squeakland November 2007

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33 participants
43 discussions

looking for some advice on teaching Squeak to advanced high school kids
by Oscar Nierstrasz 04 Dec '07

04 Dec '07

Hi Folks, I teach at University level, not high school, and have no previous experience teaching high school kids. At the end of January we will have a day and a half with a bunch of high school kids who are finalists in the Swiss Scientific Olympiads ( http://www.olympiads.ch/ ) and have the opportunity to get them excited about computer science. We will have various sessions to show them different things. (I will not be the only one to offer something. A colleague will be introducing the ones who have no background in programming to Scratch.) I wanted to take the ones who have done some programming (i.e., those who have done the Swiss Olympiad in Informatics - http://www.soi.ch/ ) and introduce them to Squeak. For the Olympiad they have been working with languages like Pascal, C and C++. I would like the session to be mainly hands-on, and get the kids to actually build something in teams of two with help from some monitors. Does anyone have any experience like this? Can you recommend some specific exercises that would be fun and would produce a real result in a few hours? My concrete goal is to show them how different a dynamic language and environment like Squeak can be from the languages they are used to. Any hints would be welcome. - on --- Prof. Dr. O. Nierstrasz -- Oscar.Nierstrasz(a)iam.unibe.ch Software Composition Group -- http://www.iam.unibe.ch/~scg University of Berne -- Tel/Fax +41 31 631.4618/3355 vcard: http://www.iam.unibe.ch/~oscar/oscarNierstrasz.vcf

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music and math
by mmille10＠comcast.net 01 Dec '07

01 Dec '07

>Date: Tue, 27 Nov 2007 21:06:01 -0500 >From: "David T. Lewis" <lewis(a)mail.msen.com> >Subject: Re: However ...Re: [Squeakland] Panel discussion: Can the >American Mind be Opened? >To: subbukk <subbukk(a)gmail.com> >Message-ID: <20071128020601.GA75166(a)shell.msen.com> >Content-Type: text/plain; charset=us-ascii > >On Mon, Nov 26, 2007 at 11:38:30PM +0530, subbukk wrote: >> Coming from a culture steeped in oral tradition, I find 'sounds' better >> than 'symbols' when doing math 'in the head'. The way I learnt to handle >> numbers (thanks to my dad) is to think of them as a phrase. 324+648 would be >> sounded out like "three hundreds two tens and four and six hundreds and four >> tens and eight. three hundreds and six hundreds makes nine hundreds, two tens >> and four tens make six tens and four and eight makes one ten and two, giving >> me a total of nine hundreds seven tens and two". Subtraction was done using >> complements. So 93-25 would be sounded out as "five more to three tens, six >> tens more to nine tens and then three more, making a total of six tens and >> eight'. The technique works for any radix - 0x3c would be "three sixteens and >> twelve'. >> >> In India, many illiterate shopkeepers and waiters in village restaurants use >> these techniques to total prices and hand out change. No written bills. >> >> The advantage with sounds is that tones/stress/volume can be used to decorate >> numbers. With pencil and paper, changing colors, sizes or weights would be >> impractical. > >Subbu, > >Thanks for sharing this. I think that it is very interesting that sound >and oral skills can be a basis for mathematical thinking. My cultural >background is less oral, so I did not even think of this as a possibility. >It seems that music and mathematics are somehow connected, but I never thought >to extend this to verbal types of music. > >Dave I took a couple music theory courses in college years ago. One of my professors mentioned that he noticed a correlation between those who were good at math and those who tended to grasp music theory readily. He had no explanation for this though. ---Mark mmille10(a)comcast.net

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Re: However ...Re: [Squeakland] Panel discussion: Can the American Mind be Opened?
by Alan Kay 01 Dec '07

