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2007/8/18, Bill Kerr <[hidden email]>:
> Student designed computer simulations using software such as Etoys / Squeak > could play an important role here. Indeed, regarding designing dynamic model with computer by and/or for students, smalltalk design and its Morphic+EToys frameworks are a huge improvement compare to the statically linked and compartmented applications available in traditional Desktop environments. With these applications it is nearly impossible (or to complicated to be done) to take some data from one application to feed "dynamically" another application. But this is needed to build dynamically dynamic model. In the other hand, within Squeak this is implemented in a way it is doable by kids and it seems to be rooted to the design of Smalltalk. Indeed with EToys it is fearly easy (kids level) to take some data from one Morphic application to feed another Morphic application. To be accurate those Morphic application could be nammed artifacts. And in case you need some more artifacts, it is fairly easy to write some more. However, where are the teachers to design more Morphic artifacts? Smalltalk is pretty accessible to math, sciences and techno teachers.. Hilaire _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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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 _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Bill Kerr
I've been listening with interest, and I've got a couple of
questions and (possible) provocations.
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"?
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.
Bob
On 8/17/07, David Corking <[hidden email]> wrote:
- using discovery or inquiry based learning as a substitute for hard facts --
-- * The best dictionary
and integrated thesaurus on the web:
http://www.wordsmyth.net
* Robert Parks -
Wordsmyth - (607) 272-2190
* "To imagine a
language is to imagine a form of life." (LW)
* "Philosophers have
only interpreted the world. The point, however, is to change it."
(KM)
* In communicating -
speaking and writing - we create community. Through this participation
we can hone our words till their meaning potential taps into the rich
voice of our full human potential.
_______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Alan Kay
On Fri, 17 Aug 2007 06:16:25 -0700, Alan Kay <[hidden email]>
wrote: > 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). Alan, I think you would find interest in a visit to the Institutes for the Achievement of Human Potential in Philadelphia (www.iahp.org), if you're not familiar with it already. (I was reminded of it when you mentioned McLuhan, whom I know made some contributions there in the '70s.) They've been wrestling with these questions for 60 years now and they have some interesting and effective answers. ===Blake=== _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Bill Kerr
On Fri, 17 Aug 2007 17:25:34 -0700, Bill Kerr <[hidden email]> wrote:
> 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 For more school board wackiness (along with a lot of other related material on science and perception) "Surely You're Joking, Mr Feynman" cannot be recommended too highly. > 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<http://www.wellingtongrey.net/articles/archive/2007-06-07--open-letter-aqa.html>about > the conversion of physics in his country from a science of precise > measurement and calculation into "... something else, something nebulous > and ill defined" It is characteristic of all government organizations except (apparently) the military to avoid actually producing anything. It is also in their nature to obscure the fact that they aren't producing anything. Obviously, teaching anything that can be measured in hard terms goes against the grain. I think also that's the reason the IQ tests were eliminated, and there's a constant shuffling of competency tests. _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Robert Parks
On Sat, 18 Aug 2007 14:44:22 -0700, Robert Parks <[hidden email]>
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. Or what about specificity? In order for the wheel to be invented, someone had to have the idea that it could be used to transport. Or perhaps the idea was the general notion that something other than pure sinew could be used to move things around, and the wheel (among other things) was a specific instance of that. I suspect the specific came first, then the generalization, then the abstraction--which in turn lead to more specifics. (At least in the case of the wheel.) _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Blake-5
Hi --
Yes, I used to visit the IAHP quite a bit 15-20 years ago. They have some excellent insights, and are certainly optimists about what babies and young children can learn to do. Cheers, Alan 05:02 PM 8/18/2007, Blake wrote: >On Fri, 17 Aug 2007 06:16:25 -0700, Alan Kay <[hidden email]> >wrote: > > > 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). > >Alan, > > I think you would find interest in a visit to the > Institutes for the >Achievement of Human Potential in Philadelphia (www.iahp.org), if you're >not familiar with it already. (I was reminded of it when you mentioned >McLuhan, whom I know made some contributions there in the '70s.) They've >been wrestling with these questions for 60 years now and they have some >interesting and effective answers. > > ===Blake=== > >_______________________________________________ >Squeakland mailing list >[hidden email] >http://squeakland.org/mailman/listinfo/squeakland _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Robert Parks
