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.)
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.
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.
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.
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?
David
On 8/17/07, David Corking lists@dcorking.com wrote:
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?
hi David,
Curriculum statements have become contentious and politicised beasts because they are the main instrument of attempted control over teachers work. Many stakeholders fighting over problematic ideologies.
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
In more recent times in Western Australia (Australian education system is a State responsibility) there has been outrage at attempts at curriculum reform. One perception has been that outcomes based education has led to a watering down and socialisation of the maths / science curriculum. To quote retired Associate Professor Steve Kessell, Science and Mathematics Education Centre, Curtin University, letter to The Sunday Times 21/5/2006: "Learning about the sociology of the cosmetics industry is not real chemistry, discussing whether air bags should be mandatory is not real physics ... A 'culturally sensitive curriculum' borders on nonsense ..." This is but one small sample of a flood of complaint. See the PLATO (People Lobbying Against Teaching Outcomes) website for a lot more detail http://www.platowa.com/ btw I'm not endorsing their approach just pointing out how contested this area has become
My understanding is that this trend is world wide: http://billkerr2.blogspot.com/2007/06/physics-teacher-begs-for-his-subject.h... "Wellington Grey, a physics teachers in the UK, has written an open letterhttp://www.wellingtongrey.net/articles/archive/2007-06-07--open-letter-aqa.htmlabout the conversion of physics in his country from a science of precise measurement and calculation into "... something else, something nebulous and ill defined"
To critique it thoroughly would require a hard look at outcomes based education.
Summarising some of the issues: - watering down, diluting, trivializing science and maths curriculum - converting science / maths content into sociological content - using discovery or inquiry based learning as a substitute for hard facts
This appears to be occurring systematically in western education systems. (Not in developing countries who are serious about catching up to the west and actively promote the importance of maths, science and computing science).
This is a big topic. Science and maths education seems to be polarising between a back to basics movement and soft sociological reform, often ineffectual "discovery learning". I believe there is a third way, that traditional science education can be reformed and still remain real science. Student designed computer simulations using software such as Etoys / Squeak could play an important role here.
2007/8/18, Bill Kerr billkerr@gmail.com:
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
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 <mailto:lists@dcorking.comlists@dcorking.com> wrote:
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?
hi David,
Curriculum statements have become contentious and politicised beasts because they are the main instrument of attempted control over teachers work. Many stakeholders fighting over problematic ideologies.
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
In more recent times in Western Australia (Australian education system is a State responsibility) there has been outrage at attempts at curriculum reform. One perception has been that outcomes based education has led to a watering down and socialisation of the maths / science curriculum. To quote retired Associate Professor Steve Kessell, Science and Mathematics Education Centre, Curtin University, letter to The Sunday Times 21/5/2006: "Learning about the sociology of the cosmetics industry is not real chemistry, discussing whether air bags should be mandatory is not real physics ... A 'culturally sensitive curriculum' borders on nonsense ..." This is but one small sample of a flood of complaint. See the PLATO (People Lobbying Against Teaching Outcomes) website for a lot more detail http://www.platowa.com/http://www.platowa.com/ btw I'm not endorsing their approach just pointing out how contested this area has become
My understanding is that this trend is world wide: http://billkerr2.blogspot.com/2007/06/physics-teacher-begs-for-his-subject.htmlhttp://billkerr2.blogspot.com/2007/06/physics-teacher-begs-for-his-subject.h... "Wellington Grey, a physics teachers in the UK, has written http://www.wellingtongrey.net/articles/archive/2007-06-07--open-letter-aqa.htmlan open letter about the conversion of physics in his country from a science of precise measurement and calculation into "... something else, something nebulous and ill defined"
To critique it thoroughly would require a hard look at outcomes based education.
Summarising some of the issues:
- watering down, diluting, trivializing science and maths curriculum
- converting science / maths content into sociological content
- using discovery or inquiry based learning as a substitute for hard facts
This appears to be occurring systematically in western education systems. (Not in developing countries who are serious about catching up to the west and actively promote the importance of maths, science and computing science).
This is a big topic. Science and maths education seems to be polarising between a back to basics movement and soft sociological reform, often ineffectual "discovery learning". I believe there is a third way, that traditional science education can be reformed and still remain real science. Student designed computer simulations using software such as Etoys / Squeak could play an important role here.
-- Bill Kerr http://billkerr2.blogspot.com/http://billkerr2.blogspot.com/
Squeakland mailing list Squeakland@squeakland.org http://squeakland.org/mailman/listinfo/squeakland
On Sat, 18 Aug 2007 14:44:22 -0700, Robert Parks bobp@lightlink.com 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.)
