abstract mathematics
  • model based science
  • equal rights
  • democracy
  • perspective drawing
  • theory of harmony (?)
  • similarities over differences (?)
  • slow deep thinking
  • agriculture
  • legal systems

These lists are really important I think as a guide to what our formal education system ought to be teaching - at least a starting point to a discourse on powerful ideas, as distinct from the dumbing down and smothering effect of generalised curriculum statements

I'm curious as to where alan got his list of "non universals" from and would like more details about them. I put a question mark after a couple I didn't understand but which sounded interesting.

When I google "non universals" anthropology not much comes up but the search universals anthropology was more successful:

http://www.amazon.com/Human-Universals-Donald-E-Brown/dp/007008209X
or
http://tinyurl.com/28n7vv

--
Bill Kerr
http://billkerr2.blogspot.com/

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Re: the non universals

dcorking
On 8/13/07, Alan Kay  wrote:

>  The non-built-in nature of the powerful ideas on the right hand list
> implies they are generally more difficult to learn -- and this seems to be
> the case. This difficulty makes educational reform very hard because a very
> large number of the gatekeepers in education do not realize these simple
> ideas and tend to perceive and react (not think) using the universal left
> hand list .....

Do you mean primary and secondary education?

This barrier is puzzling to me, as the key gatekeepers in education
(teachers, head teachers, inspectors, government education
departments) are products of the university system, which seems to me
to exist to propagate and build on the hard ideas (greek math,
relativity, quantum theory, sociology, musical harmony ... )

However, teachers have said to me,  "Whatever happened to those
turtles that were so popular when I was in school?"

There seems to me a desire among educators to help as many children
and young adults as possible make the leap from arithmetic to geometry
and calculus, from literacy to literary analysis, or indeed from
melody to harmony.    So where is the difficulty?  A lack of proven
agreed teaching methods, a perception of elitism, or the competing
desire we all feel to make sure everyone leaves school with basic
literacy and numeracy?

If Logo, Etoys and OLPC can teach calculus to 10-year-olds, and
calculus is essential to every engineering craft, and teachers love
encouraging students' creativity, why are so many schools teaching
pupils to use word processors instead?

Puzzled, David
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Re: the non universals

Bill Kerr
In reply to this post by Alan Kay
hi alan,

Thanks for extensive clarification of the items which I had left question marks on

From what you say the "non universals" group originates from you (!) which sort of explains why I couldn't find other references to it on the net

I have used your lists at a few meetings and it has provoked a response of sorts. On the one hand some people say the "non universals" is an interesting list. However, I've also noticed some reluctance or inability to discuss the items on the list in any real detail or to discuss the implications for the formal education system. ie it seems to come at people from left field

In his dissertation on the history of the Dynabook John Maxwell asks "what is a powerful idea, anyway?" and also argues that there has been a  decline of powerful idea discourse

What I'm noticing in educational discussion groups, blogs etc. on the web of late is much talk about "web 2.0", "school 2.0" but this tends to take place outside of a framework that maybe there are powerful ideas that really do have to be taught in some way.

You do say that the major stakeholders don't get it. What I see there is curriculum frameworks being used as blunt instruments of control. I'm suggesting, too, that many of the "radicals", who describe themselves as "web 2.0" are not getting it either.

In this context I like the idea of your list of "non universals" and John Maxwells' idea of the need for more powerful idea discourse. However, I'm also left feeling a bit unsure of the status of the "non universals" list, eg. how complete is it? have people argued about it and disputed it?

I could think of some non universals / powerful ideas that are not on your list, eg. Darwinian evolution, computer-human symbiosis for starters ...

I'm also curious about its connection with using computers in learning. Clearly etoys and logo can be used to assist teaching some of those concepts in constructionist fashion, esp maths and science. But for others I don't see a close connection at the moment (eg. equal rights, democracy) - although the OLPC project is becoming a part of that.

--
Bill Kerr
http://billkerr2.blogspot.com/


On 8/14/07, Alan Kay <[hidden email]> wrote:
Hi Bill --

There are various sources for "universals" on the net and off. Quite a bit more has been found out about these since the days of Lorenz and Tinbergen. One of the several fields that studies these as scientifically as possible is called "NeuroEthology" and there are a number of good books on the subject. T.G.R. Bower was one of the first to study very young humans specifically. An ancillarly field that has appeared in the last few decades is called "bio-behavior", and there also a number of illuminating books there.

I picked some of the "non-universals" that I thought were important (and some particularly to contrast items in the universal list).

To answer your question marks ...

"Theory of Harmony" is kind of like "Deductive Abstract Mathematics" in that most traditional cultures have some form of counting, adding and subtracting -- and some make music with multiple pitches at once (as did Western Culture before 1600). But the notion of harmony before 1600 was essentially as a byproduct of melodies and voice leading rather than a thing in itself in which chords have the same first class status as melodic lines. How and why this appeared is fascinating and is well known in music history.

Some of the most interesting composers in the Baroque period (especially Bach) tried to make both the old and the new schemes work completely together. Bach's harmonic language in particular was an amazing blend of harmonies and bass lines with voice leading and other contrapuntal techniques (quite a bit of his vocabulary is revealed in his harmonized chorales (some 371 or 372 of them)). That these two worlds are very different ways of looking at things is attested to by a wonderful piece by Purcell "The Contest Between Melodie and Harmonie".

As with "Greek Math", history doesn't seem to have any record of a separate and as rich invention of a harmonic theory. So it is really rare.

"Similarities over Differences" was to contrast with the standard processes of most nervous systems of most species to be more interested in "differences over similarities" (which is listed on the universal side). At most levels from reflexes to quite a bit of cognition, most similarities are accommodated and normalized while differences to the normalizations have a heightened significance (of "danger" or "pay attention").

Paying attention to differences is good for simple survival but makes it hard to think in many ways because it leads to so many cases, categories and distinctions -- and because some of the most important things may have disappeared into "normal" (in particular, things about oneself and one's own culture). So we unfortunately are much more interested in even superficial differences between humans and cultures and have a very hard time thinking of "the other" as being in the same value space as we are....

Part of the invention of modern math by the Greeks was their desire to get rid of the huge codexes of cases for geometry and arithmetic. This led to many useful abstractions which could be used as lenses to see things which looked different to normal minds as actually the same. For example, the Greek idea that there is only one triangle of each shape (because you can divide the two short sides by the long one to make a standard triangle of a given shape). This gets rid of lots of confusion and leaves room to start thinking more powerful thoughts. (The Greeks accomplished the interesting and amazing feat of using normalization to separate similarities and differences but paid attention to the similarities.) Calculus is a more subtle and tremendously useful example of separating similarities and differences. Convolution theory is yet more subtle ...

One way to think of my chart is that a lot of things we correlate with "enlightenment" and "civilization" are rather un-natural and rare inventions whose skills require us to learn how to go against many of our built in thought patterns. I think this is one of the main reasons to have an organized education (to learn the skills of being better thinkers than our nervous systems are directly set up for).

History suggests that we not lose these powerful ideas. They are not easy to get back.

The non-built-in nature of the powerful ideas on the right hand list implies they are generally more difficult to learn -- and this seems to be the case. This difficulty makes educational reform very hard because a very large number of the gatekeepers in education do not realize these simple ideas and tend to perceive and react (not think) using the universal left hand list .....

Cheers,

Alan



At 09:11 AM 8/13/2007, Bill Kerr wrote:
Alan Kay has a couple of slides in his Europython 2006 keynote, illustrating Universals and Non Universals

It's right at the start of this video:
<a href="http://mrtopf.blip.tv/file/51972" target="_blank" onclick="return top.js.OpenExtLink(window,event,this)"> http://mrtopf.blip.tv/file/51972

From anthropological research of over 3000 human cultures, he presented two lists, the first were universals, the things that all human cultures have in common. This list included things like:
  • language
  • communication
  • fantasies
  • stories
  • tools and art
  • superstition
  • religion and magic
  • play and games
  • differences over similarities (?)
  • quick reactions to patterns
  • vendetta, and more
He then presented a list of non universals, the things that humans find harder to learn. This list was shorter and included:
  • reading and writing
  • deductive abstract mathematics
  • model based science
  • equal rights
  • democracy
  • perspective drawing
  • theory of harmony (?)
  • similarities over differences (?)
  • slow deep thinking
  • agriculture
  • legal systems

These lists are really important I think as a guide to what our formal education system ought to be teaching - at least a starting point to a discourse on powerful ideas, as distinct from the dumbing down and smothering effect of generalised curriculum statements

I'm curious as to where alan got his list of "non universals" from and would like more details about them. I put a question mark after a couple I didn't understand but which sounded interesting.

