> We can safely ignore the C and D words in favor of the E and T words (or the M and S words)
hi alan, thanks for a very valuable post on the nature of educational surveys - and your reasons for not using the C (constructivism) or D (direct instruction) words unfortunately your final sentence threw me, what are the E,T, M and S words? cheers, - Bill On Wed, Jul 23, 2008 at 6:34 AM, Alan Kay <[EMAIL PROTECTED]> wrote: > Hi Bill -- > > Suppose we take as a premise that the following results of surveys over the > last 20 years were gathered well enough to form a real generalization: > - only 20% of American adults can read a well written important ideas essay > (they used Tom Paine's "Common Sense"), and understand it well enough to > discuss it, write about it, criticize it, advocate it, etc. (National > Literacy Foundation) > - only 5% of American adults are "literate/fluent" enough in math & science > to deal with mainstream ideas, have an extended conversation with a > mathematician or scientist, be operational enough to put a mathematical map > on a set of ideas and do something with them, etc. > > If we weed a few more artifacts out of this survey (and the surveyors did > some of this already -- such as not counting those who were not educated in > American schools, etc.), then we can pretty reasonably conclude that the > schemes of education employed in the US have failed (miserably) to meet the > goals of education in America. > > The reason I say "suppose ... premise" above is that we have to be very > careful about "scientific studies" outside of "science", because sometimes > only the trappings and not the substance of "science" remains. In the above > case, it looks as though (especially) the NLF did a comprehensive job of > sampling and concluding. > > However, this is not often the case in most studies of educational methods > and results. And, it is very difficult to separate out and test any method > from the testing that is also going on of evaluating how well randomly > chosen teachers in America can teach anything in any style. I would posit > that trying to do this in single trials is essentially intractable. > > I've mentioned before that just validating a piece of our curriculum > requires three years of doing it with a teacher in a classroom before enough > of the artifacts and distracters can be nudged out to get even a qualitative > judgment. (In our case, this has very often been a "no, this is not a good > way to approach this that will get more than 90% of the children above a > real fluency threshold" -- i.e. failure.) No-one wants to pay for these > extra years, so we use our discretionary research budget to support the > extra costs and time. > > A much more important kind of investigation in education is a "transfer > study", which is all about whether enough of both practical and abstract > understanding is retained and operationalized enough to be applied by the > learner in later contexts (both related to the original learning and in > areas where there could be very fruitful analogies). For example, in the 70s > Adele Goldberg and I designed an extensive transfer study to see if > "powerful ideas in programming/active-math" could be foundations for more > powerful learning and thinking in other fields (we chose major parts of > Biology). Because of the kind of setups and testing needed, we thought that > at least 7 years should be devoted to this. For example, there were several > overlapping three year implementations in the programming/active-math ideas, > and the kind of testing we had already been doing, and then there would have > to be another series of these in the later experimental and control classes > when the children started learning about Biology. > > Needless to say NSF turned this down flat, and turned down several > subsequent requests we made. > > However, even if they had funded the study, we realized that it would be > adding more of the largest problem of doing anything in a school with math > or science, which is working with teachers who don't remotely understand > their subjects -- and (even in the case of reading and writing) don't do the > activities with the children (when was the last time you saw a 5th grade > teacher assign a composition to the students and then let the students pick > a topic for them and write an essay along with the students?). (Actually, > given the excellence of your blog, you might be an exception!) > > This, along with many other reasons, is why I don't worry about the "C" > word or the "D" word, or any other simple scheme. As Marvin Minsky once > pointed out, every educational method works for some students. This is > because another deeply important factor is that children in a single > classroom exhibit a wide variation in motivations, knowledge, skills, > maturity and "wiring". Different children need different approaches. A > classroom is a tough place to learn anything (as an orchestra is a tough > place to learn how to play an instrument). The US factory approach to > education was hoping for economies of scales via method, but it forgot that > it wasn't about just turning out Model-T's, but every kind and variation of > vehicle using every kind and variation of materials and design. > > Long (very long) ago I was a professional musician (jazz guitar) and also > taught guitar for a few years. The basics for musical learning are rather > similar to sports learning, and they involve rather different approaches and > mixes of processes than in formal schools. (Of course, they might be so > different