01 Dec '07

Hi Bill -- I think the main thing in teaching "number" is to distinguish it from "name" or "numeral" -- and I think the rush towards teaching "base 10 numerals" too early is one of the big problems in early elementary mathematics. Numbers are ordered ideas that can be put in correspondence and taken apart and recombined at will. Names and numerals are symbols for these ideas that have varying degrees of usefulness for different purposes. So one of the biggest questions any math educator should ask is: what symbols should I initially employ for numbers to help children understand "number" most throughly? Most "child math" experts - like Mary Laycock, Julia Nishijima, etc. - would argue that a wide variety of analog (both unary and continuous) representations should be employed together (bundles of sticks, bags of objects, lengths of stuff, etc.), and each of these can have several labels attached ("one", 1, etc.). These can stay in use for much longer than is usually done in school. E.g. Some really great "adding slide rules" can be made from rulers, and then the children can make some really detailed large ones (even using their playground for baselines). These adding slide rules can add any two numbers together very accurately, whether "fractional" or not, and they can have scale changes to reveal what is invariant about two numbers (their ratio), etc. This can be used to make multiplication machines, etc. Another use of number that uses names in a non-destructive way is the "equality game" of "how many ways can you make a number". First graders are very good at this an even though they don't know what "1000000" stands for (except it is large) they understand that they can make this or any other number many ways by a combination of additions and subtractions that add up to zero. This is a way to start algebraic thinking without needing variables. And so forth. Wu actually makes a point against himself when he argues that phonics decoding is a good idea, even though no fluent reader decodes. This is similar to how sight reading is taught, especially for keyboards. Eventually the pattern results in a direct hand shape and mental "image" of the sound (or for text reading, a mental image of the idea). The question is how to get there, and teaching how to decode seems to help a little in early stages (maybe even just for morale purposes) rather than trying to teach either like Chinese characters. It takes 2-5 years to get fluent at such learning, so there usually need to be other supporting mechanisms (not the least is material that can be dealt with successfully after a few months or a year). So, what Wu should be asking is "what framework do children need to get started in number and mathematical thinking about number?". Another interesting example of what is not happening came out in a Mary Laycock workshop in which I was a "floor guy" (literally since I was on the floor with the children). One of Mary's games was to hand out a series of sheets of 10 by 10 squares, each divided in regions, with the question, "how many squares are in each region?" The 4th-5th grade children start by counting the squares in the regions. As the regions got more complicated, the children did not see that they could switch over to geometrical reasoning -- to see what fraction of the whole was occupied by each region and then divide -- instead they kept on trying to count the little squares and fractions of squares. Children who had learned to think mathematically would have had a strategy to look for the best representations for the problems, and these children had not acquired many (if any) math meta-skills. To bring up a musical analogy again ... one of the best collections of advice about how to teach children to play the keyboard is in Francois Couperin's 1720 treatise "The Art of Playing the Harpsichord". First, he says, keep the children away from the harpsichord because it isn't musically expressive enough. And keep away from sheet music because it "isn't music". Instead, take them to the clavichord (loud, soft, and pitch modulation -- more expressive than a piano) and teach them how to play some of their favorite songs that they like to sing, and help them be as expressive in their playing as their singing is. This is music. Play duets with the children, etc. After they have done this for a sufficient time (from 6 months to several years), then you can introduce them to the initially less expressive harpsichord (which, like the organ, can only be expressive through phrasing). But they will have learned to phrase very naturally from their clavichord experience and this will start to come out in their harpsichord playing. Finally, now that they have learned to "talk" (my metaphor), they can learn to read. Now they can be shown the written down forms of what they have been playing. And now they can start to learn to sight read music. When I was teaching guitar long ago, I used this basic scheme as much as possible, because "real guitar" has to be both music and "attention out" (so that you can mesh musically in a conversation with other musicians). Also, the guitar has some serious physical problems which have to be addressed gradually over weeks and months. Getting the students to play real stuff while all this is going on makes a foundation for the next level of much harder work. Learning to play patterns by ear allows the player to concentrate on their musicality and accuracy. Then they can be shown the patterns as both shapes and as decoded mappings in members of a key, etc. The egregiously misunderstood Suzuki violin method also follows these ideas. (It isn't mechanical -- read his books.) Couperin's essay is a pretty good set of distinctions concerning the general confusions between art and technique, and between ideas and media. You eventually have to get to all of these, but leading with art and ideas tends to preserve art and ideas, and leading with technique and media tends to kill art and ideas. I think it is really that simple. Cheers, Alan At 03:47 AM 11/25/2007, Bill Kerr wrote: >Good discussion :-) > >To be honest I've never been certain about the best way to teach >"number" and have tended to try a smorgasboard in practice > >Perhaps Alan is correct David? > >Professor Wu (good mathematician) is making a brave attempt to make >the teaching of algorithms to young children more concrete but his >approach still puts too many demands on most children. From my >experience of teaching of maths I feel that for disadvantaged >students too many eyes would glaze over for some of the steps. It >might work for his children but not for 90% of children. > >I still feel that he makes some valid points and criticisms. I like >the transparency and open-ness of his paper, as well as the >conceptual position put by its title. > >Another paper by Ellerton and Clements identifies the main issue as this: >"... many children who correctly answered pencil-and-paper fraction >questions such as 5/11 x 792 = q could not pour out one-third of a >glass of water, and of those who could, only a small proportion had >any idea of what fraction of the original full glass of the original >full glass