When I google "non universals" anthropology not much comes up but the search universals anthropology was more successful:

<a href="http://www.amazon.com/Human-Universals-Donald-E-Brown/dp/007008209X" target="_blank" onclick="return top.js.OpenExtLink(window,event,this)"> http://www.amazon.com/Human-Universals-Donald-E-Brown/dp/007008209X
or
<a href="http://tinyurl.com/28n7vv" target="_blank" onclick="return top.js.OpenExtLink(window,event,this)">http://tinyurl.com/28n7vv

--
Bill Kerr
<a href="http://billkerr2.blogspot.com/" target="_blank" onclick="return top.js.OpenExtLink(window,event,this)"> http://billkerr2.blogspot.com/

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Re: the non universals

Alan Kay
Hi Bill --

I'm in a rush, so will reply more extensively later.

But, of course, the non-universals are easy for anyone who understands a fair number of the universals and who reads a little. Most cultures on Earth have not had writing systems (and probably still most today). Etc.

Cheers,

Alan

At 08:05 AM 8/15/2007, Bill Kerr wrote:
hi alan,

Thanks for extensive clarification of the items which I had left question marks on

From what you say the "non universals" group originates from you (!) which sort of explains why I couldn't find other references to it on the net

I have used your lists at a few meetings and it has provoked a response of sorts. On the one hand some people say the "non universals" is an interesting list. However, I've also noticed some reluctance or inability to discuss the items on the list in any real detail or to discuss the implications for the formal education system. ie it seems to come at people from left field

In his dissertation on the history of the Dynabook John Maxwell asks "what is a powerful idea, anyway?" and also argues that there has been a  decline of powerful idea discourse

What I'm noticing in educational discussion groups, blogs etc. on the web of late is much talk about "web 2.0", "school 2.0" but this tends to take place outside of a framework that maybe there are powerful ideas that really do have to be taught in some way.

You do say that the major stakeholders don't get it. What I see there is curriculum frameworks being used as blunt instruments of control. I'm suggesting, too, that many of the "radicals", who describe themselves as "web 2.0" are not getting it either.

In this context I like the idea of your list of "non universals" and John Maxwells' idea of the need for more powerful idea discourse. However, I'm also left feeling a bit unsure of the status of the "non universals" list, eg. how complete is it? have people argued about it and disputed it?

I could think of some non universals / powerful ideas that are not on your list, eg. Darwinian evolution, computer-human symbiosis for starters ...

I'm also curious about its connection with using computers in learning. Clearly etoys and logo can be used to assist teaching some of those concepts in constructionist fashion, esp maths and science. But for others I don't see a close connection at the moment (eg. equal rights, democracy) - although the OLPC project is becoming a part of that.

--
Bill Kerr
http://billkerr2.blogspot.com/


On 8/14/07, Alan Kay <[hidden email]> wrote:
Hi Bill --

There are various sources for "universals" on the net and off. Quite a bit more has been found out about these since the days of Lorenz and Tinbergen. One of the several fields that studies these as scientifically as possible is called "NeuroEthology" and there are a number of good books on the subject. T.G.R. Bower was one of the first to study very young humans specifically. An ancillarly field that has appeared in the last few decades is called "bio-behavior", and there also a number of illuminating books there.

I picked some of the "non-universals" that I thought were important (and some particularly to contrast items in the universal list).

To answer your question marks ...

"Theory of Harmony" is kind of like "Deductive Abstract Mathematics" in that most traditional cultures have some form of counting, adding and subtracting -- and some make music with multiple pitches at once (as did Western Culture before 1600). But the notion of harmony before 1600 was essentially as a byproduct of melodies and voice leading rather than a thing in itself in which chords have the same first class status as melodic lines. How and why this appeared is fascinating and is well known in music history.

Some of the most interesting composers in the Baroque period (especially Bach) tried to make both the old and the new schemes work completely together. Bach's harmonic language in particular was an amazing blend of harmonies and bass lines with voice leading and other contrapuntal techniques (quite a bit of his vocabulary is revealed in his harmonized chorales (some 371 or 372 of them)). That these two worlds are very different ways of looking at things is attested to by a wonderful piece by Purcell "The Contest Between Melodie and Harmonie".

As with "Greek Math", history doesn't seem to have any record of a separate and as rich invention of a harmonic theory. So it is really rare.

"Similarities over Differences" was to contrast with the standard processes of most nervous systems of most species to be more interested in "differences over similarities" (which is listed on the universal side). At most levels from reflexes to quite a bit of cognition, most similarities are accommodated and normalized while differences to the normalizations have a heightened significance (of "danger" or "pay attention").

Paying attention to differences is good for simple survival but makes it hard to think in many ways because it leads to so many cases, categories and distinctions -- and because some of the most important things may have disappeared into "normal" (in particular, things about oneself and one's own culture). So we unfortunately are much more interested in even superficial differences between humans and cultures and have a very hard time thinking of "the other" as being in the same value space as we are....

Part of the invention of modern math by the Greeks was their desire to get rid of the huge codexes of cases for geometry and arithmetic. This led to many useful abstractions which could be used as lenses to see things which looked different to normal minds as actually the same. For example, the Greek idea that there is only one triangle of each shape (because you can divide the two short sides by the long one to make a standard triangle of a given shape). This gets rid of lots of confusion and leaves room to start thinking more powerful thoughts. (The Greeks accomplished the interesting and amazing feat of using normalization to separate similarities and differences but paid attention to the similarities.) Calculus is a more subtle and tremendously useful example of separating similarities and differences. Convolution theory is yet more subtle ...

One way to think of my chart is that a lot of things we correlate with "enlightenment" and "civilization" are rather un-natural and rare inventions whose skills require us to learn how to go against many of our built in thought patterns. I think this is one of the main reasons to have an organized education (to learn the skills of being better thinkers than our nervous systems are directly set up for).

History suggests that we not lose these powerful ideas. They are not easy to get back.

The non-built-in nature of the powerful ideas on the right hand list implies they are generally more difficult to learn -- and this seems to be the case. This difficulty makes educational reform very hard because a very large number of the gatekeepers in education do not realize these simple ideas and tend to perceive and react (not think) using the universal left hand list .....

Cheers,

Alan



At 09:11 AM 8/13/2007, Bill Kerr wrote:
Alan Kay has a couple of slides in his Europython 2006 keynote, illustrating Universals and Non Universals

It's right at the start of this video:
http://mrtopf.blip.tv/file/51972

From anthropological research of over 3000 human cultures, he presented two lists, the first were universals, the things that all human cultures have in common. This list included things like:
language
communication
fantasies
stories
tools and art
superstition
religion and magic
play and games
differences over similarities (?)
quick reactions to patterns
vendetta, and more
He then presented a list of non universals, the things that humans find harder to learn. This list was shorter and included:
reading and writing
deductive abstract mathematics
model based science
equal rights
democracy
perspective drawing
theory of harmony (?)
similarities over differences (?)
slow deep thinking
agriculture
legal systems
These lists are really important I think as a guide to what our formal education system ought to be teaching - at least a starting point to a discourse on powerful ideas, as distinct from the dumbing down and smothering effect of generalised curriculum statements

I'm curious as to where alan got his list of "non universals" from and would like more details about them. I put a question mark after a couple I didn't understand but which sounded interesting.

When I google "non universals" anthropology not much comes up but the search universals anthropology was more successful:

http://www.amazon.com/Human-Universals-Donald-E-Brown/dp/007008209X
or
http://tinyurl.com/28n7vv

--
Bill Kerr
http://billkerr2.blogspot.com/

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Re: the non universals

Alan Kay
In reply to this post by Bill Kerr
OK, a few more minutes ...

At 08:05 AM 8/15/2007, Bill Kerr wrote:
hi alan,

Thanks for extensive clarification of the items which I had left question marks on

From what you say the "non universals" group originates from you (!) which sort of explains why I couldn't find other references to it on the net

Gathering the behaviors that can scientifically be claimed to be universals is what requires diligent work by experts, since literally thousands of cultures need to be perused -- and a fair amount of experimentation with early childhood behaviors is critical. Once, gotten we can easily claim that opposites (like writing and reading) are not universal. Deductive math and model based science are also easy. As is "equal rights", etc.


