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#331
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Seeking straight A's, parents push for pills
"Herman Rubin" wrote in message ... In article , Chookie wrote: In article , Rosalie B. wrote: There are some things that just have to be memorized. Med students use "On Old Olympus Towering Top A Finn and German Viewed Some Hops" for the 12 Cranial Nerves - Olfactory, Optic, Oculomotor, Trochlear, Trigeminal, Abducens, Facial, Glossopharyngeal nerve, Vagus nerve, Spinal Accessory nerve, and Hypoglossal nerve. I like looking at mnemonics, but I've never been able to make them work for me. Not only do you have to remember the mnemonic, you have to remember what it's associated with, *and* the words you had trouble remembering in the first place! The only aide-memoire I use is "Thirty days hath September..." The particular mnemonic listed here would not help me at all. About the only non-trivial one that I have seen which could be used is the one for the order of the classes of stars, as each class is designated by only one letter. G I know the feeling...there is another one--make a fist, and "count" your months on the exposed knecked on the back of your hands, with January on the knuckle, February in the crease, March on the knuckle, etc...August starts the next round, on top of a knuckle...the ones up high have 31 days, the ones down low do not.......a visual representation G -- Buny " Nobody realizes that some people expend tremendous energy merely to be normal." ~ Albert Camus |
#332
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Seeking straight A's, parents push for pills
Herman Rubin wrote:
In article . com, laraine wrote: Herman Rubin wrote: I also question the utility of English literature, unless you are going to discuss that literature. Well, discussion is the core of liberal arts, IMO. (And, as far as rigor, literary critism might be going in the direction of philosophy in its logical sense, I believe, or is trying to do so --I just saw a reference to a book on the philosophy of feminism.) But, here's another example of the utility of English literatu Dr. Rubin writes a book, non-fiction or fiction, describing a math classroom as he would like it to be taught. Perhaps he could just outline ideas, or perhaps he could write a story where an intelligent student was not able to make a difference in the world because she was not properly taught the concepts, or something like that. You are assuming that mathematics should be taught in a classroom run as the typical present elementary school classrooms are run. No, I haven't assumed that--I don't yet feel knowledgeable enough to make a judgment about it. Consider that when those who understood the concepts taught it, the original "new math" was hardly a failure, or it would never have been adopted. I think that I was taught 'new math' in elementary school in the 70's. In any case, I personally found the textbooks excellent, and I don't recall too many people having trouble with them. My recollection is that people did reasonably well until they got to algebra. The 'new math' was not as complex as what Tom Lehrer makes fun of, though, when I studied it. What I didn't like was the year and a half I had in 6th and part of 7th grade when there were no math lectures, and we essentially worked independently. It would have been better, I think, if a computer could have given us each the right kinds of problems geared to our individual abilities, but we were essentially on our own (with a teacher who would privately answer questions). Also, we have evidence that strong logic can be taught in elementary school, I recall learning a lot of elementary set theory. That seems similar. and that a good proportion of high school students could handle "Euclid" geometry. In my time, in Chicago the high school enrollment was quite high. We also know that 60 years ago (and earlier) the standard high school curriculum for going to college required a good proof-oriented geometry course. It's funny--I have met people who have told me that they found geometry much easier than algebra. Now, I found algebra much easier than geometry. I don't know the reason for that. That would be much easier and possibly more sobering to read than the many letters on this newsgroup, which, while they are quite enlightening and entertaining at times (and a sort of literature in themselves), are also repetitive, disorganized, and don't seem to lead to many clear suggestions of solutions. The existence of such books might also encourage discussion from educators or at least mathematicians everywhere. The books will almost entirely have to be written. So perhaps you are proposing that a new textbook needs to be written specifically for exceptionally gifted children in math. The books that my son studied to learn logic are available, but I doubt that many primary school children can handle them. The one he learned algebra from might be a possibility for someone who has already learned to read. The book which I recommend for "adults" to learn the ordinal approach to the integers was definitely written for those who were adept at using algebra and had some idea of a proof, and who were willing to see that the details could be filled in. It is not appropriate for beginning teaching, and in fact it is even inadequate in its treatment of the integers, as it does not go into positional notation. But making sense of positional notation requires ordinals. I recall learning about different bases in elementary school--it didn't seem like a big issue. Wasn't that part of the 'new math?' Those who produced the new math materials did not start with a finished product. We can to some extent go back to the old structured materials we had before the idea that children should always be with their age groups was imposed, and the idea of "relevance" instead of learning for the distant future, and doing things in a manner removing repetition, were the rule. -- So, you mean to start more from scratch than what those who designed 'new math' started with? C. |
#333
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Seeking straight A's, parents push for pills
In article om,