Hi Bob --
At 02:44 PM 8/18/2007, Robert Parks wrote: I've been listening with interest, and I've got a couple of questions and (possible) provocations. I don't see why it should, but there are few bounds on rhetoric and innuendo. I like Bruner's term "scaffolded learning" because real discoveries are rare -- we've learned how to teach 10 year olds a good and mathematical version of calculus but no child has ever discovered calculus without guidance (and it took 200,000 years for two smart adults to do it with hints). Much of the "discovery and inquiry learning" curricula I've seen is pretty soft. But learning and teaching would be easy if it could be transmitted by words or actions. Instead, some changes have to happen in the learner's mind/brain through some actions on their part (which could involve doing something or just sitting in a chair pondering). Things are sometimes not obvious because they are literally invisible, or because the explanations fall outside of existing commonsense thinking patterns. Or some new set of coordinations have to be learned/built that were not there before. These have many of the trappings of creativity and the having of ideas that are not simple increments from the ideas of the surrounding context. The phrase I use for this is "Learning a powerful idea requires a lot of the same kinds of creativity as it took to invent it in the first place". This is because it has to be invented anew by the learner. The good news is that learners for already invented ideas almost never have to be as smart and unusual as the original inventors (calculus can be learned by pretty much everybody, but Newton and Leibniz were unusual). On the other side, some real work has to be done to "cross the barriers". Tim Gallwey (the incredible tennis teacher) use to say: you have to hit thousands of balls to learn to play tennis -- my method gets you to hit those thousands of balls, but feeling and thinking differently. A good method in mathematics (like Mary Laycock's or Seymours) still requires you to do lots of things (to get your mind/brain fluent) but can be and feel mathematical for most of the journey rather than painful in many ways. This is what we've called "Hard fun", and it is a process that is shared by any set of arts/sports/skills that have been developed. Another way to look at it is "If you don't read for fun, you will never get fluent enough to read for purpose". The big problem with the "standard algebraic route" is not so much algebra, but that the standard route requires lots of work but doesn't deliver "real math" very well. It's not situated in mathematical thinking, but much more in rule learning and following. People have turned Logo (and other computing) into rule learning and following, etc. It can be done to any initially terrific subject. 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. Seymour and I have tried to characterize "powerful ideas" operationally rather than by structure. Even though there are not a lot of powerful ideas (hundreds or so) there are enough of different types to make simple structural definitions difficult. For example, "modern science" itself is a powerful idea: it is one of the greatest sets of processes ever devised for getting around many of the defects of the human mind/brain/genetic/culture system that has been so confusing and dangerous over our species time on the planet. On the other hand, "increase-by" as we use it in Etoys is the essential building block of the calculus (especially for children) and it is a "powerful idea" because it can be used in so many different kinds of "change situation" and it illuminates the change processes and makes them easier to think about and to calculate. These two "powerful ideas" are on different scales and in different domains. But operationally they have the power to greatly amplify and channel our thinking processes. A phrase I've used in the past is "Point of view equals 80 IQ points". Choosing and using a context can be like adding an extra brain. This is why today's scientists and engineers -- who are not better endowed by nature to work in their fields -- are so much more effective than some of the great geniuses in the past. Some of the most important "powerful ideas" can be drawn from Anthropology, Bio-behavior, Neuroethology, etc., (how History can be interpreted in the light of these, etc.) and have to do with insights about ourselves that are critical and have remained hidden for 10s of centuries. Our research project is ultimately about getting children to start learning these, but we decided that we needed to learn how to teach math and physical science (and what kinds of each of these) to children first. Jerome Bruner saw this earlier than anyone and pioneered one of the greatest curriculum designs for elementary school children in "Man A Course Of Study" (MACOS), an intellectually honest presentation of Anthropology to 5th graders. This was implemented in more than 10,000 schools in the US in the late 60s, was a masterpiece, and ultimately was destroyed by religious fundamentalists in Congress. But it and other deep insight powerful ideas curricula need to be done again, better, and with more support. Cheers, Alan Bob _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Bill Kerr