I have used your lists at a few meetings and it has provoked a response of sorts. On the one hand some people say the "non universals" is an interesting list. However, I've also noticed some reluctance or inability to discuss the items on the list in any real detail or to discuss the implications for the formal education system. ie it seems to come at people from left field

It requires some "perspective and knowledge" (which was what education used to be correlated with) to do the discussion. E.g. if one is not fluent in math and/or science it is difficult to understand just how qualitatively different are the modern versions of these. Most educational reform stalls in large part from the below threshold educations of the adults in the system. For most people, most powerful ideas come at them from left field.


In his dissertation on the history of the Dynabook John Maxwell asks "what is a powerful idea, anyway?" and also argues that there has been a  decline of powerful idea discourse

Well, "powerful ideas" is a nice metaphor that Seymour made up to heighten people's understanding (and the significance) of the relatively few and rare inventions that have made huge differences in how humans meet and think about the world. It is normal behavior to accommodate to what is present (especially what one was born into) and so most people think of the powerful ideas as part of normal, and since most Americans have not traveled in a way that gets them to appreciate the wide range of situations that humans are in around the world, they completely miss the wonder and mystery of "better intellectual architectures". This is why there are so few scientists (because most people take things as they seem and completely miss what deeper curiosity and better methods can find out).


What I'm noticing in educational discussion groups, blogs etc. on the web of late is much talk about "web 2.0", "school 2.0" but this tends to take place outside of a framework that maybe there are powerful ideas that really do have to be taught in some way.

You do say that the major stakeholders don't get it. What I see there is curriculum frameworks being used as blunt instruments of control. I'm suggesting, too, that many of the "radicals", who describe themselves as "web 2.0" are not getting it either.

Most of this is just a cargo cult.


In this context I like the idea of your list of "non universals" and John Maxwells' idea of the need for more powerful idea discourse. However, I'm also left feeling a bit unsure of the status of the "non universals" list, eg. how complete is it? have people argued about it and disputed it?

Neither list is complete. But the important property of the universals list is that most the items are well vetted. The importance of my non-universal list is just that 5 or 7 items are the most important changes that humans have made in their 200,000 years on the planet (and most of these came very recently (even agriculture)). What more do people need to start thinking with? What more arguments about modern science need to be made? (And if they do need to be made, then what new kind of argument would work?)

In other words, if the items on my list are ignored then it really doesn't matter much what else could be on the list. For example, the notion that there are "powerful ideas" could be the number one powerful idea, since it should lead to trying to understand powerful ideas, and to trying to find more of them.


I could think of some non universals / powerful ideas that are not on your list, eg. Darwinian evolution, computer-human symbiosis for starters ...

Sure. There are lots (and they should be paid attention to). But certainly Darwinian Evolution (and a lot of other things fall under Science), etc. Computer-human symbiosis falls under the larger topics of how human thinking can be changed by the use of media (for better or for worse), etc, For a short list, it's best to use the biggies. Similarly, if we listed every built-in human trait (especially the zillions of bad ones), the list would be too long for any discussion purposes.


I'm also curious about its connection with using computers in learning. Clearly etoys and logo can be used to assist teaching some of those concepts in constructionist fashion, esp maths and science. But for others I don't see a close connection at the moment (eg. equal rights, democracy) - although the OLPC project is becoming a part of that.

Some music needs to be sung by human voices, and the best instruments in the world won't help (and will usually detract). Similarly, some theatrical expressions have to be done directly in person live, and will be diminished by inserting even high resolution media. Similarly, even the wondrous nature of mathematics often is too visible so it can obscure what's most interesting about what is being described.

We are talking about human thinking and perspective, not computers here.

However, consider this wonderful phrase from Marshall McLuhan "You can argue about a lot of things with stained glass windows, but Democracy is not one of them!" He meant that not just non-visual oral language, but only written, even printed language was disembodied and abstract enough to handle the critical issues and subtleties of this discourse. This itself is a powerful insight and a powerful idea that most adults in the world today have no notion of, and most would find it almost crazy.

In other words, as Neil Postman liked to point out, the relationship between human thought and the languages/media used to form and express it is not a separated one, but is a non-linear ecology. Dropping something like TV into a society is like introducing rabbits into Australia. Not really thinking about computing and networking as new kinds of rabbits for good and ill can lead (and has led) to disastrous effects already. On the other hand, geniuses (like Montesorri, Papert, Bruner, McLuhan, Engelbart, etc.) who have thought about how environments of any kind condition "normal" and thus much of human thought and behavior have come up with very powerful and positive ways to use new and old environments to help humans more successfully struggle with their less well fitted internal behavior patterns.

The basic approach here is to hold focus on what is really important, and to design new media and environments to help people learn what is important. As Seymour pointed out long ago, not even in the educational swamps of America do they use the phrase "paper based education" since it is patently ridiculous. But because people don't understand computers (and because magical thinking is one of the human universals) any new technology is treated as a talisman -- and they have no trouble in generating phrases like "computer based education" or "computer based curriculum" or "web based learning" etc. This is also cargo cult behavior.

Most people "take the world as it seems" as I mentioned above, and so they completely miss most of the important properties and issues. This is why having general discussions about powerful ideas often leads nowhere.

(And most discussions on the web similarly get nowhere -- opinion gets exchanged, but opinions have always been exchanged for 200,000 years with nothing much happening. The concatenation of opinions almost never leads to a better set of ideas -- this is a big bug in "web myth" and "collective behavior myths" in general. This is because the opinions in order to be understood have to share quite a bit of the same outlook, but progress usually comes from big changes in outlook. What we need are not more opinions and endless discussions, but more hooks to find stronger outlooks (aka "powerful ideas").

Cheers,

Alan


--
Bill Kerr
http://billkerr2.blogspot.com/


On 8/14/07, Alan Kay <[hidden email]> wrote:
Hi Bill --

There are various sources for "universals" on the net and off. Quite a bit more has been found out about these since the days of Lorenz and Tinbergen. One of the several fields that studies these as scientifically as possible is called "NeuroEthology" and there are a number of good books on the subject. T.G.R. Bower was one of the first to study very young humans specifically. An ancillarly field that has appeared in the last few decades is called "bio-behavior", and there also a number of illuminating books there.

I picked some of the "non-universals" that I thought were important (and some particularly to contrast items in the universal list).

To answer your question marks ...

"Theory of Harmony" is kind of like "Deductive Abstract Mathematics" in that most traditional cultures have some form of counting, adding and subtracting -- and some make music with multiple pitches at once (as did Western Culture before 1600). But the notion of harmony before 1600 was essentially as a byproduct of melodies and voice leading rather than a thing in itself in which chords have the same first class status as melodic lines. How and why this appeared is fascinating and is well known in music history.

Some of the most interesting composers in the Baroque period (especially Bach) tried to make both the old and the new schemes work completely together. Bach's harmonic language in particular was an amazing blend of harmonies and bass lines with voice leading and other contrapuntal techniques (quite a bit of his vocabulary is revealed in his harmonized chorales (some 371 or 372 of them)). That these two worlds are very different ways of looking at things is attested to by a wonderful piece by Purcell "The Contest Between Melodie and Harmonie".

As with "Greek Math", history doesn't seem to have any record of a separate and as rich invention of a harmonic theory. So it is really rare.

"Similarities over Differences" was to contrast with the standard processes of most nervous systems of most species to be more interested in "differences over similarities" (which is listed on the universal side). At most levels from reflexes to quite a bit of cognition, most similarities are accommodated and normalized while differences to the normalizations have a heightened significance (of "danger" or "pay attention").

Paying attention to differences is good for simple survival but makes it hard to think in many ways because it leads to so many cases, categories and distinctions -- and because some of the most important things may have disappeared into "normal" (in particular, things about oneself and one's own culture). So we unfortunately are much more interested in even superficial differences between humans and cultures and have a very hard time thinking of "the other" as being in the same value space as we are....

Part of the invention of modern math by the Greeks was their desire to get rid of the huge codexes of cases for geometry and arithmetic. This led to many useful abstractions which could be used as lenses to see things which looked different to normal minds as actually the same. For example, the Greek idea that there is only one triangle of each shape (because you can divide the two short sides by the long one to make a standard triangle of a given shape). This gets rid of lots of confusion and leaves room to start thinking more powerful thoughts. (The Greeks accomplished the interesting and amazing feat of using normalization to separate similarities and differences but paid attention to the similarities.) Calculus is a more subtle and tremendously useful example of separating similarities and differences. Convolution theory is yet more subtle ...