from learning math that no analogies will hold -- but let's > pretend that they aren't so different.) > > The goal in music-sports is fluent playing. It is not known how to do this > without having the learners undergo a lot of "doing of playing". However, > there is not a lot of discovery to be done early on that is going to help > and not hinder later on (i.e. most ideas are mediocre down to bad -- this is > why good ideas are so rare and precious). But, as Tim Gallwey the great > tennis teacher says, "The problem with most theories of learning is that the > parts of your body that need to learn, don't understand English!" Saying it > a different way, the parts of our mind that do understand natural language, > aren't often able to do other subjects well. We can see this is also true > for math and science -- otherwise we could just write the best expositional > essay on each subject (called "great books") and just get the learners to > read them! And, imagine how easy it would be to teach teen-agers to drive a > car! Obviously, other elements are vital. > > If we combine a few ideas -- e.g. discovery is really difficult, it's hard > to learn via language, we have limited capacity for dealing with ideas at > one time (7+-2 according to George Miller), etc. -- then we can see that > Jerry Bruner's notion of "scaffolding" starts to come front and center as a > way to devise strategies for learning sequences. For example, a teacher can > set things up so that only a few degrees of freedom remain, and now there is > a much higher chance of actual discovery, or homing in on what is best to > concentrate on. This is done all the time in music-sports. > > For example, Ted Williams introduced the batting tee into professional > baseball and was pooh-poohed for "silly, unmanly, etc.". But he was the > greatest hitter of his day (and one of the greatest of all time) so > gradually others began to surreptitiously practice. His idea was that it was > almost impossible even getting the muscular feeling and memory for a level > swing if you are going against a moving target of "round thing against round > thing". Now the batting tee is found in every training facility for all > levels of baseball and there is even a league for very young players. > > Scaffolding has to be carefully vetted. For example, short skis really seem > to work for learning beginning skiing, but putting frets on a violin doesn't > (even though they seem to help in the beginning - then they hurt badly). > However, "multiperson African Drumming" really does help all aspects of > music learning, including classical music. > > Showing" often helps. If you can't feel the phrasing of a musical sequence, > sometimes it's just best for the teacher to play various phrasings to be > judged. Or to get you to watch them serve (the flip side of this is that the > top tennis pros have rather different strokes and serves -- i.e. personal > wirings and idiosyncrasies have to be tolerated -- it is very difficult to > learn exactly what someone else does -- but one can learn "just as well > though a little differently"). > > This hurts badly in school when the teachers don't know enough math or > science to be flexible about perspectives, etc. We would be surprised if our > music or tennis teacher weren't fluent and refused to play with us (for one > thing, that's the best way for them to assess where their students are) -- > we would doubtless drop a "non-doing" teacher. But the opposite is > egregiously true for most school teachers, most are not and have never been > practitioners. However, we only see a few parents take their kids out of > public school for such reasons. > > We could well imagine that one form of instruction might score better than > another if teachers are not up to snuff (however, as mentioned above, the > "better" is not nearly good enough to get the eventual American adults above > any reasonable threshold). If we are going for "evidence" and "scientific > evaluation", then we have to include getting to real thresholds, not just > relative differences. Here, all methods currently fail -- and probably will > until better conceptions and thresholds are created for teachers. > > Gallwey again: "You still have to hit thousands of balls to learn tennis, > the difference is what you are thinking about and how you are focusing while > doing". > > This is as good a key to progress as any. > > An interesting paper by one of your countrymen that Mark Guzdial pointed me > to (After the Gold Rush: Toward Sustainable Scholarship in Computing, by > Raymond Lister, University of Technology, Sydney, Australia -- > http://crpit.com/confpapers/CRPITV78Lister.pdf ) shows some of the > difficulties of dealing with this very complex area. I don't know quite how > to do justice to a counter argument in a very short space here, but I think > there are real parallels with what happens with learning programming (he > gives his POV as a college teacher of programming) to what happens with > learning music, sports, and even driving a car, if the learners don't do > enough of the actual processes. For example, he makes the (to me) astounding > statement that: > > I taught a first semester programming subject, where the final exam > consisted entirely of multiple-choice questions (Lister & Leaney, 2003a&b; > Lister, 2005). I adopted that style of exam because it was clear to me > that many students could not write code by the end of first semester, and > I was tired of setting and marking exams where I pretended that students > could write