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.
- 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"?
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.
- 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
On 8/17/07, David Corking <mailto:lists@dcorking.comlists@dcorking.com> wrote:
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?
hi David,
Curriculum statements have become contentious and politicised beasts because they are the main instrument of attempted control over teachers work. Many stakeholders fighting over problematic ideologies.
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
In more recent times in Western Australia (Australian education system is a State responsibility) there has been outrage at attempts at curriculum reform. One perception has been that outcomes based education has led to a watering down and socialisation of the maths / science curriculum. To quote retired Associate Professor Steve Kessell, Science and Mathematics Education Centre, Curtin University, letter to The Sunday Times 21/5/2006: "Learning about the sociology of the cosmetics industry is not real chemistry, discussing whether air bags should be mandatory is not real physics ... A 'culturally sensitive curriculum' borders on nonsense ..." This is but one small sample of a flood of complaint. See the PLATO (People Lobbying Against Teaching Outcomes) website for a lot more detail http://www.platowa.com/http://www.platowa.com/ btw I'm not endorsing their approach just pointing out how contested this area has become
My understanding is that this trend is world wide: http://billkerr2.blogspot.com/2007/06/physics-teacher-begs-for-his-subject.htmlhttp://billkerr2.blogspot.com/2007/06/physics-teacher-begs-for-his-subject.h... "Wellington Grey, a physics teachers in the UK, has written http://www.wellingtongrey.net/articles/archive/2007-06-07--open-letter-aqa.htmlan open letter about the conversion of physics in his country from a science of precise measurement and calculation into "... something else, something nebulous and ill defined"
To critique it thoroughly would require a hard look at outcomes based education.
Summarising some of the issues:
- watering down, diluting, trivializing science and maths curriculum
- converting science / maths content into sociological content
- using discovery or inquiry based learning as a substitute for hard facts
This appears to be occurring systematically in western education systems. (Not in developing countries who are serious about catching up to the west and actively promote the importance of maths, science and computing science).
This is a big topic. Science and maths education seems to be polarising between a back to basics movement and soft sociological reform, often ineffectual "discovery learning". I believe there is a third way, that traditional science education can be reformed and still remain real science. Student designed computer simulations using software such as Etoys / Squeak could play an important role here.
-- Bill Kerr http://billkerr2.blogspot.com/http://billkerr2.blogspot.com/
Squeakland mailing list Squeakland@squeakland.org http://squeakland.org/mailman/listinfo/squeakland
--
- The best dictionary and integrated thesaurus on the web:
- 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 Squeakland@squeakland.org http://squeakland.org/mailman/listinfo/squeakland
though I'd pass this along for another viewpoint. Mark Guzdial's latest perspective on powerful ideas, abstractions and design patterns:
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 Squeakland@squeakland.org http://squeakland.org/mailman/listinfo/squeakland
Hi Alan! Thanks for taking the time to read my blog posting and respond!
The eToys work is amazing--it's a tremendous demonstration that it is possible to explore a broad swath of science and mathematics with a relatively simple computational model. I'm particularly impressed with the range of projects available for the OLPC. I love Kim and BJ's book. It successfully communicates how these activities work, and helps teachers use them in their classrooms.
None of my blog comments were critiques of that work generally. I was making a very specific critique.
I have watched the Squeakers DVD many times and do completely agree that students depicted develop a model of gravity that is more sophisticated than most college students. (I'm a fan of Lillian McDermott's work, too -- I used it a lot in my dissertation work.) 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.
- When Tyrone is faced with another problem related to rates (maybe disease propagation, rates of decay, etc.) in eToys, can he use those tools to analyze the new situation? 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.
- 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. 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.
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.
I'd like to argue with your claim from cognitive psychology, though. "Length of exposure" is an ill-defined variable which has since been better refined and tested. What does "length of exposure" mean? One hour a day for two years? One hour a week for two years? Here's a brief thought experiment to address this point: I'll bet everyone on this list remembers exactly where they were and what they were doing when they first learned of the 9/11 attacks. That wasn't a very long exposure, yet everyone remembers it. Why?
The two new variables that are more often studied are: - Time on task. The more time you spend on an activity, the more likely that you will remember the experience and lessons of that activity later. - Amount of reflection. The more often that you reuse an association, the more often you think about and talk about an experience, the more likely you will retain it. That's the best explanation I know for the 9/11 effect (or the Challenger effect, or the JFK assassination effect). You thought about that moment later that day, and the next day, and you've discussed it with your friends. That leads to longer term learning.