One way to think of my chart is that a lot of things we correlate with "enlightenment" and "civilization" are rather un-natural and rare inventions whose skills require us to learn how to go against many of our built in thought patterns. I think this is one of the main reasons to have an organized education (to learn the skills of being better thinkers than our nervous systems are directly set up for).

History suggests that we not lose these powerful ideas. They are not easy to get back.

The non-built-in nature of the powerful ideas on the right hand list implies they are generally more difficult to learn -- and this seems to be the case. This difficulty makes educational reform very hard because a very large number of the gatekeepers in education do not realize these simple ideas and tend to perceive and react (not think) using the universal left hand list .....

Cheers,

Alan



At 09:11 AM 8/13/2007, Bill Kerr wrote:
Alan Kay has a couple of slides in his Europython 2006 keynote, illustrating Universals and Non Universals

It's right at the start of this video:
http://mrtopf.blip.tv/file/51972

From anthropological research of over 3000 human cultures, he presented two lists, the first were universals, the things that all human cultures have in common. This list included things like:
language
communication
fantasies
stories
tools and art
superstition
religion and magic
play and games
differences over similarities (?)
quick reactions to patterns
vendetta, and more
He then presented a list of non universals, the things that humans find harder to learn. This list was shorter and included:
reading and writing
deductive abstract mathematics
model based science
equal rights
democracy
perspective drawing
theory of harmony (?)
similarities over differences (?)
slow deep thinking
agriculture
legal systems
These lists are really important I think as a guide to what our formal education system ought to be teaching - at least a starting point to a discourse on powerful ideas, as distinct from the dumbing down and smothering effect of generalised curriculum statements

I'm curious as to where alan got his list of "non universals" from and would like more details about them. I put a question mark after a couple I didn't understand but which sounded interesting.

When I google "non universals" anthropology not much comes up but the search universals anthropology was more successful:

http://www.amazon.com/Human-Universals-Donald-E-Brown/dp/007008209X
or
http://tinyurl.com/28n7vv

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Re: the non universals

Brad Fuller-2
In reply to this post by dcorking
On Wed August 15 2007 4:18 am, David Corking wrote:
> If Logo, Etoys and OLPC can teach calculus to 10-year-olds, and
> calculus is essential to every engineering craft, and teachers love
> encouraging students' creativity, why are so many schools teaching
> pupils to use word processors instead?
>
> Puzzled, David

This is a question I ask often of teachers. Here I am, probably in an area
that is one of the most financially rich with highly educated people on the
planet (Silicon Valley, CA) and I have never been given a satisfactory
answer. It's not that the teachers don't want help nor more tricks in their
bag. The vast majority of teachers I've met are very dedicated to their
students. But, the local highschool's "Computer" class is how to run MS
Office. Their advance "Computer" class is more MS Office. I don't get it.

brad
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Re: the non universals

Kim Rose-2
Hi, Brad -

I think it's a common finding (at least in the U.S.) that schools are
trying to prepare students "for the workplace" and thus today's
education is largely vocational.  Therefore, the belief holds that
teaching word processing will ultimately be more valuable to students
than calculus.  My experience is that parents' attitudes perpetuate
this phenomenon.  Another reason may be that more teachers understand
word processing and are more comfortable *teaching*  "MS Office" than
calculus.

   --  Kim


At 11:34 AM -0700 8/15/07, Brad Fuller wrote:

>On Wed August 15 2007 4:18 am, David Corking wrote:
>>  If Logo, Etoys and OLPC can teach calculus to 10-year-olds, and
>>  calculus is essential to every engineering craft, and teachers love
>>  encouraging students' creativity, why are so many schools teaching
>>  pupils to use word processors instead?
>>
>>  Puzzled, David
>
>This is a question I ask often of teachers. Here I am, probably in an area
>that is one of the most financially rich with highly educated people on the
>planet (Silicon Valley, CA) and I have never been given a satisfactory
>answer. It's not that the teachers don't want help nor more tricks in their
>bag. The vast majority of teachers I've met are very dedicated to their
>students. But, the local highschool's "Computer" class is how to run MS
>Office. Their advance "Computer" class is more MS Office. I don't get it.
>
>brad
>_______________________________________________
>Squeakland mailing list
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>http://squeakland.org/mailman/listinfo/squeakland

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Re: the non universals

Alan Kay
In reply to this post by dcorking
Hi David --

Someone once asked Mohandas Gandhi what he thought of Western Civilization, and he said he "thought it would be a good idea!" Similarly, if you asked me what I thought of University Education, I would say that "it would be a good idea!".

There seems to me a desire among educators to help as many children
and young adults as possible make the leap from arithmetic to geometry
and calculus, from literacy to literary analysis, or indeed from
melody to harmony.    So where is the difficulty?  A lack of proven
agreed teaching methods, a perception of elitism, or the competing
desire we all feel to make sure everyone leaves school with basic
literacy and numeracy?

My perception of your first sentence is very different than yours. Most educators in K-8 do not seem to know anything about calculus and precious little about geometry or algebra (and their knowledge of arithmetic is rule-based not math-based) so I don't see whatever desires they might espouse about these progressions as having much substance. I do think that one is likely to get much better instruction and coaching from music teachers and sports coaches -- in no small part because they are usually fluent practitioners, and do have some real contact with the entire chain of meaning and action of their subjects.

I don't have deep direct scientific knowledge of the nature of the difficulties, just thousands of encounters with various educational systems around the world and educators over the last 35+ years. So I could have just been continually unlucky in my travels....

In the early 80's I went to Atari as its Chief Scientist to try to get some of Papert's and my ideas into consumer electronics. The Atari 800 and especially the 400 were tremendous computers for their price, and Brian Silverman made a great version of Logo to go on these machines. (There were also Logos on most of the other 8-bit micros.) And, there was a Logo-vogue for a time, both in the US and in the UK. Many early adopter teachers got Atari's or Apple IIs in their classrooms and got their students started on it.

This was exciting until examined closely. Essentially none of the teachers actually understood enough mathematics to see what Logo was really about. And for a variety of reasons Logo gradually slid away and disappeared.

We should look a bit at three different kinds of understanding:  rote understanding, operational understanding, and meta-understanding. If we leave out the majority of teachers who don't really understand math in any strong way, we still find that the kinds of understandings that are left are not up to the task of being able to see the meaning and value of a new perspective on mathematics. For example, it is possible to understand calculus a little in the narrow form in which it was learned, and still not be able to see "calculus" in a different form (even if the new way is a stronger way to look at it). Real fluency in a subject allows many of the most powerful ideas in the subject to be somewhat detached from specific forms. This is meta-understanding.

For example, the school version of calculus is based on a numeric continuum and algebraic manipulations. But the idea of calculus is not really strongly tied to this.

The idea has to do with separating out the similarities and differences of change to produce and allow much simpler and easier to understand relationships to be created. This can be done so that the connection between one state and the next one of interest is a simple addition. Actual continuity can be replaced by a notion of "you pick and then I pick" so that non-continuities don't get seen. This other view of calculus as a form of calculation was used by Babbage in his first "difference engines" because a computing machine that can do lots of additions for you can make this other way to look at calculus very practical and worthwhile. The side benefit is that it is much easier to understand than the algebraic rubrics. If we then add to this the idea of using vectors (as "supernumbers") instead of regular numbers, we are able to dispense with coordinate systems except when convenient, and are able to operate in multiple dimensions.

All of this was worked out in the 19th century and quite a bit was adopted enthusiastically by science and is in main use today.

To cut to the chase, Seymour Papert (who was a very good mathematician) was one of the first to realize that this kind of math (called "vector differential geometry") fit very well into young children's thinking patterns, and that the new personal computers would be able to manifest Babbage's dream to be able to compute and think in terms of an incremental calculus for complex change.

Any one fluent in mathematics can recognize this (but it took a Papert to first point it out). But, virtually no one without fluency in mathematics can recognize this. And surveys have shown that less than 5% of Americans are fluent in math or science. Many of the 95% were able to go through 16 years of schooling and successfully get a college degree without attaining any fluency in math or science.