On 8/19/07, Robert Parks <[hidden email]> wrote:
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"
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 <a href="http://billkerr2.blogspot.com/" target="_blank" onclick="return top.js.OpenExtLink(window,event,this)">http://billkerr2.blogspot.com/ <a href="http://www.users.on.net/%7Ebillkerr/" target="_blank" onclick="return top.js.OpenExtLink(window,event,this)"> _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Bill Kerr
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 abo! ut 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 [hidden email] http://tekkie.wordpress.com _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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Mark Miller wrote:
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"I think that's an accurate description of what has been happening in formal education in Australia and probably the "west". In the name of egalitarianism in government schools in Australia the curriculum is being watered down. One effect of this has been a migration of some of the best students from government schools to private schools. So something done in the name of equal outcomes ends up having the opposite impact. The thing I like about Alan's non universals list is that it is a valid attempt to suggest that some knowledge might be more important than other knowledge. This is based on scientific anthropological evidence. The egalitarian assumption (and it is an assumption more than an argument) that all curriculum areas ought to be equal is hard to change - it has become institutionalised. But it's valuable to have a counter argument that is more than just an assertion or a bald belief. Other parts of your post indicate that there is an endless stream of proposals which superficially might sound like "good ideas" (computer literacy, vocational training, emotional intelligence) but which in all likelihood just tap into the more mainstream universals thinking. Once again, for me, the non universals list provide a coherent rallying point to resist this sort of thing. 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 .... I disagree with you on the 3 paragraphs beginning with the above. Say, take intelligent design. My feeling is that rather than banning it, it would be better to debate it. This sharpens up peoples understanding of the issues. The real problem here I think is lack of democracy in schools. ie. a teacher may express a poltical view and students feel they don't have the right to contradict it. I feel that we need to learn to debate and argue better and this takes practice! btw I reckon your blog, http://tekkie.wordpress.com, is great, especially some of the historical information you have written up about squeak Bill Kerr http://billkerr2.blogspot.com/ On 8/21/07, [hidden email] <[hidden email]> wrote: 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. _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Alan Kay
though I'd pass this along for another viewpoint. Mark Guzdial's latest
perspective on powerful ideas, abstractions and design patterns: http://www.amazon.com/gp/blog/post/PLNK13L1MC1Q3613J _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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Of course, Mark didn't look carefully enough at either the Squeakers
DVD or the Kim Rose and BJ Conn book "Powerful Ideas in the Classroom" and other materials which show what we actually do with the kids (actually in 5th grade for this example). We don't teach any abstractions, but work our way out from various kinds of animated movement in Etoys (constant velocity, random velocities, steadily increasing velocity, etc.). From a number of such examples the children gradually associate both a relationship "increase by" and a history of the movements (shown by leaving dots behind on the screen). Later (about 3 and one half months later, in the case of the first time we tried this) we got them to think about and investigate falling bodies. One example on the Squeakers DVD showed 11 year old Tyrone explaining just how he worked out and derived the actual differential equations of motion (in intellectually honest and mathematical version that computers make very practical). He did this by recognizing accelerated motion in the pattern of pictures of the dropping ball, measured the differences to find out what kind of acceleration (constant) and made the script for vertical motion partly using the memory of how he had done the horizontal motion in Etoys 3 months before. He explained how he did this very well on the video. Also, by luck, I happened to be in the classroom on the day he actually made his discoveries and derivations. Most the children were able to do this. The important things about this experience was that Tyrone and the other children had learned a model of acceleration and velocity that was quite meaningful to them. Months later they were able to remember these ideas and adapt them to observations of the real-world. According to Lillian McDermott at the U of Wash, 70% of