[Squeakland] the non universals

[Alan Kay]

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