of water remained" >- Fractions: A Weeping Sore in Mathematics Education ><http://www.aare.edu.au/92pap/ellen92208.txt>http://www.aare.edu.au/92pap/ellen92208.txt > >Some form of effective kitchen maths needs to come before algorithms. > >At this stage I'm left with more questions than answers. > >-- >Bill Kerr ><http://billkerr2.blogspot.com/>http://billkerr2.blogspot.com/ > > > > >On Nov 25, 2007 3:28 AM, Alan Kay ><<mailto:alan.kay@vpri.org>alan.kay(a)vpri.org> wrote: >Hi Bill -- > >I just read Professor Wu's paper. I agree in the large with his >assertion that the dichotomy is bogus, but I worry a lot about his >arguments, assumptions and examples. There are some close analogies >here to some of the mistakes that professional musicians make when >they try to teach beginners -- for example, what can a beginner >handle, and especially, how does a young beginner think? > >Young children are very good at learning individual operations, but >they are not well set up for chains of reasoning/operations. Take a >look at the chains of reasoning that Wu thinks 4th and 5th graders >should be able to do. > >Another thing that stands out (that Wu as a mathematician is very >well aware of at some level) is that while people of all ages >traditionally have problems with "invert and multiply", the actual >tricky relationship for fractions is the multiplicative one > a/b * c/d = (a * c)/(b * d) >which in normal 2D notation, looks quite natural. However, it was >one of the triumphs of Greek mathematics to puzzle this out (they >thought about this a little differently: as comeasuration, which is >perhaps a more interesting way to approach the problem). > >A few years ago I did a bunch of iconic derivations for fractions >and made Etoys that tried to lead (adults mostly) through the >reasoning. One of the best things about the divide one is that it >doesn't need the multiplication relationship but is able to go >directly to the formula. So these could be used in the 5th grade. > >But why?, when there are much deeper and more important >relationships and thinking strategies that can be learned? What is >the actual point of "official fractions" in 5th grade? There are >many other ways to approach fractional thinking and computation. I >like teaching math with understanding, and this particular topic at >this time - and provided as a "law" that children have to memorize - >seems really misplaced and wrong. Etc. > >Cheers, > >Alan > >At 05:53 AM 11/24/2007, Bill Kerr wrote: >>David: >>>Further, but perhaps drifting off topic for squeakland, is it provable >>>that 'back to basics' and 'progressivism' are equally as inadequate? >>Alan: >>I said above that the simplistic versions of both are quite >>wrongheaded in my opinion. If you don't understand mathematics, >>then it doesn't matter what your educational persuasion might be -- >>the odds are greatly in favor that it will be quite misinterpreted. >> >> >>David, >> >>I read the original maths history >><http://www.csun.edu/%7Evcmth00m/AHistory.html>http://www.csun.edu/~vcmth00m/AHistory.html >>that prompted your initial questions about constructivism and agree >>that it critiques the cluster of overlapping outlooks that go under >>the names of progressivism / discovery learning / constructivism - >>fuzzy descriptors >> >>But more importantly IMO it also takes the position that the >>dichotomy b/w "back to basics" and "conceptual understandings" is a >>bogus one. ie. that you need a solid foundation to build conceptual >>understandings. The problem here is that some people in the name of >>constructivism have argued that some basics are not accessible to >>children. (refer to the H Wu paper cited at the bottom of this post) >> >>I think the issue is that real mathematicians who also understand >>children development ought to be the ones working out the >>curriculum guidelines. This would exclude those who understand >>children development in some other field but who are not real >>mathematicians and would also exclude those who understand maths >>deeply but not children development. >> >>This has not been our experience in Australia. I cited a book in an >>earlier discussion by 2 outstanding maths educators documenting how >>their input into curriculum development was sidelined. National >>Curriculum Debacle by Clements and Ellerton >><http://squeakland.org/pipermail/squeakland/2007-August/003741.html>http://squeakland.org/pipermail/squeakland/2007-August/003741.html >>For some reason the way curriculum is written excludes the people >>who would be able to write a good curriculum -> those with both >>subject and child development expertise >> >>For me the key section of the history was this: >>"Sifting through the claims and counterclaims, journalists of the >>1990s tended to portray the math wars as an extended disagreement >>between those who wanted basic skills versus those who favored >>conceptual understanding of mathematics. The parents and >>mathematicians who criticized the NCTM aligned curricula were >>portrayed as proponents of basic skills, while educational >>administrators, professors of education, and other defenders of >>these programs, were portrayed as proponents of conceptual >>understanding, and sometimes even "higher order thinking." This >>dichotomy is implausible. The parents leading the opposition to the >>NCTM Standards, as discussed below, had considerable expertise in >>mathematics, generally exceeding that of the education >>professionals. This was even more the case of the large number of >>mathematicians who criticized these programs. Among them were some >>of the world's most distinguished mathematicians, in some cases >>with mathematical capabilities near the very limits of human >>ability. By contrast, many of the education professionals who spoke >>of "conceptual understanding" lacked even a rudimentary knowledge >>of mathematics. >> >>More fundamentally, the separation of conceptual understanding from >>basic skills in mathematics is misguided. It is not possible to >>teach conceptual understanding in mathematics without the >>supporting basic skills, and basic skills are weakened by a lack of >>understanding. The essential connection between basic skills and >>understanding of concepts in mathematics was perhaps most >>eloquently explained by U.C. Berkeley mathematician Hung-Hsi Wu in >>his paper, Basic Skills Versus Conceptual Understanding: A Bogus >>Dichotomy in Mathematics Education.75" >> >>Papert is also critical of NCTM but is clearly both a good >>mathematician and someone who understands child development - and >>has put himself into the constructivist / constructionist group >> >>I followed that link in the history to this paper which is a more >>direct and concrete critique of discovery learning taken too far, >>with well explained examples of different approaches: >> >><http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf>http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf >> >>BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING >>A Bogus Dichotomy in Mathematics Education >>BY H. WU >> >>cheers, >>-- >>Bill Kerr >><http://billkerr2.blogspot.com/>http://billkerr2.blogspot.com/ >