all college students (including science majors) are unable to understand the Galilean model of gravity (which uses a very different pedagogy in college). The most important piece of knowledge from cog psych is a study done in the late 60s or early 70s that showed exposure to any enriched environment for less than 2 years was not retained. But two or more years of exposure tended to be retained. This also correlates to habit formation and habit unlearning. So, I would argue that Mark's three examples are very different and don't really deserve to go together. And, in any case, all we know about the 5th graders is that using this pedagogy and Etoys they are generally able to be more successful in both the math and the science of accelerated change than most college students. This particular way of looking at differential equations has become more and more standard as computers have become more and more the workhorses of science (partly because they are in a form well set up for creating a simulation -- and for the kids, because they are much easier to understand than the previous standards for DEs). Cheers, Alan At 03:23 PM 8/23/2007, Brad Fuller wrote: >though I'd pass this along for another viewpoint. Mark Guzdial's latest >perspective on powerful ideas, abstractions and design patterns: > >http://www.amazon.com/gp/blog/post/PLNK13L1MC1Q3613J >_______________________________________________ >Squeakland mailing list >[hidden email] >http://squeakland.org/mailman/listinfo/squeakland _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Brad Fuller-2
Mark Guzdial's blog is a great discussion point (in general I think Mark's blog is really good but he has slipped up here). Alan has left a comprehensive response there, which does refute part of what Mark is saying
"Doing with images to make symbols" (derived from Bruner) is a good slogan here I think, the gradual process of linking the kinesthenic to the visual to the abstract. Play, play, play in a suitable rich environment and later there maybe a significant AHA experience at the level of abstraction. So, we need great teachers who can construct these environments and gently nudge children down these pathways. Then we will build the great education system that we presently and most definitely do not have. Yes, it takes time, but is a very worthwhile path to go down. The same point is stressed on the etoys car tutorial from the squeakland list (I've left it in bold it needs to be shouted out, maybe). For children of this age, the textual form of these properties doesn't look as exciting as the iconic car that can be directly manipulated. A couple of other related points. A Harvard course is using Scratch as an introduction to Java! Scratch for budding computer scientists http://www.eecs.harvard.edu/%7Emalan/publications/fp079-malan.pdf "We propose Scratch as a first language for first-time programmers in introductory courses, for majors and non-majors alike. Scratch allows students to program with a mouse: programmatic constructs are represented as puzzle pieces that only fit together if "syntactically" appropriate. We argue that this environment allows students not only to master programmatic constructs be fore syntax but also to focus on problems of logic before syntax. We view Scratch as a gateway to languages like Java." The feedback section of this paper contains this gem: Comments from one negative respondent were bitter-sweet: I think this is relevant in showing the importance of "Doing with images to make symbols" for more adult learners as well as children With regard to the related issue of using blogs to establish meaningful writing, writing that actually alters semantic relationships. Konrad Glogowski's blog of proximal development provides evidence that children need to immerse themselves in writes for at least 18 months with a teacher who is sensitive to their needs for exploration before meaningful change happens. I'll dig up some direct evidence from Kondrad's blog (I had a quick look then but have lost it - it's buried somewhere in a comment on my blog) if anyone wants to follow up on this. This relates to a point Alan made in his comment on Mark's blog: The most important piece of knowledge from cog psych is a study done in the late 60s or early 70s that showed exposure to any enriched environment for less than 2 years was not retained. But two or more years of exposure tended to be retained. This also correlates to habit formation and habit unlearning. Konrad's blog relates more to Vygotsky but that can be connected back to Papert's constructionist learning theory, eg. when keeping a journal about logo learning for instance, as happened with Idit Harel's ISDP work. cheers, -- Bill Kerr http://billkerr2.blogspot.com/ On 8/24/07, Brad Fuller <[hidden email]> wrote: though I'd pass this along for another viewpoint. Mark Guzdial's latest _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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On Thu, 23 Aug 2007 19:04:18 -0700, Bill Kerr <[hidden email]> wrote:
> Mark Guzdial's blog is a great discussion point (in general I think > Mark's blog is really good but he has slipped up here). Alan has left a > comprehensive response there, which does refute part of what Mark is > saying His basic point is right, even if two of his examples are wrong. The problem I've had with design patterns is that they're not all that meaningful until you've had to build them, and once you've built them, they seem fairly obvious. I've found them more useful for communication than anything. In contrast to his point about Etoys, the problem I've had with them is that they're too concrete.<s> _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Bill Kerr
On Thu, 23 Aug 2007 22:33:37 -0700, <[hidden email]> wrote:
> No, they didn't use the term "office suite" back then. I was relating > the curriculum to what it would be called now. We did learn about how to > use a word processor, spreadsheet, and database application, though. > Yes, they were separate applications. May be I didn't make that clearin > what I wrote. I remember we used AppleWriter (I think), and VisiCalc,and > some database app. whose name I can't remember, all on Apple II's. Well, let me apologize if I sounded overly picky. There was a very short window (historically speaking) for when "office suite" might have meant anything other than "Microsoft Office". It's depressing to hear that (at least in your experience) the needle went from oddball geek hobby to mundane replacement for typewriter, ledger and filing system. To their current state: Monopoly perpetuators. I'm maybe 2 years older than you and my experience was at two different extremes: I went to a private school which was ahead of the curve as far as computers go (having a PDP-11 and several Apple ][s for all those who were interested, which was not many), and then to a public school which had never seen a computer--put still, net percentage, the difference between the two in terms of population that knew or cared about computers was probably about the same. But you know, it doesn't seem to matter much what subject it is, I've seen the same thing in all of them: if the student is interested, nothing will stop him; if not, nothing will help. Some of this is a matter of native interest: We are not all interested in the same things, and no matter how delightfully presented, the subject will remain at best a mild curiosity. Too much of it is a matter of interest destroyed: A student attacks a subject vigorously but is crushed in some manner or another, say with the sort of ritualistic kind of "teaching" Alan describes, where there is no understanding, and these days where the rituals have been replaced with a shadow of something that "builds self-esteem" while even denigrating understanding. And of course the usual brutal traditions of bad teachers. There are few techniques to rehabilitate blunted interest and fewer people who know how to apply them. _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Blake-5
And they are concrete in the way they are precisely because children
of this age don't generalize the way older children and adults do, but by "carrying a bushel basket of 'similar things that work similarly' ". They are not patterns from the outside but are more like analogies that the child gathers together from doing many kinds of thing with a powerful idea like "increase by". Later the bushel basket starts to become an idea of its own, first as a heuristic to try when thinking in problem solving, and finally by enlarging itself into a kind of thing on its own. This is interestingly like Vygotsky's theory of concept formation in much younger children, but the resemblences could be accidental. Cheers, Alan At 10:02 PM 8/23/2007, Blake wrote: >On Thu, 23 Aug 2007 19:04:18 -0700, Bill Kerr <[hidden email]> wrote: > > > Mark Guzdial's blog is a great discussion point (in general I think > > Mark's blog is really good but he has slipped up here). Alan has left a > > comprehensive response there, which does refute part of what Mark is > > saying > >His basic point is right, even if two of his examples are wrong. The >problem I've had with design patterns is that they're not all that >meaningful until you've had to build them, and once you've built them, >they seem fairly obvious. I've found them more useful for communication >than anything. > >In contrast to his point about Etoys, the problem I've had with them is >that they're too concrete.<s> >_______________________________________________ >Squeakland mailing list >[hidden email] >http://squeakland.org/mailman/listinfo/squeakland _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Blake-5
But here's where we should give the special cases amongst the much
maligned (and quite a bit for good reason) teacher corps great credit. Every once in a while a great teacher does light the fires, and those that are affected by this never forget it. To me this is the way it should be, because many children are close to the intense interest that you describe, and contact with another person can be just what they need to give them a little more confidence and courage, to get them to look at something a little closer. I've had just a few of these, but they were huge experiences in my life. Cheers, Alan At 01:01 AM 8/24/2007, Blake wrote: >On Thu, 23 Aug 2007 22:33:37 -0700, <[hidden email]> wrote: > > > No, they didn't use the term "office suite" back then. I was relating > > the curriculum to what it would be called now. We did learn about how to > > use a word processor, spreadsheet, and database application, though. > > Yes, they were separate applications. May be I didn't make that