squeakland August 2007

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27 participants
31 discussions

Re: [Squeakland] the non universals
by mmille10＠comcast.net 23 Aug '07

23 Aug '07

Bill Kerr wrote a blog post about this discussion. I posted some comments about it there, and he asked me to share my thoughts here, to help broaden the discussion. For what it's worth, I'll put forth a version of what I said on his blog. I hope you will find it relevant. I don't mean to "pollute" the discussion. This discussion is interesting to me, particularly as it pertains to "school culture". I can speak to direct experience from the POV of someone who was a student in U.S. public schools in the 1980s, and got a BSCS degree in the 1990s. We had Logo instruction as part of a programming class when I was in junior high school (now called middle school). One of the shapes we were taught to draw was a circle. We were not taught the math involved. We were just given the algorithm. Looking back on it I think our teacher just used Logo to teach us about procedural programming, and perhaps some geometry concepts. We built what I'd call "procedures" (I don't remember what they were called in Logo) and then called them from our code to repeat patterns. We were then asked to create our own drawings in Logo. That was pretty much it. I didn't learn until I got to college, and only by listening to a casual conversation between a student and a computer science professor who taught graphics, that this method for drawing a circle in Logo was implementing a form of Calculus. I remember listening to that conversation and feeling kind of "dumb" and perhaps a bit cheated. I wondered how this student came to know this. Even though the full power of Logo was not taught to us, I think programming classes then were more interesting and fun than what I hear is being taught now. I talked with another blogger about this recently (in the U.S.). He said his son was taking a computer course where all they're teaching is how to use Office, and how to write "practical" programs in Java. Re: why are computer teachers just teaching word processing/Office? Around my 6th grade year, around 1982, "computer literacy" was starting to become the "thing to do" to "prepare for the future". Back then computer literacy was defined as computer programming. So even though computers hadn't made a widespread appearance in schools every effort was made to encourage kids to learn to program them. When I got to junior high we had only 3 computers in the school. We had a math teacher who held a small computer club after school, showing us how to work with it, and letting us try our hand at it. The teaching style was to show parts of programming in a language, show an example using those parts, and then let us experiment, or try to solve a programming problem: "Write a program that does X". It was typically math-oriented. We were more free to try to bring forth what was in our imagination. Eventually the school got a whole lab so more kids could get exposed to them. By my 9th grade year the emphasis had started to change. I remember reading about it. The powers that be in the education systems had changed their minds about "computer literacy". Now instead of teaching kids to program, more emphasis would be put on teaching kids to use what you would now call an "office suite": word processing, working with spreadsheets, and databases. The focus was largely vocational the whole time, even when they taught programming. In the early years of this things had not yet come into focus about where this "computer thing" was going to go. Computers in those days were largely custom programmed to do certain things. So I'm sure people looked at that and felt it was necessary to teach kids for that purpose. Once the software market started to mature, people said, "Okay. So they don't need to learn to program to be literate." I took one of the first courses my junior high school offered for these office computing skills. I figured I should learn them. I don't regret it, but I do regret that over the years there has been a watering down of that passion for getting kids literate in programming. Maybe that's changed of late, but whatever is being done now it doesn't sound as interesting. Re: how Calculus is taught I don't know if things have changed, but I wasn't taught Calculus until I entered college in 1988, and there weren't that many proofs. High schools did have AP Calculus courses then. You could get college credit for passing the AP test. As Alan Kay said earlier, it was largely memorization of formulas, pattern matching, and doing symbol manipulation according to rules. Not that these are useless skills. I use them in programming, but I had a different conception of what we would be learning when I came into it. At the time I didn't see much of the point in it. I had a tendency to not learn well when memorization was all that was required. I did much better if I understood the concept. Most of the math we learned was about the concepts of infinity and limits. The most exciting math class I had was geometry in high school, and it was probably because we literally built knowledge as we went through the course. We were doing proofs all the time, starting with simple concepts, at the beginning, building to complex concepts at the end. The most exciting part of Calculus for me was learning about Taylor and MacLaurin Series. I had been curious for a long time how calculators were able to compute logarithms and roots. I got part of my answer in pre-Calc, when we studied how to compute power functions using logs and anti-logs. I remember asking my pre-Calc teacher in high school about how calculators computed logs and anti-logs. He assumed that there were tables built into the memory of the calculators, which it used to give the