This is not a matter of intelligence at all, but is more of a "two cultures" phenomenon. So I am not able to agree with this sentence of yours:

This barrier is puzzling to me, as the key gatekeepers in education
(teachers, head teachers, inspectors, government education
departments) are products of the university system, which seems to me
to exist to propagate and build on the hard ideas (greek math,
relativity, quantum theory, sociology, musical harmony ... )

It is possible to learn about these ideas in university (and outside of university), but I don't know of any universities today whose goal it is to invest its graduates with fluency in these ideas or any other powerful ideas. That is, the concept of a general education for the 21st century that should include these ideas doesn't seem to be in any American university I'm familiar with.

If Logo, Etoys and OLPC can teach calculus to 10-year-olds, and
calculus is essential to every engineering craft, and teachers love
encouraging students' creativity, why are so many schools teaching
pupils to use word processors instead?

The problem is that Logo, Etoys and OLPC can't teach calculus to 10 year olds. The good news is that adults who understand the subject matter can indeed teach calculus to 10 year olds with the aid of Logo, Etoys and OLPC.

If you put a piano in a classroom, children will do something with it, and perhaps even produce a "chopsticks culture". But the music isn't in the piano. It has to be brought forth from the children. And the possibilities of music are not in the children, but right now has to be manifested in the teachers and other mentors. (It took several centuries to develop keyboard technique, and much longer than that to invent and develop the rich genres of music of the last 6 centuries.)

Math and science were difficult to invent in the first place (so Rousseau-like optimism for discovery learning is misplaced), and both subjects have been developed for centuries by experts. Children need experts to help them, not retreaded social studies teachers.

One of the goals of 19th century education was to teach children how to learn from books. This was a great idea because (a) oral instruction is quite inefficient (b) you can get around bad teachers (c) you can contact experts in ways that you might not be able to directly (especially if they are deceased) (d) you can self-pace (e) you can employ multiple perspectives on the subject matter (f) you are not in the quicksand of social norming, etc. A small percentage of children still are able to learn from books, and similar small percentages of children can and do learn powerful ideas by themselves without much adult aid.

But since general education is primarily about helping to grow citizens who can try to become more civilized, the big work that has to be done is with those who are not inclined to learn powerful ideas of any kind.

Best wishes,

Alan



At 04:18 AM 8/15/2007, David Corking wrote:
On 8/13/07, Alan Kay  wrote:

>  The non-built-in nature of the powerful ideas on the right hand list
> implies they are generally more difficult to learn -- and this seems to be
> the case. This difficulty makes educational reform very hard because a very
> large number of the gatekeepers in education do not realize these simple
> ideas and tend to perceive and react (not think) using the universal left
> hand list .....

Do you mean primary and secondary education?

This barrier is puzzling to me, as the key gatekeepers in education
(teachers, head teachers, inspectors, government education
departments) are products of the university system, which seems to me
to exist to propagate and build on the hard ideas (greek math,
relativity, quantum theory, sociology, musical harmony ... )

However, teachers have said to me,  "Whatever happened to those
turtles that were so popular when I was in school?"

There seems to me a desire among educators to help as many children
and young adults as possible make the leap from arithmetic to geometry
and calculus, from literacy to literary analysis, or indeed from
melody to harmony.    So where is the difficulty?  A lack of proven
agreed teaching methods, a perception of elitism, or the competing
desire we all feel to make sure everyone leaves school with basic
literacy and numeracy?

If Logo, Etoys and OLPC can teach calculus to 10-year-olds, and
calculus is essential to every engineering craft, and teachers love
encouraging students' creativity, why are so many schools teaching
pupils to use word processors instead?

Puzzled, David
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Re: the non universals

Bill Kerr
In reply to this post by dcorking
hi David

This barrier is puzzling to me, as the key gatekeepers in education
(teachers, head teachers, inspectors, government education
departments) are products of the university system, which seems to me
to exist to propagate and build on the hard ideas (greek math,
relativity, quantum theory, sociology, musical harmony ... )

...

There seems to me a desire among educators to help as many children
and young adults as possible make the leap from arithmetic to geometry
and calculus, from literacy to literary analysis, or indeed from
melody to harmony.    So where is the difficulty?  A lack of proven
agreed teaching methods, a perception of elitism, or the competing
desire we all feel to make sure everyone leaves school with basic
literacy and numeracy?

I think some of the powerful ideas (eg. calculus) are  in the curriculum statements but  most of the excitement (power) has been taken out of  them. 

How?

In part because these ideas are taught out of textbooks which are dry and didactic and don't capture the earth shaking importance - how these ideas have dramatically changed the world we live in. Now, you could argue that some good teachers try to achieve this and I would *partly* agree, but ...

The powerful ideas are also presented alongside a multitude of other (not so powerful) ideas in the curriculum as though all the ideas and subject domains were equal and equivalent. eg. in South Australia all 7 curriculum areas are treated as equal and equivalent and equal amounts of time are devoted to each one. I could point to extreme examples here (Bushwalking is equivalent to advanced maths for getting accreditation points at Year 11) but the overall impact is what really matters. Every idea is treated as equal to every other idea and in the process the importance of the powerful ideas is lost

Alan described a similar sort of thing (the context was Doug Engelbart's work) in 'The Early History of Smalltalk' as a tyranny of subgoals:

"Their larger metaphor of human-computer symbiosis helped the community avoid making a religion of their subgoals and kept them focused on the abstract holy grail of "augmentation."

Now what is the larger metaphor of education departments? It's much more like "no child left behind" than "powerful ideas"

Curriculum committees in Schools are mainly turf wars where the heads of various departments fight over their ongoing right for equal time - irrespective of the power of their ideas - and computing is a latecomer to this feast, normally subsumed into Technology, while efforts are made to "integrate" it into all the curriculum areas, ie. non specialists who don't understand the potential of the computer are given equal access to computer labs. It doesn't work.


If Logo, Etoys and OLPC can teach calculus to 10-year-olds, and
calculus is essential to every engineering craft, and teachers love
encouraging students' creativity, why are so many schools teaching
pupils to use word processors instead?

I've used logo in the classroom in powerful ways in the 90s, eg. emulating some of the things described in Idit Harel's thesis, and have written up the results:

1) I was in a school which supported innovation, this is rare
2) Because of my interest I was given a room of old XT computers (some didn't even have hard drives). I had exclusive use of those computers and could setup an immersive environment because no one else in the school wanted to use them, they were too old and broken
3) To understand how to teach it properly I needed to read Idit's PhD thesis as well as Seymour's books, not many teachers are prepared to do things like that
4) When I wrote up my results and sent them to the maths journal - that students could learn fractions and much else without formal teaching of fractions - my paper was rejected for publication,  the results  were not impressive enough or some such feedback. The paper is here:
http://www.users.on.net/~billkerr/a/isdp.htm
5) When I ran logo inservice for other teachers in the school then a core group did come along regularly and the feedback was positive but of the 7 or so teachers only one of them actually tried the ideas in their . I later realised that most of the teachers were just taking the opportunity to rack up some hours required to get a week off at the end of the school year.
6) Later when I tried to do similar things with different classes by visiting a computer lab twice a week (ie. non immersive environment) it just did not work in the same way, without the magic of ready access to the computers

Seymour Papert discusses the interaction between "the children's machine" and School quite poetically in his writings, for example:
"The shift from a radically subversive instrument in the classroom to a blunted conservative instrument in the computer lab came neither from lack of knowledge nor from a lack of software. I explain it by an innate intelligence of School, which acted like any living organism in defending itself against a foreign body. It put into motion an immune reaction whose end result would be to digest and assimilate the intruder. Progressive teachers knew very well how to use the computer for their own ends as an instrument of change. Schools knew very well how to nip this subversion in the bud. No one in the story acted out of ignorance about computers, although they might have been naive in failing to understand the sociological drama in which they were actors."

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Re: the non universals

Alan Kay
Below is a recent article from Education Week. In (only) my opinion, it should be impossible for 93% of American teachers to like their jobs if they had any perspective on what they are doing, how they are doing it, and what they are supposed to do. There are a few other mildly interesting tidbits at the very end of the article.

To me this is an example of how a field can and does select the personalities and skills that fit to its actual mission. I saw this very strongly when I was in the Air Force (whose general way of doing things I really did not like). I left after my required term, but many re-upped, and they were the ones that fit into that particular scheme.