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Ideas for SqueakFest '08?
by Kim Rose 30 Nov '07

30 Nov '07

Greetings, Squeaklanders - Viewpoints has recently been informed that after a long and successful run hosting "SqueakFest" each summer for 5 years, Columbia College will take a break in hosting the event in 2008. I think all who attended any SqueakFest will agree what a wonderful job the group at Columbia did to host our group to not only their "campus" but to the city of Chicago. We are so grateful for this longer-than- anticipated run and to our friends at Columbia for all their hard work and effort each year. Originally the thought was that the venue for SqueakFest would change from year to year, enabling the community and venue to travel around the world, have a variety of organizations to host, etc., etc. but the first year was such a success in Chicago, we all wanted to "do it again" and so, now, here we are. I would like to ask you, the community, for feedback and ideas for the future.... Should there be another SqueakFest? Ideas for venue? Hosts? Sponsoring organizations? Is it time to create more regional events? Perhaps in addition to an annual international gathering? Who would like to be involved in planning, organizing, etc..,etc? I'd love to start a discussion on this topic, so please send your thoughts and ideas. cheers, Kim

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Re: [Squeakland] music and math
by Alan Kay 29 Nov '07

29 Nov '07

Sounds as though the music teacher didn't understand math and what it is all about. (By "music theory" he probably meant the kinds of ("keyboard") harmony that are covered in the first year or two of college.) The kinds of thinking here are a lot like what is done in geometry. For example, one way to think of chords is as shapes whose "side lengths" are measured in semi-tone intervals (the smallest interval between two adjacent notes on a piano keyboard). These "distances" have been made uniform since the late 18th or early 19th century (not without musical penalty, see below). So a major chord in closed position has the shape 4-3 and a minor chord has the shape 3-4. So a chord of any kind can be built by starting on any note and counting intervals. This scheme normalizes chords in the same way triangles are normalized by their shapes. Scales are normalized in the same way, and thus this also normalizes keys. In harmonic theory, we are interested in how melodies can be harmonized by adding chords, how a sequence of chords (called a "chord pattern") "works" musically, how movements to other keys and returns can be made, etc. The first order and second order theories of these are very different. There is a famous 18th century piece by Purcell called "The Contest Between Melodie and Harmonie", and this sums up what Baroque music was all about. The golden age of Jazz (roughly, the 20th century until the late 50s or so) followed a very similar pathway in how melody and harmony were thought about (and not entirely by separate invention). The first order theory is very much about how tensions are introduced and relaxed, how the notion of a "key center" can be used to provide stability (and length) for excursions, how bass lines can be used to solidify movements, etc. The second order theory was used very strongly by Bach then less so until roughly Wagner, and then in highly developed show and pop music (by stage bands, etc.) to try to intertwine melodic devices (like voice leading) with larger harmonic schemes that would force "emergent harmonizations" that are not easily described by the first order theory. What is called "chord substitution" (alternate harmonizations, sometimes of breathtaking beauty) in Jazz heavily rely on such mechanisms. "Mathematics" is a plural because it is about many different ways of "thinking very carefully" with invented representations and inference rules. So this kind of thinking about music is mathematics (i.e. rather than "like math", it is math). And, within music, there are lots of ways of making generalizations that help with styles. For example, my pipe organ and harpsichord have the older tuning schemes used in the 17th century. Why would anyone revert? Here's the problem (as first discovered to their horror by the Pythagoreans). Octaves are multiples of 2. The harmonic 5th is the third harmonic, which is a multiple of 3. So if you try to make a scale by running out the 5ths (of 5ths etc.) they will never come back to the original note (2 and 3 are relatively prime). One way of running