[Squeakland] the non universals

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 >_______________________________________________ >Squeakland mailing list >Squeakland at squeakland.org >http://squeakland.org/mailman/listinfo/squeakland -------------- next part -------------- An HTML attachment was scrubbed... URL: http://squeakland.org/pipermail/squeakland/attachments/20070815/c9bb1021/attachment-0001.htm