Another example of the ecological power of environments and the co-evolution and selection of environments and traits.

Cheers,

Alan

--------------
Education Week

Published Online: August 1, 2007

Teachers Tell Researchers They Like Their Jobs

By Vaishali Honawar

Ninety-three percent of teachers reported satisfaction with their jobs 10 years after entering the field, according to a new survey that also found attrition rates for teachers were actually lower than for other professionals.

The report, released this week by the National Center for Education Statistics, surveyed 9,000 graduates who received their bachelorÂ’s degrees in various disciplines in the 1992-93 school year. Nearly 20 percent of those graduates entered the teaching profession.

The findings from the survey debunk several long-held views on teacher pay, turnover, and job satisfaction. For instance, it found that only 18 percent of those who entered teaching changed occupations within four years of getting a degree. Given that other professions experienced attrition rates between 17 percent and 75 percent during that period, the number of career-switchers from teaching was on the low end of the scale, according to the data. More than half those who became teachers were still teaching 10 years later.

Teacher advocates and unions have long claimed that turnover among new teachers ranges from 30 percent to 50 percent within the first five years.

“The take for a long time was that there is this incredibly high attrition among teachers from schools,” said Mark Schneider, the commissioner of NCES, an arm of the U.S. Department of Education. The report, he said, shows that teacher-turnover rates are actually lower than those in other professions.

“I understand why schools and school districts are upset about losing teachers, but it is part of the normal sorting process” in a dynamic job market, Mr. Schneider added.

The survey also stands on their head some commonly held beliefs about teacher salaries. TeachersÂ’ unions have often cited low pay as a major reason for teacher dissatisfaction. But only 13 percent of those who left teaching by 2003 gave it as the reason for leaving. Forty-eight percent of those who remained in the profession said they were satisfied with their salaries.

Kate Walsh, the president of the National Council on Teacher Quality, a research and advocacy group in Washington, called the findings “explosive.”

“What was surprising is how cheery the [teachers’] responses were,” she said. Education groups, including the unions, she contended, often cite teachers’ unhappiness in order to pressure districts and states for concessions.

Spokesmen for the National Education Association and the American Federation of Teachers said they were unable to comment on the report before the story was posted.

Racial Differences

The reportÂ’s findings are based on the NCESÂ’ survey of baccalaureate-degree recipients conducted between 1993 and 2003. Participants answered questions via phone and the Internet and during in-person interviews. The report was prepared by MPR Associates in Berkeley, Calif.

Of those surveyed who were still teaching 10 years after earning their degrees, 90 percent said they would choose the same career again, and 67 percent said they would remain in teaching for the rest of their working lives.

The rate among African-American teachers, however, was significantly lower, with 37 percent saying they would choose to remain in the profession, compared with 70 percent of white teachers.

Nearly 20 percent of black teachers said they would leave if something better came along, compared with fewer than 10 percent of white teachers.

Ms. Walsh said the higher rates of dissatisfaction among black teachers could be due to the fact that more black teachers teach in high-poverty schools.

The study reaffirmed that attrition rates were higher among male teachers. While women (29 percent) were more likely to leave for family-related reasons, men (32 percent) usually left for a job outside the field of education.

A candidateÂ’s age when he or she attended college also appeared to play a role in attrition rates: Those 30 or older when they obtained their degrees were more likely than younger graduates to remain in teaching.

Those who earned better grades in college were more likely than those with lower grades to remain in teaching.

The study offers a window into how college graduates perceive teaching. For instance, nearly half of all bachelorÂ’s degree recipients in 1992-93 said they had never considered teaching or taken any steps to become educators.

Lack of interest, having another job in hand, and inadequate pay were the most commonly cited reasons for not pursuing teaching.

Math, science, and engineering graduates were among those most likely to leave teaching jobs to work outside education.

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Re: the non universals

dcorking
Alan,

I am afraid I cannot yet share your pessimism (if that is indeed what
you intended to convey in your earlier posts)

On 8/16/07, Alan Kay wrote:

>  Any one fluent in mathematics can recognize this (but it took a Papert to
> first point it out). But, virtually no one without fluency in mathematics
> can recognize this. And surveys have shown that less than 5% of Americans
> are fluent in math or science. Many of the 95% were able to go through 16
> years of schooling and successfully get a college degree without attaining
> any fluency in math or science.

I am no historian, but I would like to guess that 5% is quite a large
number compared to previous centuries, and these fluent mathematicians
should be heavily overrepresented among secondary school math and
science teachers.  I concede that such a person will be rare among
primary school teachers (excepting those who frequent squeakland.org
of course)

I hope, perhaps optimistically, that most high schools and
universities across the world teach 19th century applied math (I don't
know - I only went to one or two of each - and one of those high
schools taught a kind of dusty tedious rote algebra, without ever even
hinting that applied math was a much wider, richer and more
interesting field.)

I was wrong to point to the purpose of universities - individual
university teachers are more important - and those who are interested
in teaching students, I would argue, aim to nurture creative and
powerful thought.  I really hope they did so for the math and science
teachers passing through their halls.

While for the next generation primary (K-6) teachers may be a lost
cause, what I want to understand is why you (Alan) don't find large
numbers of secondary (grades 7 - 12/13) math and science teachers
becoming advocates and allies of the reforms you are proposing.

So perhaps I will  attempt a better phrasing of my question:

1. Are the math and science teachers not aware that calculus is a
'powerful idea'?

2. If they are, are they not sufficiently fluent in it to understand
that their current teaching method (whatever that is) is not engaging
and developing nearly as many pupils as have the potential to get it,
enjoy it and use it?

3. Or is there some other reason, such as suspicion of new methods,
waiting for something better, or insufficient time after concentrating
on basic numeracy?

The reason for the question is my big worry, inspired by your original
post: if Papert's ideas don't engage secondary school math teachers,
they have few other advocates left.  There is no back door to get
around these gatekeepers.

David
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Re: the non universals

Blake-5
In reply to this post by Alan Kay
On Wed, 15 Aug 2007 16:59:48 -0700, Alan Kay <[hidden email]>  
wrote:

> In the early 80's I went to Atari as its Chief Scientist to try to
> get some of Papert's and my ideas into consumer electronics. The
> Atari 800 and especially the 400 were tremendous computers for their
> price, and Brian Silverman made a great version of Logo to go on
> these machines. (There were also Logos on most of the other 8-bit
> micros.) And, there was a Logo-vogue for a time, both in the US and
> in the UK. Many early adopter teachers got Atari's or Apple IIs in
> their classrooms and got their students started on it.

Wow, those Ataris were great! I had an Apple ][ (which was something like  
triple the price--some things never change, eh?) and the Atari was the  
only other machine that truly piqued my interest.

I had some poor math teachers in my day but on teaching my own kids, I've  
discovered how much I've backfilled over the years from computer  
programming. Concepts my teachers were unable to explain became intuitive  
when they translated into action.

At least one of my children is blessed with the ability to do "instant"  
math. Whereas most people think in symbols, like "2 + 2 = 4", instant math  
types think "\\ + \\ = \\\\". Most adults max out at about 8 or 9, I  
think, whereas babies (we are all born with the ability apparently) and  
those who retain the ability can see into the hundreds or a thousand or  
more.

Instant-mathers get into trouble in school because they don't show their  
work--because there is no work to show, and most teachers can't comprehend  
that.

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Re: the non universals

Alan Kay
In reply to this post by Bill Kerr
Hi David --

I'm not pessimistic. If I were, then I would pursue other ventures.
I'm just thinking like a scientist (which is trying to figure out a
near version of how things actually are). If you look closer, I think
you will find that I'm being quite even-handed.

Bush and his administration (among many others) think scientists are
pessimists because they don't make up stories "that are so nice they
must be true" as most people do, but instead are skeptical (not the
same as pessimistic at all) and try to be "realistic" (as science
thinks of that term), and are certainly optimistic, since they think
they can uncover mysteries and make models of important things in the
universe that have baffled humans for hundreds of thousands of years.
There's a certain amount of arrogation (and some plain arrogance) in
science, but not a lot of pessimism.

>While for the next generation primary (K-6) teachers may be a lost
>cause, what I want to understand is why you (Alan) don't find large
>numbers of secondary (grades 7 - 12/13) math and science teachers
>becoming advocates and allies of the reforms you are proposing.

If mathematics shares some traits with language and muscular learning
(and there is evidence it does), then the big disaster is in K-6.