out the "circle of 5ths" creates a discrepency of about 1/75th of an octave. The equal tuning system mentioned above divides out this glitch evenly by making every 5th a little bit flat (and this results in rather wide 3rds). This works (sort of) OK on a piano because it doesn't have a lot of harmonics and most people are not very sensitive to in-tune-ness. Here, every chord is equally out of tune! On an organ or harpsichord (which are very rich in harmonics), the result of equal tuning is that major chords don't hold still, and minor chords are jangly. The older tuning schemes made some chords much more perfect and sacrificed others. This results in a harmonic theory that is partly about "sunlight" and "storms" depending on what keys you are playing in and how the harmonic progressions are devised. Because the harmonics are different on organs, harpsichords, clavichords, fortepianos, etc., it is not unusual for each to have a somewhat different unequal tuning to deal with the strengths and weaknesses provided. Some of the greatest music in the world was composed using these different bases for thinking, and much of this music loses much of its meaning in a modern tuning scheme. And, there is a math to these other ways of thinking about how things go together, but it is a somewhat different math. The analogy is to the many kinds of geometries - all mathematical - that have been devised starting in the 19th century. Referencing back to "art" and "technique". Learning all this doesn't necessarily make you into a composer or a better player, just as learning painting technique doesn't necessarily produce art. But if the artistic impulses are working then all this technique is tremendously helpful. Unfortunately for education, knowing technique is often all that is asked of a teacher .... oops! Cheers, Alan At 10:01 PM 11/28/2007, mmille10(a)comcast.net wrote: > >Date: Tue, 27 Nov 2007 21:06:01 -0500 > >From: "David T. Lewis" > <<http://mailcenter.comcast.net/wmc/v/wm/474DD3ED0001F7050000103B2200750744CF…>lewis(a)mail.msen.com> > >Subject: Re: However ...Re: [Squeakland] Panel discussion: Can the > >AmericanMind be Opened? > >To: subbukk > <<http://mailcenter.comcast.net/wmc/v/wm/474DD3ED0001F7050000103B2200750744CF…>subbukk(a)gmail.com> > >Message-ID: > <<http://mailcenter.comcast.net/wmc/v/wm/474DD3ED0001F7050000103B2200750744CF…>20071128020601.GA75166(a)shell.msen.com> > >Content-Type: text/plain; charset=us-ascii > > > >On Mon, Nov 26, 2007 at 11:38:30PM +0530, subbukk wrote: > >> Coming from a culture steeped in oral tradition, I find 'sounds' better > >> than 'symbols' when doing math 'in the head'. The way I learnt to handle > >> numbers (thanks to my dad) is to think of them as a phrase. > 324+648 would be > >> sounded out like "three hundreds two tens and four and six > hundreds and four > >> tens and eight. three hundreds and six hundreds makes nine > hundreds, two tens > >> and four tens make six tens and four and eight makes one ten and > two, giving > >> me a total of nine hundreds seven tens and two". Subtraction was > done using > >> complements. So 93-25 would be sounded out as "five more to > three tens, six > >> tens more to nine tens and then three more, making a total of > six tens and > >> eight'. The technique works for any radix - 0x3c would be "three > sixteens and > >> twelve'. > >> > >> In Ind ia, many illiterate shopkeepers and waiters in village > restaurants use > >> these techniques to total prices and hand out change. No written bills. > >> > >> The advantage with sounds is that tones/stress/volume can be > used to decorate > >> numbers. With pencil and paper, changing colors, sizes or > weights would be > >> impractical. > > > >Subbu, > > > >Thanks for sharing this. I think that it is very interesting that sound > >and oral skills can be a basis for mathematical thinking. My cultural > >background is less oral, so I did not even think of this as a possibility. > >It seems that music and mathematics are somehow connected, but I > never thought > >to extend this to verbal types of music. > > > >Dave > >I took a couple music theory courses in college years ago. One of my >professors mentioned that he noticed a correlation between those who >were good at math and those who tended to grasp mus ic theory >readily. He had no explanation for this though. > >---Mark ><mailto:mmille10@comcast.net>mmille10(a)comcast.net >_______________________________________________ >Squeakland mailing list >Squeakland(a)squeakland.org >http://squeakland.org/mailman/listinfo/squeakland