result, but I pressed further. I said that you could put in any number, even a fraction, and still get an accurate result. Further, you could use the opposite function to get the original number back. How would you use tables to do that? I had stumped him. He had no idea. Perhaps my "computer literacy", if you will, had provided me with an insight he didn't have. Though we didn't explore this in Calculus, I felt as though I had found my answer. Re: Teachers vying for equal time for their subjects I've seen this dynamic show up in other contexts (outside of schools). This is just an intuitive reaction to this topic, but it seems to me it's a case of "too many cooks in the kitchen". Each has their own ego to please. Over the decades there's been a tearing down of authority. Now it's expected it will be distributed rather than narrowly focused, at least in more "liberal" environments (forgive my use of a political term). It seems like these are exercises in egalitarianism, where that's the primary value, rather than merit of the subject matter, because after all, who's to say one subject is more important than the other? By what authority do you claim one subject is worth less than another? In an environment where the "gods" have been torn down, seen as flawed and not worth listening to because their motives are suspect, everybody is a "god". Perhaps the indirect consumers of the knowledge schools are supposed to be imparting to students, industry, can speak up and provide some motivation to prioritize the skills that students should learn. I don't consider this the ideal, because when this happened in the past, schools created students who fit well into assembly lines. Maybe they still do. It's hard for me to judge that. Personally I like Alan Kay's approach of "teaching to maintain civilization". I think that unfortunately there are quite a few in educational establishments who don't see Western civilization as something that's worth maintaining. They take it for granted. What I would ask is, "What's the alternative you'd prefer?" Give me a Dr. Wafa Sultan anytime over these folks. One of the things I lament about the U.S. public school system is it's becoming increasingly politicized in the sense that teachers are literally bringing political topics into classrooms where they don't fit well. For example, a year ago I heard about a case of a geography teacher in the course of giving a lecture questioning the validity of capitalism (of which he had no expertise), and suggested that a certain president could be compared to a certain dictator (maybe he had expertise here, but how does this fit into geography?). And this was in a high income area where relative educational excellence is typically expected. In any case this sort of approach sounds anti-intellectual to me. Maybe I don't understand. There is such a thing as post-modernist philosophy, though I don't have much respect for it. Whenever somebody complains about this sort of thing in the classrooms, the retort that always comes back is "We're teaching students critical thinking." To which I say, "Is that what you call critical thinking? Bringing the 'village idiot' into a class and letting them blab on about their POV on the world whether they have expertise or not?" IMO the kids deserve better than this. Not to say these expressed opinions are invalid, but I think there's a time and place for them in the context of school, and if someone's going to make the argument, they should have the educational background and context to justify making them in front of students. In other words, they should know what they're talking about. I don't recall experiencing this sort of thing when I was in public schools. Teachers tended to stick to their subjects. What I suspect might be going on is the result of people bringing in a concept I used to hear about from time to time: teaching for "emotional intelligence", or so-called "EQ". I don't see how schools as they are currently structured being able to do this very well. Unfortunately I think it's been brought in under a political context as well. Some time ago I watched an interview with George Lucas on the Charlie Rose show, and he said he believed that schools should inculcate emotional intelligence, saying it was at least as important as technical intelligence. He said that in terms of hiring people, he found that emotional intelligence was more important than technical. He said that he didn't need people for the long term in his own business who were just technically intelligent, but rather people who could inspire, motivate, and lead. I imagine his ideal would be people who had both in equal measure, but he indicated he prefered leadership qualities, which he put in the "EQ" category. I suppose it's a matter of his perspective, working in large part with artists. A different industry titan might have a very different perspective. Re: "93% of teachers like their jobs" This reminded me of a quote I used in a blog post I just put up myself. This is from Stephen Friedman, Chairman of Stone Point Capital at a panel discussion held by the Aspen Institute in July: "I think the real question is why are the average parents in America willing to live with a school--You know, when they do the studies they find that people tend to be satisfied with their own school system. They're underdemanding consumers. Why are they satisfied with a system that has their kids' comparative standings on the standardized tests so poor against the rest of the world? I don't understand it. I don't understand. There's a market failure." I am going away on a trip soon so I probably won't be able to respond immediately to follow-ups to this. Just wanted to get this off while this discussion was still fresh in people's minds. --Mark Miller mmille10(a)comcast.net http://tekkie.wordpress.com