With best regards, Mark
-----Original Message----- From: squeakland-bounces@squeakland.org on behalf of Alan Kay Sent: Thu 8/23/2007 6:49 PM To: bradallenfuller@yahoo.com; squeakland@squeakland.org Subject: Re: [Squeakland] the non universals
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 Squeakland@squeakland.org http://squeakland.org/mailman/listinfo/squeakland
_______________________________________________ Squeakland mailing list Squeakland@squeakland.org http://squeakland.org/mailman/listinfo/squeakland
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.
- When Tyrone is faced with another problem related to rates (maybe
disease propagation, rates of decay, etc.) in eToys, can he use those tools to analyze the new situation?
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.
I'd like to argue with your claim from cognitive psychology, though. "Length of exposure" is an ill-defined variable which has since been better refined and tested. What does "length of exposure" mean? One hour a day for two years? One hour a week for two years? Here's a brief thought experiment to address this point: I'll bet everyone on this list remembers exactly where they were and what they were doing when they first learned of the 9/11 attacks. That wasn't a very long exposure, yet everyone remembers it. Why?
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:
- Time on task. The more time you spend on an activity, the more
likely that you will remember the experience and lessons of that activity later.
- Amount of reflection. The more often that you reuse an
association, the more often you think about and talk about an experience, the more likely you will retain it. That's the best explanation I know for the 9/11 effect (or the Challenger effect, or the JFK assassination effect). You thought about that moment later that day, and the next day, and you've discussed it with your friends. That leads to longer term learning.
To me, these are not as interesting (nor are they parallels) to large scale epistemological shifts.
Cheers,
Alan
With best regards, Mark
-----Original Message----- From: squeakland-bounces@squeakland.org on behalf of Alan Kay Sent: Thu 8/23/2007 6:49 PM To: bradallenfuller@yahoo.com; squeakland@squeakland.org Subject: Re: [Squeakland] the non universals
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/PLNK13L1MC1Q3613Jhttp://www.am
azon.com/gp/blog/post/PLNK13L1MC1Q3613J
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On 8/24/07, Alan Kay alan.kay@squeakland.org wrote:
Hi Mark --At 05:01 AM 8/24/2007, Guzdial, Mark wrote:
I'd like to argue with your claim from cognitive psychology, though.
"Length of exposure" is an ill-defined variable which has since been better refined and tested. What does "length of exposure" mean? One hour a day for two years? One hour a week for two years? Here's a brief thought experiment to address this point: I'll bet everyone on this list remembers exactly where they were and what they were doing when they first learned of the 9/11 attacks. That wasn't a very long exposure, yet everyone remembers it. Why?
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:
- Time on task. The more time you spend on an activity, the more likely
that you will remember the experience and lessons of that activity later.
- Amount of reflection. The more often that you reuse an association, the
more often you think about and talk about an experience, the more likely you will retain it. That's the best explanation I know for the 9/11 effect (or the Challenger effect, or the JFK assassination effect). You thought about that moment later that day, and the next day, and you've discussed it with your friends. That leads to longer term learning.
To me, these are not as interesting (nor are they parallels) to large scale epistemological shifts.
A connection can be made between "time on task", "amount of reflection" and large scale epistemological shifts but not through reference to sensational events like 9/11. Remembering 9/11 does not imply deepening reflection about it.
However, Seymour Papert made this connection through the concept of building a relationship or falling in love with a subject domain
I think much of Seymour's mathetics, as outline in The Children's Machine, can be fairly directly connected to "time on task" and "amount of reflection". To present this briefly more in the form of slogans than detailed comments:
- Play is OK - The emotional precedes the cognitive - Our knowledge is like our relationships with other people - Take risks - Take your time (aka slow deep thinking) - A good discussion promotes learning
If you immerse yourself - out of passionate interest - in something (eg. gears, LEGO, logo) that connects in some way to the powerful ideas on the non universals list then increased time on task and reflection are likely to flow from that
So our task as educators is to provide the materials which allow powerful and not trivial relationships to be formed.
Some controversy takes place around what the powerful materials are. eg. playing computer games such as World of Warcraft, is that powerful or trivial?
Other discussion takes place around how to make the powerful materials more accessible to unsophisticated learners eg. etoys (visual programming) is more accessible than text base python programming
Alan's claim that a significant paradigm shift takes more than a year is crucial to our analysis of what happens in School, since School is organised on a one year teacher-student turnaround. If the claim is correct then perhaps School ought to be organised on at least a two year teacher-student turn around. I have taught in one secondary school that encouraged teachers to double up on both subjects (eg. take the same students for maths and science) and time (take the same classes of students for more than one year). I did notice some remarkable changes happening at around the 18 month mark.