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Re: [Squeakland] Panel discussion: Can the American Mind be Opened?
by Alan Kay 27 Nov '07

27 Nov '07

Hi David -- At 05:29 PM 11/23/2007, David Corking wrote: >It was not my intention earlier in this thread to challenge the work >of Viewpoints. I certainly didn't take it that way - in part because we claim almost nothing. What we have been interested in is whether 90% of the children we've worked with -- taught by a teacher, not by us -- gain real fluency in what we are trying to teach them. We found that it took 3 years to introduce each new curriculum element (as described in my last post). >Instead I wanted to get a foothold into understanding >how the powerful 'progressive' and 'back to basics' movements could be >rationally compared with alternatives. I disagree with the simplistic versions of both of these. If "progressive" means what it meant long ago - "Dewey education" - then I am very much in favor of what he was trying to do and what he wrote about. If "back to basics" means "Bennet or E.D. Hirsh", then I'm very much in disagreement with what they are trying to do, and their general view of "education". Subjects like real math and real science, with a goal to help children get fluent, are best assessed by real mathematicians and real scientists. Separate issues are: what parts of the real stuff should be taught to children, how should the teaching be done, etc. This is very important in its own right - recall the very bad choices made by real mathematicians when they chose set theory, numerals as short-hand for polynomials, etc. during the "new math" debacle. This is why Seymour Papert was so impressive -- he was that rarity, a first class mathematician who both cared about and understood important principles of how children think. He chose real math that was both deep and in rhythm with how children think about relationships. >Thank you for taking my question as a provocation I didn't > - it is very >illuminating to read the work of Rose, Kay et al justified from this >perspective. > >I need to confess now that I have read 'Mindstorms' but not yet >'Powerful Ideas' - does the book address whether or not there is a >'Hawthorne effect' in the trials? "Powerful Ideas" is written to help teachers teach a dozen or so projects in real math and real science, using Etoys. It makes no claims and leaves a tiny bit of philosophy to the Afterword. http://www.vpri.org/pdf/human_condition.pdf > In other words, could simply the >intensive attention of all involved, coupled with the novelty, >willingness to persevere for the second and third year, and the >involvement of real subject matter experts, have been sufficient in >itself to produce a fluency result that is well above acceptable >threshold? Schools should be all about the Hawthorne Effect. The ones that aren't should be closed. I think you misunderstood one part of my description of the process. The 3 years is with the same teacher but with three different groups of children. Each group deals with the materials and process for the same amount of time. The other part of your question wasn't asked or answered by what we did (since we wanted the children to express the math and science they learned in terms of working Etoy models). That's what we tried to do, and that's what we assessed. If the "it takes 3 years" story seems reasonable to you, then imagine what it would take to do a real longitudinal transfer experiment using control groups (about 7 years). We have never been able to find a funder that is willing to fund what it really takes. > Is it provable(*) that the student creation of computer >models, for example, is a necessary condition of learning 'real math' >fluency? It's provable that it isn't (people have been learning "real math fluency" for thousands of years without computers). The important thing (Papert again) is what math and when? Computers make a huge difference here for pretty much everyone. Also, see the Afterword in the book for what science learning is really about (hint: computers are not at all required, but they allow more rich choices in the world of the child). I've used many analogies to music in the past. You don't need musical instruments to teach music, they just help (and in no small part because there are lots of different kinds). A child who is not that interesting in singing might be very interested in learning the guitar, one that is not interested in guitar might be interested in a sax, etc. Different learners need lots of different entry points. Computers can provide many different entry points, and can be the medium for the kinds of mathematics that science uses. A pretty good combination. >* By 'provable', I mean: "could a future experiment be designed to >prove my assertion, or, even better, could a reasoned argument prove >my assertion?" No. But something might be done with a goal of more than 90% fluency -- computers could almost be indispensable here ... >Further, but perhaps drifting off topic for squeakland, is it provable >that 'back to basics' and 'progressivism' are equally as inadequate? I said above that the simplistic versions of both are quite wrongheaded in my opinion. If you don't understand mathematics, then it doesn't matter what your educational persuasion might be -- the odds are greatly in favor that it will be quite misinterpreted. >Or is the poor performance of public education in some countries a >consequence, not of the learning theory nor curriculum, but caused by >the 'received wisdom' not being applied properly, or even some >external factors, such as low resources, attitudes to authority, or >the currently fashionable complaint of students' learning styles not >being catered for? If you like multiple choice tests, then (e) all of the above. Cheers, Alan ---------- David