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Technical problems / nothing showing
by Louis Fleming 23 Aug '07

23 Aug '07

Windows XP Pro Pentium 3.4 GHZ Administrator Mode Radeon X300 Video 1.5 GB Ram IE6 Installed plugin repeatedly surfed to check site - never saw any animation went to some of the games on the site and clicked - after long delay - all that happened was it tried to reinstall the squeak plug in. Trying to get this running for a brand new computer lab to be able to use with guided study students. Is there some XP / IE security setting I am overlooking? Tried everything possible to get this working for last 2 hours. Thanks for any and all help Louis Fleming Andrews High School Andrews, Texas

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purpose, culture, ambit of squeakland list
by Bill Kerr 22 Aug '07

22 Aug '07

Other programs have developed or are in the process of developing large, very communities of young people Scratch forum: http://scratch.mit.edu/forums/ Currently 8 guests on line, no registered users gallery: http://scratch.mit.edu/galleries/?page=150 150 pages of projects, 10 projects per page GameMaker http://gmc.yoyogames.com/ 230 users active in the past 15 minutes http://www.yoyogames.com/make/browse?page=1&beta=1 40 pages of beta games, 20 projects per page 52 pages of games in progress, 20 projects per page I don't see anything equivalent to this activity for etoys / squeak I'd like to see this change. Is this something we ought to talk about? -- Bill Kerr http://billkerr2.blogspot.com/

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Re: [Squeakland] the non universals (Robert Parks)
by John Maxwell 20 Aug '07

20 Aug '07

Robert wrote: > 2. What IS a "powerful idea", and how does it become powerful? > I'm particularly interested in asking whether ideas get their power > from abstraction (finding similarity in structure), or generalization > (finding similarity in features) - or from both. Extrapolating just a little bit from contemporary science studies (people like Bruno Latour, John Law, etc.), I think it's possible to define "powerful" as "well-connected," in the sense that those ideas which are capable of doing the most work, of carrying you farthest, are the ones that are strongly connected to others -- the process part of experimental science is all about establishing connections. Conversely, powerful ideas are the ones which allow you to *make* connections, to explain thing x in terms of thing y, or draw analogies, or generalize; good theories do that. I think the "connectedness" notion is a little less unwieldy than "abstraction," which can be hard to pin down precisely. Things can be very well connected while remaining very concrete. - John Maxwell jmax(a)sfu.ca NEW PHONE #: 778-782-5287

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Re: [Squeakland] the non universals
by Bill Kerr 19 Aug '07