code. > > They couldn't write code at the end of a semester? Was the course about > anything else? What kind of grades could he be giving? "Air guitar" grades > for "air programming"? > > Much other of interest will be found herein. > > There aren't enough details in the paper to comment on his teaching style > or to guess why his students couldn't program at the end of a semester. > (This is not the only such story that has been written up over the years.) > In some of the latter cases, I knew some of the instructors and they were > not dunderheads by any means. So we could certainly give Mr. Lister the > benefit of the doubt, and wonder instead about the processes in his class > and in universities in general. > > Now, if we do the (so far unwarranted) act of substituting music, sports or > even driving a car, we might guess that the main reason the students were in > this unhappy state at the end of a semester is because of the pace, depth > and amount (if not also the nature) of the doing experience. > > Another unwarranted comparison is to the way programmers were created in > the military services in the 50s and 60s. Virtually all participants were > enlisted personnel without college educations and some without high school. > Programming was needed, but was not glamorous enough to be within the ken of > the college educated officers. > > Prospects (in this case, the Air Force) were given a short aptitude test > (about 45 minutes) made up by IBM that essentially assessed interests and > latent abilities in patterns of various kinds. Only people who got through > this went to the next state -- which was a one week wall-to-wall (40 hours > of class plus lots of assignments) of instruction in how to program a > computer. This was also conducted by IBM, and in my memory was just about > perfect in the balance of description, advice, examples, and many doings > with one's own code. (I had similar favorable impressions with the rest of > the training I got while in the military -- the only thing left out was > "education", meaning that "theory" was scant -- every other aspect could not > have been better thought through and presented.) > > One hectic week later, one knew the machine code and assembler and could > write many programs for the real computer that was back on base, and that > was what we did to other's goals for several months. This was intensive and > literally "on the job training". One thing that people find unusual today, > was that not only was there no interactive programming (punched cards were > submitted for a batch run), but one was allowed a maximum of five minutes > actual contact each day, not with the machine, but via an operator who ran > the machine, could punch in addresses, etc. One had one's listing draped > over the card reader and was kept well away from the console. Basically, the > only way you could get a program to run was to have it be "almost perfect" > before testing. This was accomplished via another developed skill called > "desk checking" (Don Knuth attributes his facility with programming to this > quaint process as well.) > > Then there was another intensive week of wall-to-wall "Advanced > Programming" in which one learned a little more architecture and how to use > the extensive macro facility in the assembler, etc. I will only compare the > first intensive week and month or so which resulted in real programming > skills to Lister's very different experience in university. > > The point here is that the armed services scheme had almost no failures, > everyone who went through it was successful. The instructors weren't any > better than the college professors, but the process really was. And the > goals were very different. There wasn't any class to pass, no multiple > choice tests to take, no grading on the curve, only a few hours of "lecture" > (and just when needed), and (no small matter) there was nothing to do but to > learn programming that "semester". The basic idea here in 1961 (I think) was > that if you can think a little, then a "summer music camp" approach is the > best way to really get going on something. If you can't think a little (play > a musical instrument a little) then you should get across this threshold and > then go to summer camp. > > (Way afield, CMU did something quite similar and very wonderful and > successful for their incoming CS grad students wrt CS at CMU.) > > Again, this successful scheme doesn't necessarily generalize to every > subject. But it's strong enough to be worth considering in areas where > "doing skills" are an important part of the subject. (One problem with > "math" in the US is that it isn't actually "math" but only simple > calculation skills. This isn't enough to help with actual math thinking > (which is a special skill all its own that can indeed be taught, but isn't.) > > An important aspect of this approach is that it nicely avoids having to > categorize methods: it is really about a somewhat vague but readily > understandable approach in which the only real goal is to help the learner > achieve fluency in "something that is done". We can safely ignore the C and > D words in favor of the E and T words (or the M and S words). > > > Best wishes, > > Alan > > ----- Original Message ---- > From: Bill Kerr <[EMAIL PROTECTED]> > To: Albert Cahalan <[EMAIL PROTECTED]> > Cc: [EMAIL PROTECTED] > Sent: Monday, July 21, 2008 7:08:49 PM > Subject: Re: [IAEP] reconstructed maths > > On Thu, Jul 17, 2008 at 7:16 PM, Albert Cahalan <[EMAIL PROTECTED]> > wrote: > >> Alan Kay writes: >> >> > Similarly, from the