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Collecting Alan Kay's knowledge
by mmille10＠comcast.net 26 Nov '07

26 Nov '07

I've had the same sense of urgency as John Maxwell expressed, from time to time, that I wish Alan Kay would "collect his knowledge" as it were in some "volumes" that people could read comprehensively, rather than getting smatters of insight from him. However, Kay has set up a reading list at http://www.squeakland.org/sqmedia/books/book_list.html related to Squeak. It's pretty extensive. It covers all sorts of subjects, including computing and education. I've gotten into a few of the books in the list so far, and I've found each of them to be of good quality, and to be quite insightful in and of themselves. ---Mark mmille10(a)comcast.net

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Re: Squeakland Digest, Vol 55, Issue 32
by John Maxwell 26 Nov '07

26 Nov '07

On 26-Nov-07, at 8:17 AM, Alan Kay wrote: > I think the main thing in teaching "number" is... ...and so follows yet another amazingly eloquent, erudite lesson on the topic of the day, the likes of which we've seen for years on this mailing list and others. OK, I thought this most recent was a particularly good one. As somebody who has spent considerable time trying to collect and interpret the works of Alan Kay, and who, on reading almost every one of these little e-mails, finds that here again is yet another gem, another insight, that I've missed... I find myself increasingly asking myself, When is Alan Kay going to publish a book? Seriously, considering the depth and (perhaps more crucially) breadth of accumulated thinking that is evident in Kay's various talks, lectures, the odd article, and these e-mails, it truly is shame that our primary means of accessing this body of thought is the laborious work of sifting through the hundreds of fragments laid down over the years. Alan, I appeal to you and to the spirit of scholarship; your work is not done justice by the occasional articles and talks that appear, nor by these 'lessons' (and I mean that in the best possible sense) that appear sporadically on the mailing lists. Surely you've considered collecting it... I think the value of such a thing would be enormous. Respectfully and sincerely(!), - John Maxwell http://thinkubator.ccsp.sfu.ca/Dynabook jmax(a)sfu.ca

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Need advice about teaching programming to children
by nigen 26 Nov '07

26 Nov '07

I am a Delphi programmer. I have start to taught programming to 4 grade elementary student using Scratch for about 1 month. I have seen that the programming concept can be understood easily by the student. I have learned "squeak learn programming with robot" . Currently, I am learning smalltalk. I found that smalltalk is really powerful programming environment. I hope I can eventually teach children real programming. But I found that GUI programming like Delphi is much simpler in the term of GUI. I believe elementary student can do programming like adult if we have a good method to teach them programming skill. (Please advice me if I am wrong). I need advise to how I should proceed my programming class. I have some scenario Scratch --> Etoys--> BotsInc. --> smalltalk or Scratch --> BotsInc --> smalltalk or Etoys --> BotsInc. --> Smalltalk or Scratch --> Lazarus (Delphi like Open source). thanks.

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However ...Re: [Squeakland] Panel discussion: Can the American Mind be Opened?
by Alan Kay 25 Nov '07