7-12 has many of its own problems, judging both from what I've read
and from participating in STEM workshops in many parts of the US this summer.

Most of the 7th and 8th grade teachers we worked with were retreads
from non math and non science teaching. The simplest generalization
is that almost none of them showed any heuristic sense and aim for
math of any kind. They knew a few facts but did not know how to think
about even what they could remember.

There is a wider range in high school teachers, and we found more
than a few percent (maybe 10% to 20%) who could follow the
relationships between familiar ways of looking at things and other
ways of looking at the same underlying ideas. This is better and lots
could be done with these teachers. This is not a high enough percent
to make big changes but it would be a good start if the system would
allow the goals and methods to be different.

Of course, this is far from a scientific survey ....

>1. Are the math and science teachers not aware that calculus is a
>'powerful idea'?

Not in the sense that Seymour uses the term. This is partly because
almost no math and science teachers in HS were ever practitioners,
and most were never math or science majors. Some may have majored in
"math education" etc., but there is a huge qualitative difference
there. Remember that most HS science is done without calculus
(because it is still an optional AP subject that is taken usually in
the last year of HS).

Also, there is the interesting survey result which I sent out earlier
this morning which indicates that 93% of the teachers in the system
like their jobs. This is quite incompatible with any real
understanding of math and science.


>2. If they are, are they not sufficiently fluent in it ...

I think they are indeen not sufficiently fluent in it, especially in
the "what it actually is" sense (as opposed to "this particular way").

>  to understand
>that their current teaching method (whatever that is) is not engaging
>and developing nearly as many pupils as have the potential to get it,
>enjoy it and use it?

This is strongly combined with the standards, SAT, and AP criteria to
make the teachers who do have some sense of other ways to feel
completely trapped in HS. But it's not just the teaching methods,
it's the actual form of the knowledge for learners of mathematics and science.


>3. Or is there some other reason, such as suspicion of new methods,
>waiting for something better, or insufficient time after concentrating
>on basic numeracy?

Sure, and etc. Pretty much everything in American High Schools has
high levels of trying to reteach virtually all of what the kids were
supposed to have learned in the earlier grades. Hence, the need to
look earlier for solutions. Couple this with the difficulty of
learning new outlooks once you have already committed to outlooks
that are not so fruitful, and the earlier grades are the place to work on.


>The reason for the question is my big worry, inspired by your original
>post: if Papert's ideas don't engage secondary school math teachers,
>they have few other advocates left.  There is no back door to get
>around these gatekeepers.

That is one of the big problems, amongst a dozen others. Cargo cults
are difficult to reform once they get going. But what if the
secondary math teachers complained loudly? I don't think they are in
any decision process that I can find.

Cheers,

Alan

------------



At 08:23 AM 8/16/2007, David Corking wrote:

>Alan,
>
>I am afraid I cannot yet share your pessimism (if that is indeed what
>you intended to convey in your earlier posts)
>
>On 8/16/07, Alan Kay wrote:
>
> >  Any one fluent in mathematics can recognize this (but it took a Papert to
> > first point it out). But, virtually no one without fluency in mathematics
> > can recognize this. And surveys have shown that less than 5% of Americans
> > are fluent in math or science. Many of the 95% were able to go through 16
> > years of schooling and successfully get a college degree without attaining
> > any fluency in math or science.
>
>I am no historian, but I would like to guess that 5% is quite a large
>number compared to previous centuries, and these fluent mathematicians
>should be heavily overrepresented among secondary school math and
>science teachers.  I concede that such a person will be rare among
>primary school teachers (excepting those who frequent squeakland.org
>of course)
>
>I hope, perhaps optimistically, that most high schools and
>universities across the world teach 19th century applied math (I don't
>know - I only went to one or two of each - and one of those high
>schools taught a kind of dusty tedious rote algebra, without ever even
>hinting that applied math was a much wider, richer and more
>interesting field.)
>
>I was wrong to point to the purpose of universities - individual
>university teachers are more important - and those who are interested
>in teaching students, I would argue, aim to nurture creative and
>powerful thought.  I really hope they did so for the math and science
>teachers passing through their halls.
>
>While for the next generation primary (K-6) teachers may be a lost
>cause, what I want to understand is why you (Alan) don't find large
>numbers of secondary (grades 7 - 12/13) math and science teachers
>becoming advocates and allies of the reforms you are proposing.
>
>So perhaps I will  attempt a better phrasing of my question:
>
>1. Are the math and science teachers not aware that calculus is a
>'powerful idea'?
>
>2. If they are, are they not sufficiently fluent in it to understand
>that their current teaching method (whatever that is) is not engaging
>and developing nearly as many pupils as have the potential to get it,
>enjoy it and use it?
>
>3. Or is there some other reason, such as suspicion of new methods,
>waiting for something better, or insufficient time after concentrating
>on basic numeracy?
>
>The reason for the question is my big worry, inspired by your original
>post: if Papert's ideas don't engage secondary school math teachers,
>they have few other advocates left.  There is no back door to get
>around these gatekeepers.
>
>David

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Re: the non universals

dcorking
Thanks for wrestling with my questioning, Alan  (btw - it seems we
forgot to share our last two exchanges with the mailing list - my
fault - I refrained from repeating your responses extensively here in
case it not your intent to post them.)

On 8/16/07, Alan Kay wrote:
> Of course, this is far from a scientific survey ....

You clearly know far more teachers than I do.  I am shocked to hear
that so few US math and science teachers were math and science majors,
or were even educated in any college level math and science.

I suspect it is normal worldwide to postpone calculus until the
equivalent of  "Advanced Placement" courses in years 11 and 12 - I
hope it is mandatory to know calculus before going to college for
math, science or engineering (and perhaps for social science too.)
Perhaps by the delay we then rob many kids the chance to (1) see its
beauty and (2) see that it underpins so much of modern science and
engineering.

As you point out, the algebraic model of calculus is not interesting
to many people, but the difference model would, I imagine, be useful
to every aspiring mechanic, lab technician or customer service
supervisor.

> 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?

David
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Re: the non universals

Alan Kay
Hi David --

At 02:58 PM 8/16/2007, David Corking wrote:
Thanks for wrestling with my questioning, Alan  (btw - it seems we
forgot to share our last two exchanges with the mailing list - my
fault - I refrained from repeating your responses extensively here in
case it not your intent to post them.)

I didn't notice this, so just reposted the previous reply to the list.


On 8/16/07, Alan Kay wrote:
> Of course, this is far from a scientific survey ....

You clearly know far more teachers than I do.  I am shocked to hear
that so few US math and science teachers were math and science majors,
or were even educated in any college level math and science.

As I said, my little survey this summer wasn't scientific ... it would be nice to have a much better assessment of this done in a more rigorous fashion.

But I don't think it is an exaggeration to guess that most teachers lack the kind of operational mathematical thinking that is the most important part of mathematical fluency. And it is very likely that "most" is almost total in the elementary grades and means "very sparse" in high school.


I suspect it is normal worldwide to postpone calculus until the
equivalent of  "Advanced Placement" courses in years 11 and 12 - I
hope it is mandatory to know calculus before going to college for
math, science or engineering (and perhaps for social science too.)
Perhaps by the delay we then rob many kids the chance to (1) see its
beauty and (2) see that it underpins so much of modern science and
engineering.

"Knowing calculus" is a tricky phrase. An important idea here (that I originally got from Ivan Sutherland) is to ask whether skills are "10 hour skills", "100 hour skills", "1000 hour skills", etc. Ivan once pointed out that e.g. learning to play piano was not a "10 hour skill" no matter how much latent talent you might have. And, though talent does play a part in time to learn and get fluent at something, it takes time for people's brain/minds to build the structures needed for doing the thinking in question, and doing it fluently enough, etc.

As I recall, this discussion came up when a bunch of us grad students and Ivan at Utah were working out the mathematical transforms for 3D graphics (much of which constitutes OpenGL today). We had some terrific French grad students, who were better prepared mathematically than most of the Americans. I had an undergrad math degree, etc. Ivan is quite a bit smarter than most people, etc. Yet, this was a real struggle for all of us to "get operational" in a theory that we all "kind of knew" really well: the transformations of vectors using matrices, with the addition of the homogenous coordinates idea from projective geometry that Larry Roberts had suggested.