POV of a former guitar teacher and player, >> > "playing guitar" has a threshold that excludes "air guitar", >> > "Guitar Hero", certain kinds of noise, and "not enough fluency >> > to make music yet". We can use "air guitar" as a metaphor for >> > (a) taking such a small subset of an activity that only some >> > form and essentially no important content is being done, and >> > (b) for using form over content to fool ourselves that we are >> > "players" and "part of the club". >> >> That works. I also like the term "math appreciation". >> Like a music appreciation course, it doesn't get you >> to be competent. >> >> > Two of Seymour Papert's most important insights about above >> > threshold math-with-computers for children were to (a) find and >> > use the real mathematical thinking that children could do at each >> > stage of development, and (b) to both pick from the large body of >> > existing mathematics and to invent new mathematics that embody the >> > most "powerful ideas" that humans have come up with. One of many >> > such examples is how to use the children's ability to add (and to >> > think additively) and to physically move their bodies to make for >> > them a powerful and valid version of Gauss' Differential Geometry >> > which covers some of the most important parts of vector calculus >> > in a way easily learnable by children. >> >> I do believe that many children can learn vector calculus, and that >> this might have some value. However... >> >> When you put the cart before the horse, trying to skip all of the >> arithmetic and such, you're teaching math appreciation. It's air math. >> >> An actual bake-off has been conducted. It was the largest educational >> study ever done, covering 79000 children in 180 communities. I'm sure >> you've heard of it: Project Follow Through. >> >> In that study, Direct Instruction (sage on the stage) trounced all >> other programs in multiple ways. More here: >> >> http://www.jefflindsay.com/EducData.shtml >> http://www.illinoisloop.org/oswegomath.html >> http://www.heartland.org/Article.cfm?artId=19790 >> >> That last article has a lovely graph of the results. >> >> One may question the ethics of such an experiment, since it does in >> fact involve experimenting on children in a life-effecting way. >> I see no alternative though, so I'm glad it was done. Now it is time >> to accept the results, eat some humble pie as required, and teach >> children math. >> >> It is unethical to endlessly repeat the experiment, hoping that you >> will somehow get results that support a well-loved hypothesis. >> >> Vector calculus is a fine subject for children. Set high expectations >> for daily progress, eliminate distractions, and soon enough most kids >> will reach vector calculus. (for real, not vector calculus appreciation) >> >> High expectations go something like this: >> >> multi-digit add/subtract with traditional procedure: 1st year >> multiplication table memorized: 1st year >> long division: 2nd year >> 2-step word problems: 2nd year >> 4 basic operations on fractions: 3rd year >> 4-step word problems: 4th year >> order of operations: 4th year >> algebra (with proofs): 5th year >> geometry (with proofs) and trig: 6th year >> regular calculus: 7th year >> vector calculus: 8th year >> >> It's doable, but you won't get there if you waste time or if you use >> educational methods that are proven to be horrible. >> >> In case anybody wants to look at current curriculum that work: >> >> The two best math programs, unfortunately subject to copyright, are >> Saxon Math and Singapore Math. Saxon Math is better for the slower >> students, particularly if students are missing school or transferring >> in from places that use a different math program. Singapore Math is >> better for the faster students. Both are available for purchase. > > > > hi albert, > > thanks for raising an issue sharply that does need to be discussed > > misunderstandings and misrepresentations aside, I'd raise this point in > response - your assumption is that a large scale study is more important > than the individual research and findings of one person > > I don't see why this assumption should necessarily be true - ie. > historically it has been shown many times that lone individuals or small > groups have turned out to be correct and the predominant or mainstream way > of doing things has eventually been displaced - that is the nature of > scientific revolutions > > it could be that whole systems have been built and maintained for > generations on principles of direct instruction - that various challenges to > this have arisen and been trialled, some good, some not so good - but > throughout this process the predominant form of teaching has remained direct > instruction > > it seems to me that in a system that has evolved in that way, that due to > forces of inertia and group think mainstream studies would tend to show that > mainstream ways of doing things are the "best way" > > Piaget did many studies and wrote many books and papers based on the study > of 3 children - that does not in itself make him wrong. He might be wrong > but I can see many advantages of doing in depth studies based on a small > group. > > I would like to discuss this issue more, just raising it here in simple > form --> minority views are not wrong because they are minority views > > Of course your challenge still applies as a practical issue for those who > want to go beyond direct instruction at least in some respects > > cheers, > - Bill > >
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