25 Nov '07

Hi Bill -- I just read Professor Wu's paper. I agree in the large with his assertion that the dichotomy is bogus, but I worry a lot about his arguments, assumptions and examples. There are some close analogies here to some of the mistakes that professional musicians make when they try to teach beginners -- for example, what can a beginner handle, and especially, how does a young beginner think? Young children are very good at learning individual operations, but they are not well set up for chains of reasoning/operations. Take a look at the chains of reasoning that Wu thinks 4th and 5th graders should be able to do. Another thing that stands out (that Wu as a mathematician is very well aware of at some level) is that while people of all ages traditionally have problems with "invert and multiply", the actual tricky relationship for fractions is the multiplicative one a/b * c/d = (a * c)/(b * d) which in normal 2D notation, looks quite natural. However, it was one of the triumphs of Greek mathematics to puzzle this out (they thought about this a little differently: as comeasuration, which is perhaps a more interesting way to approach the problem). A few years ago I did a bunch of iconic derivations for fractions and made Etoys that tried to lead (adults mostly) through the reasoning. One of the best things about the divide one is that it doesn't need the multiplication relationship but is able to go directly to the formula. So these could be used in the 5th grade. But why?, when there are much deeper and more important relationships and thinking strategies that can be learned? What is the actual point of "official fractions" in 5th grade? There are many other ways to approach fractional thinking and computation. I like teaching math with understanding, and this particular topic at this time - and provided as a "law" that children have to memorize - seems really misplaced and wrong. Etc. Cheers, Alan At 05:53 AM 11/24/2007, Bill Kerr wrote: >David: >>Further, but perhaps drifting off topic for squeakland, is it provable >>that 'back to basics' and 'progressivism' are equally as inadequate? >Alan: >I said above that the simplistic versions of both are quite >wrongheaded in my opinion. If you don't understand mathematics, then >it doesn't matter what your educational persuasion might be -- the >odds are greatly in favor that it will be quite misinterpreted. > > >David, > >I read the original maths history ><http://www.csun.edu/~vcmth00m/AHistory.html>http://www.csun.edu/~vcmth00m/AHistory.html >that prompted your initial questions about constructivism and agree >that it critiques the cluster of overlapping outlooks that go under >the names of progressivism / discovery learning / constructivism - >fuzzy descriptors > >But more importantly IMO it also takes the position that the >dichotomy b/w "back to basics" and "conceptual understandings" is a >bogus one. ie. that you need a solid foundation to build conceptual >understandings. The problem here is that some people in the name of >constructivism have argued that some basics are not accessible to >children. (refer to the H Wu paper cited at the bottom of this post) > >I think the issue is that real mathematicians who also understand >children development ought to be the ones working out the curriculum >guidelines. This would exclude those who understand children >development in some other field but who are not real mathematicians >and would also exclude those who understand maths deeply but not >children development. > >This has not been our experience in Australia. I cited a book in an >earlier discussion by 2 outstanding maths educators documenting how >their input into curriculum development was sidelined. National >Curriculum Debacle by Clements and Ellerton ><http://squeakland.org/pipermail/squeakland/2007-August/003741.html>http://squeakland.org/pipermail/squeakland/2007-August/003741.html >For some reason the way curriculum is written excludes the people >who would be able to write a good curriculum -> those with both >subject and child development expertise > >For me the key section of the history was this: >"Sifting through the claims and counterclaims, journalists of the >1990s tended to portray the math wars as an extended disagreement >between those who wanted basic skills versus those who favored >conceptual understanding of mathematics. The parents and >mathematicians who criticized the NCTM aligned curricula were >portrayed as proponents of basic skills, while educational >administrators, professors of education, and other defenders of >these programs, were portrayed as proponents of conceptual >understanding, and sometimes even "higher order thinking." This >dichotomy is implausible. The parents leading the opposition to the >NCTM Standards, as discussed below, had considerable expertise in >mathematics, generally exceeding that of the education >professionals. This was even more the case of the large number of >mathematicians who criticized these programs. Among them were some >of the world's most distinguished mathematicians, in some cases with >mathematical capabilities near the very limits of human ability. By >contrast, many of the education professionals who spoke of >"conceptual understanding" lacked even a rudimentary knowledge of mathematics. > >More fundamentally, the separation of conceptual understanding from >basic skills in mathematics is misguided. It is not possible to >teach conceptual understanding in mathematics without the supporting >basic skills, and basic skills are weakened by a lack of >understanding. The essential connection between basic skills and >understanding of concepts in mathematics was perhaps most eloquently >explained by U.C. Berkeley mathematician Hung-Hsi Wu in his paper, >Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in >Mathematics Education.75" > >Papert is also critical of NCTM but is clearly both a good >mathematician and someone who understands child development - and >has put himself into the constructivist / constructionist group > >I followed that link in the history to this paper which is a more >direct and concrete critique of discovery learning taken too far, >with well explained examples of different approaches: > ><http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf>http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf > >BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING >A Bogus Dichotomy in Mathematics Education >BY H. WU > >cheers, >-- >Bill Kerr ><http://billkerr2.blogspot.com/>http://billkerr2.blogspot.com/

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squeakland November 2007