On Fri, 24 Aug 2007 19:17:03 -0700, Bill Kerr billkerr@gmail.com wrote:
refined and tested. What does "length of exposure" mean? One hour a day for two years? One hour a week for two years? Here's a brief thought experiment to address this point: I'll bet everyone on this list remembers exactly where they were and what they were doing when they first learned of the 9/11 attacks. That wasn't a very long exposure, yet everyone remembers it. Why?
Again citing Glenn Doman and the IAHP, there are three factors in retention of data: Frequency, intensity and duration. Number of times of exposure, the intensity of that exposure and the length of that exposure.
9/11 was a very intense exposure and, you know what, it was a pretty long one, too. Little else occupied a lot of people's minds for a solid week. Then you have the frequency of subsequent exposure: 9/11, the moon landing, the Kennedy Assassination...I would imagine the firing on Fort Sumter...it's not like these things happen in their brief moment and are never mentioned again.
Some controversy takes place around what the powerful materials are. eg. playing computer games such as World of Warcraft, is that powerful or trivial?
World of Warcraft is extremely powerful. It conveys things that are of highly limited value, but it does so in a very effective fashion. The intensity is probably as high as a virtual environment can get (I'm guessing, I've never played), and it encourages both frequency and duration.
The guys to ask about that, I guess, would be the America's Army guys. They've been giving away their free combat game as a recruitment tool--but it was initially a training tool as well.
On Friday 24 August 2007 4:19 am, Alan Kay wrote:
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).
Alan,
I read the Powerful Ideas book (over and over!) and watched Tyrone on video. What I couldn't factor out in this experiment is the extent of BJ's influence in the outcomes. She comes across as a person who helps kids "learn to learn". Such talented people are rare. Would'nt such people figure out a way to get the same outcome without Etoys? In what ways did Etoys amplify her teaching abilities?
To take an extreme case - what if a child does not have access (or has rare access) to teachers? Would Etoys continue to nudge the kids along the right direction the same way?
Regards .. Subbu
Good question --
This is not really about Etoys but about what it takes to make use of a variety of perspectives on ideas in math, science (and elsewhere).
One of the big insights of Seymour Papert was that an incremental discrete form of differential equations that is extremely simple but computationally intensive would fit very well with the kinds of thinking that children can readily do. Babbage was one of the first who proposed that "these calculations should be executed by steam" because he realized that machinery could open up this way of looking at calculus.
Gauss upped the ante considerably by being one of several top mathematicians in the 19th century who moved geometry from a global to a local perspective. Papert realized that the child had this "coordinate system" of having all changes be relative to them wherever they were. And the additive form of DEs also applied here if you used vectors (and that vectors were a very good internal way to think about numbers).
Seymour proposed that you could use an interactive computer to make a "Mathland" in which a powerful mathematics could be situated as the way to talk about and cause phenomena of interest to a child (and most importantly to start building some ways to think about things in ways different than stories that would eventually constitute a new outlook on both thinking and phenomena).
So the key idea here is made of several important insights that include new ways to look at things, but also to make them happen. This last has partly to do with emotional payoff. For example, in the case of Galilean gravity it is possible to use something like Galileo's lute strings (see the afterword in BJ and Kim's book) or e.g. rolling a toy truck carrying a baggie filled with ink with a hole in it down an inclined plane to get the constant acceleration spacings that lead to the two stage incremental relations. This can all be done without a computer, but it is much more difficult to motivate the level of precision that we want the kids to employ, and to provide a vehicle for both checking their analysis (this is supposed to be science after all), and to make really fun things that now use the gravity model (like Lunar Lander, firing a cannon, shoot the alien, etc.). This is supposed to be fun after all.
Etoys is just one of a number of approaches done by people who got really interested in Seymour's insights (and Etoys itself is actually an amalgam of the ideas from many contributors outside of our immediate research group).
Right now, to get above threshold science and math, we need highly motivated teachers like BJ. But if the highly motivated teacher does not have an environment that situates the ideas and approaches (and curricula) then many (if not most) important things won't happen (except perhaps for a very few children).
An even rarer case is the highly motivated teacher who has a deep understanding of the subject and of the learners. For example, Julia Nishijima of the Open School (of whom I've written about elsewhere) showed what could be done with 6 year olds, and it is really impressive. Her curriculum was "almost perfect" in balance and depth. A small part of this curriculum used the computer (again for what only the computer could do as an "educational material").
If we look out in the world, in the US, Europe, Asia, and much wider, we do not find enough adults who can carry the powerful ideas of math and science and help children make them their own. This is especially acute wrt parents, because here we have a much better "student-teacher ratio" and we also have a great social environment for learning. Quite a bit of success in children learning to read has quite a bit of correlation with how parents deal with reading in the home. It would be great if this could be true for "real math" and "real science".