19 Aug '07

On 8/19/07, Robert Parks <bobp(a)lightlink.com> wrote: > > 1. would learning calculus as a "powerful idea" (rather than through > the duller algebraic approach) be counted as "using discovery or inquiry > based learning as a substitute for hard facts"? > No (based mainly on my reading of Seymour Papert) Papert's metaphor is that learning maths ought to be like a relationship, similar to getting to know a person or becoming a member of a community The idea is to restructure the learning environment to create a maths-land where playing with the right sort of objects (eg. logo, LEGO logo) can lead to the gradual acquisition of powerful ideas (eg. that a curve can be formed from a series of v small straight lines) in ways that are natural for children (eg. body syntonic - you can also make a circle by walking around one) There is "discovery" and "inquiry" involved in this but I'm pretty sure that Papert didn't describe his theories with those terms - instead he used the term constructionist, a combination of the words constructivism (Piaget hypothesised internal structures) and external construction (eg. with logo or LEGO). Papert claims that its tapping into natural ways of learning. It's more like joining a community where you learn to think in certain ways. There is more to being a mathematician or scientist than knowing facts and skills. Skills based learning being another approach which can be viewed differently from either "hard facts" or "discovery / inquiry" The critique of discovery / inquiry approaches would be that at least some of them are either unrealistic or mundane. Unrealistic - we can't expect children to discover unaided what has taken the best human minds thousands of years to discover Mundane - if we ask children to duplicate a scientific discovery like a recipe out of a cookbook then we can't expect a high sense of personal ownership of the process I'm not saying that all discovery / inquiry approaches are hopeless but they are different from what Papert was proposing. In Ch 6 of Mindstorms Papert constructs a pretend conversation b/w Galileo and Aristotle. Rather than refuting Aristotle by an experiment, instead Galileo takes Aristotle's logic as his starting point and pulls that apart. He asks ARI if we drop two one-pound weights simultaneously then how long will they take to reach the ground. ARI says 4 seconds each. Then GAL asks what if we connect the two weights with a gossamer thread, how long will they take to fall then? This dialogue illustrates the point that GAL and ARI think about objects differently, that GAL sees them as composed of parts whereas ARI thinks of them as undivided wholes. It's a different way of thinking, a world view - not just based on an experiment or an inquiry or a skill btw James Gee says that this approach (learning to become a member of a community of thinking in certain ways) can be simulated using computer games in his book, "What Video Games Have to Teach Us about Learning and Literacy" 2. What IS a "powerful idea", and how does it become powerful? I'm > particularly interested in asking whether ideas get their power from > abstraction (finding similarity in structure), or generalization (finding > similarity in features) - or from both. > Blake made a point about specificity in reply to your points of abstraction and / or generalization, which I agree with. One of the powerful ideas is the scientific method and I think that involves an ongoing theory / practice spiral, which could also be seen as shifting back and forward between abstraction and specificity In general, I think the powerful ideas on the non universal list are the ideas that arose with the Enlightenment / printing press / industrial revolution etc., the overthrow of the State power of the Church, the origins of modernity, science, rule of Law, democracy, the decline of feudalism, the rise of capitalism, what we call modern civilisation. -- Bill Kerr http://billkerr2.blogspot.com/ <http://www.users.on.net/%7Ebillkerr/>

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Re: [Squeakland] the non universals
by Alan Kay 19 Aug '07

19 Aug '07

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 >_______________________________________________ >Squeakland mailing list >Squeakland(a)squeakland.org >http://squeakland.org/mailman/listinfo/squeakland

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Resources of Interest
by Hilaire Fernandes 19 Aug '07

19 Aug '07

These resources about science and technology education from the UNESCO may be of some interest to Squeaker teachers http://www.unesco.org/education/educprog/ste/projects/2000/formative.htm Hilaire -- http://blog.ofset.org/hilaire Smalltalkers do: [:it | All with: Class, (And love: it)]

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Re: [Squeakland] the non universals
by Alan Kay 18 Aug '07

18 Aug '07

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: [Squeakland] the non universals
by Alan Kay 17 Aug '07

17 Aug '07

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 <http://www.edweek.org/ew/contributors/vaishali.honawar.html>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 <http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2007163>report, released this week by the National Center for Education Statistics, surveyed 9,000 graduates who received their bachelor'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. Teachers' 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 report's findings are based on the NCES' 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 candidate'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 bachelor'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: [Squeakland] the non universals
by Alan Kay 17 Aug '07

17 Aug '07

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>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>http://www.amazon.com/Human-Universals-Donald-E-Brown/dp/007008209X > >or ><http://tinyurl.com/28n7vv>http://tinyurl.com/28n7vv > >-- >Bill Kerr ><http://billkerr2.blogspot.com/>http://billkerr2.blogspot.com/ > >_______________________________________________ >Squeakland mailing list >Squeakland(a)squeakland.org >http://squeakland.org/mailman/listinfo/squeakland

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squeakland August 2007