Ivan's observation was that we had attained the "100 hour skill" version of transformations, but not the "1000 hour skill" version. And this led to discussions of other skills in other areas. This idea is particularly striking and easy to understand in sports and music. And also overlaps with some of the findings in cognitive psychology about habit formation and habit unlearning. For example, if you put in 10 hours a week trying to learn something (2 hours a day, 5 days a week) and take a two week vacation, etc., then you will be spending about 500 hours a year doing your learning and practicing. Two years of this is 1000 hours.

Lots of good things can be learned to the solid mid-intermediate level in two years. And 18 months to 2 years is also the time that cog psych says it takes to form a solid habit (or unlearn one). Also very interesting are the results from many studies of the attempts at educational reforms in the 60s which showed that one year of a super enriched experience didn't stick, but two or more years did.

So the concept of a "1000 hour skill" is worth contemplating when looking at instructional systems.

Back to calculus for a second: I really didn't understand calculus in worthwhile ways (that is, to think in terms of what it meant rather than just trying to apply the techniques) until I took Advanced Calculus with a very good prof (who was a fabulous mathematical thinker and teacher). This was quite shocking to me (because I didn't really have a sense that I didn't understand calculus until I understood it so much better). And all of us working with Ivan a few years later had a similar sense about transformations. We only thought we understood them until we understood them deeply enough to think in terms of them, not just try to use them.

I think there are also real analogies here to stages of learning a foreign language. Seymour and I have talked a lot about this, and he thinks so also. The differences between being able to use another language a little and being able to think in "its perfume" are profound.

This is where more longitudinal approaches and immersion are critical. One of the reasons I loved Seymour's ideas and approach was that it would be possible to have children immersed in "CalculusLand" in ways meaningful to them for years so they could gradually build up real "CalculusThink".


As you point out, the algebraic model of calculus is not interesting
to many people, but the difference model would, I imagine, be useful
to every aspiring mechanic, lab technician or customer service
supervisor.

Its not that the algebraic model of calculus is not interesting (it really is) but it is much further removed from most people's fluencies. The difference model is just simple accumulation by addition, and the equivalent of higher order differential equations is just more accumulations by addition lined up. I have written about how Julia Nishijima (the first grade teacher who had a real mathematical sense) could set up projects that would induce the children to discover and derive second order discrete DEs (first order is steady growth, second order is quadratic, etc.), These are the very  same progressions that can be used for velocity and acceleration, F = ma, Galilean gravity, etc. so it is terrific to get started with these as tools one has derived in first grade.

We have a nice way to (later, perhaps in 7th or 8th grade) reconcile the easier incremental approach to the algebraic formulas by deriving the latter from the former. This is not just pro forma but is a very useful way to start thinking about what it is that is being said (and how universally) using quantification. It's also very illuminating to start thinking about integration and what it means in the universally quantified world (leading to the fundamental theorem of calculus).

But having quite a few years of calculus thinking and doing under one's belt is a much better way (in my opinion) to approach some of the deep and initially non-intuitive properties of calculus.


> 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?

It's very tricky in the US -- in part because there are 25,000 or more individual school districts. There are state and national standards. Professionals are consulted. Etc. I only have speculations on how the system has not managed to do better with mathematics curricula.

One thing that seems to be almost universal around the world, is that the notion of children learning some subject (like mathematics) is almost always posed as "how can children be taught the adult version of this subject?", rather than, as Montessori, Piaget, Bruner and Papert have shown "how can we find an honest children's version of this subject?".

Another important idea here is that there are likely to be other approaches that are also better than the standard ones. Seymour (and I and others in his footsteps) simply have worked out one set of insights that can allow children to actually be real mathematicians starting at an early age. This is not a religion, nor is it exclusive to "the Seymour way".

Over the last 30+ years of my own experience I have been greatly surprised at some of the things children have shown they can do (the 4 year olds at Reggio Emilia, the 6 year olds of Julia Nishijima, that 5th graders could do the Galilean gravity project I designed for 9th graders, etc.). Basically, we still don't really know what children can learn at different ages if the subject matter is properly formed. The experiments are very difficult to do, and lots of them need to be done (in part because there are so many things that can prevent a good reading of the children).

Cheers,

Alan




David
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Re: the non universals

K. K. Subramaniam
In reply to this post by Kim Rose-2
On Thursday 16 August 2007 4:55 am, Kim Rose wrote:
> I think it's a common finding (at least in the U.S.) that schools are
> trying to prepare students "for the workplace" and thus today's
> education is largely vocational.  Therefore, the belief holds that
> teaching word processing will ultimately be more valuable to students
> than calculus.  My experience is that parents' attitudes perpetuate
> this phenomenon.  Another reason may be that more teachers understand
> word processing and are more comfortable *teaching*  "MS Office" than
> calculus.
The issue is not very different in Bangalore and its suburbs. Here, a parent
faces a difficult choice between vocational education and valuable education.

A school is a rather broad unit. A lot depends on how a teacher handles a
class. The teachers I have met so far fall into two broad kinds - factory
teachers and thinking teachers. The factory teachers adopt mass production
methods and processes - standard curriculum, drills, exams, grades,
certificates. The learning levels of students matters only to the extent it
crosses a predefined minimum level that qualifies him/her for a job. Thinking
teachers setup a learning environment and guide children into a learning
mode. The process of learning is more important than the outcomes achieved.
The environment is more or less homely.

Unfortunately, the latter type cannot scale into handling large number of
students. Schools that face a huge student demand (40+ per teacher!)  hire
the former types and run like a factory :-(. In fine arts like dance and
music where the demand is much less (<20 per teacher), I see more of the
latter. They run a gurukul-type school to impart holistic education. Such
schools are far too few to make any significant impact. They handle less than
1% of the demand for general education :-(.

Is there an education model that works holistically but also scales well into
millions of students?

Regards .. Subbu
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Re: the non universals

Brad Fuller-2
In reply to this post by Alan Kay
On Thu August 16 2007 6:34 am, Alan Kay wrote:
> To me this is an example of how a field can and does select the
> personalities and skills that fit to its actual mission.

Of course, the statement can be applied to the business world as well.

Contrary to the focus of most hiring managers, I was lucky enough to learn
from a manager who would always hire people (be them engineers or musicians)
that were superior at their craft but not necessarily fit the goals of his
group nor socially fit with others in the group (oh, the stories I could tell
you!) He hired people because they were very good at what they did, no matter
what it was. He possessed the skills to cultivate the individual skills into
new group directions which resulted in innovative products that the whole
team stood behind. Eventually they celebrated their individual differences
and their group differneces by making T-Shirts which read:
    Maloney's  
     Misfits

(not his real name)

In politics too. I've read that A. Lincoln built his cabinet on political
rivals. In fact, they thought he was some dumb backwoods bumpkin who would
lead the union to ruin. Convincing them to join his cabinet and focusing each
on the real job at hand is testamant to his superior managerial skills.

brad
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Re: the non universals

Alan Kay
Bob Taylor (the ARPA funder who later set up Xerox PARC computing
research) was an absolute master at this.

Cheers,

Alan

-----------

At 10:10 AM 8/17/2007, Brad Fuller wrote:

>On Thu August 16 2007 6:34 am, Alan Kay wrote:
> > To me this is an example of how a field can and does select the
> > personalities and skills that fit to its actual mission.
>
>Of course, the statement can be applied to the business world as well.
>
>Contrary to the focus of most hiring managers, I was lucky enough to learn
>from a manager who would always hire people (be them engineers or musicians)
>that were superior at their craft but not necessarily fit the goals of his
>group nor socially fit with others in the group (oh, the stories I could tell
>you!) He hired people because they were very good at what they did, no matter
>what it was. He possessed the skills to cultivate the individual skills into
>new group directions which resulted in innovative products that the whole
>team stood behind. Eventually they celebrated their individual differences
>and their group differneces by making T-Shirts which read:
>     Maloney's
>      Misfits
>
>(not his real name)
>
>In politics too. I've read that A. Lincoln built his cabinet on political
>rivals. In fact, they thought he was some dumb backwoods bumpkin who would
>lead the union to ruin. Convincing them to join his cabinet and focusing each
>on the real job at hand is testamant to his superior managerial skills.
>
>brad

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Re: the non universals

Bill Kerr
In reply to this post by dcorking
On 8/17/07, David Corking <[hidden email]> 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/ 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
"Wellington Grey, a physics teachers in the UK, has written 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/


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