So utopian enterprises like OLPC really need to think about using the computer not just for an environment, but as a guide (something "better than no teacher and better than a bad teacher"). This is perhaps the most important and high stakes way to interpret "the computer as a dynamic book" (that is it could be a kind of book that can also teach people how to read and write it).
I think of this as one of the great and most important "Grand Challenges" for the 21st century.
Cheers,
Alan
At 11:08 AM 8/24/2007, subbukk wrote:
On Friday 24 August 2007 4:19 am, Alan Kay wrote:
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).
Alan,
I read the Powerful Ideas book (over and over!) and watched Tyrone on video. What I couldn't factor out in this experiment is the extent of BJ's influence in the outcomes. She comes across as a person who helps kids "learn to learn". Such talented people are rare. Would'nt such people figure out a way to get the same outcome without Etoys? In what ways did Etoys amplify her teaching abilities?
To take an extreme case - what if a child does not have access (or has rare access) to teachers? Would Etoys continue to nudge the kids along the right direction the same way?
Regards .. Subbu _______________________________________________ Squeakland mailing list Squeakland@squeakland.org http://squeakland.org/mailman/listinfo/squeakland
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.
*The "Montessori game" here is for the children to get most of their pay-off playing in the hand-eye arena, while gradually and subliminally gaining fluency and appreciation of the power of symbols.*
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 feel Scratch negatively influenced me for the rest of the course. Scratch was a lot of fun to use, and it was really easy. Then we started coding in Java and its [sic] about 100 times harder than Scratch, and the results are much less enjoyable than what I could easily achieve in Scratch. I think Scratch would have been better to have fun with after . . .Java."
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,
On Thu, 23 Aug 2007 19:04:18 -0700, Bill Kerr billkerr@gmail.com 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>
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 billkerr@gmail.com 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 Squeakland@squeakland.org http://squeakland.org/mailman/listinfo/squeakland
In response to another part of Mark's blog post at http://www.amazon.com/gp/blog/post/PLNK13L1MC1Q3613J
I haven't seen the arguments for and against teaching design patterns early. My guess is that the argument for would be that a design pattern might be something easier to have a conversation about than code or pseudo code - and that the conversation is good for learning the structure of complex systems
But the complaint about your blog is really that, to quote alan, that the "three examples are very different and don't really deserve to go together"
I just reread Seymour Papert's "The Gears of My Childhood" and I think you do oversimplify what he was saying to a level which degrades his real communication
He is saying that his early childhood playing with gears, especially the differential gear, played a big part in his creation of a mental model that was invaluable for his later understanding of some aspects of maths, including: - that a system could be lawful and comprehensible without being rigidly deterministic - multiplication tables - equations with two variables
It also served as a model to help him understand Piaget's assimilation. At this point he pauses to mention / criticise Piaget for not saying more about the emotional ("affective") aspect of assimilation, only focusing on the cognitive side.
A bit later Papert says: "I fell in love with the gears. This is something that cannot be reduced to purely 'cognitive' terms. Something very personal happened ..."
Papert's argument is that intense immersion in certain "objects to think with" (eg. gears in his individual case, logo and LEGO) can lead to the development of internal useful mental models that can be applied to new learning at a later date
I think what Papert is saying is consistent or at least not inconsistent with what you say in paragraph four of your original:
"... As we think about and generalize across our concrete associations, we create new associations that abstract the concrete knowledge we have. These newly inferred associations generalize the concrete details, in the sense that they make clear what's an important detail and what isn't, based on what are the common parts of the concrete associations we're connecting. As we learn new concrete associations, we might recognize the abstractions as being immediately applicable, because they match the common and unnecessary details of other experiences we know. We might also infer new abstractions that take into account both older concrete associations, older abstractions, and new associations."
btw I'm not saying that Papert is necessarily correct. From my reading of more recent research about the mind (eg. Andy Clark, Daniel Dennett) the whole idea of internal mental models (and Minsky's frames) seems to be now regarded as suspect. I don't really know. Nevertheless, my gut feeling is still that Papert's position here does provide a useful guide to good practice. Since there is no unified learning theory we have to cherry pick the best bits.
cheers,
On Fri, 17 Aug 2007 17:25:34 -0700, Bill Kerr billkerr@gmail.com 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.h... "Wellington Grey, a physics teachers in the UK, has written an open letterhttp://www.wellingtongrey.net/articles/archive/2007-06-07--open-letter-aqa.htmlabout 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.
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