[Squeakland] the non universals

[Alan Kay]

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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>Squeakland mailing list
>Squeakland at squeakland.org
>http://squeakland.org/mailman/listinfo/squeakland
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