clearin > > what I wrote. I remember we used AppleWriter (I think), and VisiCalc,and > > some database app. whose name I can't remember, all on Apple II's. > >Well, let me apologize if I sounded overly picky. There was a very short >window (historically speaking) for when "office suite" might have meant >anything other than "Microsoft Office". It's depressing to hear that (at >least in your experience) the needle went from oddball geek hobby to >mundane replacement for typewriter, ledger and filing system. To their >current state: Monopoly perpetuators. > >I'm maybe 2 years older than you and my experience was at two different >extremes: I went to a private school which was ahead of the curve as far >as computers go (having a PDP-11 and several Apple ][s for all those who >were interested, which was not many), and then to a public school which >had never seen a computer--put still, net percentage, the difference >between the two in terms of population that knew or cared about computers >was probably about the same. > >But you know, it doesn't seem to matter much what subject it is, I've seen >the same thing in all of them: if the student is interested, nothing will >stop him; if not, nothing will help. Some of this is a matter of native >interest: We are not all interested in the same things, and no matter how >delightfully presented, the subject will remain at best a mild curiosity. >Too much of it is a matter of interest destroyed: A student attacks a >subject vigorously but is crushed in some manner or another, say with the >sort of ritualistic kind of "teaching" Alan describes, where there is no >understanding, and these days where the rituals have been replaced with a >shadow of something that "builds self-esteem" while even denigrating >understanding. And of course the usual brutal traditions of bad teachers. > >There are few techniques to rehabilitate blunted interest and fewer people >who know how to apply them. >_______________________________________________ >Squeakland mailing list >[hidden email] >http://squeakland.org/mailman/listinfo/squeakland _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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In reply to this post by Alan Kay
Hi Alan! Thanks for taking the time to read my blog posting and respond! _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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Hi Mark --At 05:01 AM 8/24/2007, Guzdial, Mark wrote:
Snip Tyrone is eloquent in his explanations--I believe he understands what he's doing. Here's my concern: Does he really understand differential equations? Let me break that down into two parts. I think most of the children after a few months of using "increase by" in various ways, do recognize rates in many other contexts. Does he recognize the situation as similar and that his same tools would apply? That would convince me that he has developed an understanding of the powerful idea of differential equations. I would doubt that his understanding of these kinds of DEs is total or even "supremely comprehensive", but it is "operational" very along the lines that any mathematician would characterize as "mathematical thinking". Our goal was to make an environment in which more than 90% of the children exhibited real fluency in this kind of thinking. "Real fluency" implies a degree of understanding above an important threshold. - When Tyrone gets to college and studies differential equations, will he recognize them as the same thing? I doubt that. They won't look the same. A much more important question is "will Tyrone understand mathematics by the time he gets to college?". If the answer is "yes", then he will recognize them as the same thing. If "no" then everything will be special cases of rules (which they are to most college students). His calculus course may not even relate to differential equations to modeling gravity. He will have too few cues to make that connection. A reasonable response to this should be that the calculus course might be taught with eToys, too, and that would help make the connection. I would agree. It's just unlikely that many (any?) college calculus courses will use eToys. Again, the question is whether he is actually learning math or not. It has nothing to do with Etoys. What I do believe is that the students in BJ's course have developed an understanding of the power of computation (*programmable* computation) in problem-solving and knowledge transformation. That's tremendous, and likely will transfer to other situations using computers. All I can say is that this was very thoroughly studied in the 60s (as was deep habit formation). What they were testing were not memories of isolated unusual incidents (nor of "movie recognition memory" which is also from one trial). What they were doing was testing changes of paradigms in outlook, and for most children these took immersion in an environment for well over a year to be strongly detectable years later. The two new variables that are more often studied are: To me, these are not as interesting (nor are they parallels) to large scale epistemological shifts. Cheers, Alan With best regards, _______________________________________________ Squeakland mailing list [hidden email] http://squeakland.org/mailman/listinfo/squeakland |
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