laraine wrote: Herman Rubin wrote: In article . com, laraine wrote: Herman Rubin wrote: I also question the utility of English literature, unless you are going to discuss that literature. Well, discussion is the core of liberal arts, IMO. (And, as far as rigor, literary critism might be going in the direction of philosophy in its logical sense, I believe, or is trying to do so --I just saw a reference to a book on the philosophy of feminism.) But, here's another example of the utility of English literatu Dr. Rubin writes a book, non-fiction or fiction, describing a math classroom as he would like it to be taught. Perhaps he could just outline ideas, or perhaps he could write a story where an intelligent student was not able to make a difference in the world because she was not properly taught the concepts, or something like that. You are assuming that mathematics should be taught in a classroom run as the typical present elementary school classrooms are run. No, I haven't assumed that--I don't yet feel knowledgeable enough to make a judgment about it. Consider that when those who understood the concepts taught it, the original "new math" was hardly a failure, or it would never have been adopted. I think that I was taught 'new math' in elementary school in the 70's. In any case, I personally found the textbooks excellent, and I don't recall too many people having trouble with them. My recollection is that people did reasonably well until they got to algebra. The 'new math' was not as complex as what Tom Lehrer makes fun of, though, when I studied it. This was not that common; the big problem was the teachers. Many new math books had considerable use of variables. As I keep pointing out, it is the linguistic use of these which is the important one, and do not try to skimp on how many are used. Most algebra books discuss solution of one equation in one unknown, and then give many problems which should not even be tried with one unknown. Use as many as you want, and use the rule of equality to eliminate. What I didn't like was the year and a half I had in 6th and part of 7th grade when there were no math lectures, and we essentially worked independently. It would have been better, I think, if a computer could have given us each the right kinds of problems geared to our individual abilities, but we were essentially on our own (with a teacher who would privately answer questions). Also, we have evidence that strong logic can be taught in elementary school, I recall learning a lot of elementary set theory. That seems similar. No, this is merely sentential logic. Very little can be done with it; what is needed is predicate logic, with quantification only over individuals. This is definitely more complicated, but not that much, in its rules, and when it comes to using it, it is much harder. It is adequate for all of mathematics, and any question in sentential calculus can be automatically answered. and that a good proportion of high school students could handle "Euclid" geometry. In my time, in Chicago the high school enrollment was quite high. We also know that 60 years ago (and earlier) the standard high school curriculum for going to college required a good proof-oriented geometry course. It's funny--I have met people who have told me that they found geometry much easier than algebra. Now, I found algebra much easier than geometry. I don't know the reason for that. Which geometry? The "Euclid" course is rarely given now, except as an honors course. But Euclidean geometry is a totally different subject than algebra; high school level algebra essentially deals with real numbers, while geometry deals with idealized points, lines, circles, etc. It does contain some algebra, in that it uses special cases of the rule of equality. That would be much easier and possibly more sobering to read than the many letters on this newsgroup, which, while they are quite enlightening and entertaining at times (and a sort of literature in themselves), are also repetitive, disorganized, and don't seem to lead to many clear suggestions of solutions. The existence of such books might also encourage discussion from educators or at least mathematicians everywhere. The books will almost entirely have to be written. So perhaps you are proposing that a new textbook needs to be written specifically for exceptionally gifted children in math. An exceptionally gifted child can use the existing books. My son did, with not that much help. In fact, for logic he used two books, with somewhat different notations, around age 6. It would not be difficult to write a logic text which could be used by average elementary school children with a good teacher; with some modifications, my late wife's book can almost do this, although it was written for juniors in college. If someone is interested in making the modifications, I would be glad to cooperate, including introductory material on variables which could be used with beginning reading. I am NOT a writer, and I know how much work is involved in writing a book. In this case, there are good templates to work from, so it will be easier. The books that my son studied to learn logic are available, but I doubt that many primary school children can handle them. The one he learned algebra from might be a possibility for someone who has already learned to read. The book which I recommend for "adults" to learn the ordinal approach to the integers was definitely written for those who were adept at using algebra and had some idea of a proof, and who were willing to see that the details could be filled in. It is not appropriate for beginning teaching, and in fact it is even inadequate in its treatment of the integers, as it does not go into positional notation. But making sense of positional notation requires ordinals. I recall learning about different bases in elementary school--it didn't seem like a big issue. Wasn't that part of the 'new math?' It is a minor part. The important aspect of this is that there are lots of representations for numbers, and it is mainly a matter of convenience which to use. I am not that familiar with the Mayan representation, but most of the representations did not use the same characters in different positions, which requires the "zero" character. It does not make that much difference, until one gets into numbers with large numbers of digits, which is relatively modern. Those who produced the new math materials did not start with a finished product. We can to some extent go back to the old structured materials we had before the idea that children should always be with their age groups was imposed, and the idea of "relevance" instead of learning for the distant future, and doing things in a manner removing repetition, were the rule. So, you mean to start more from scratch than what those who designed 'new math' started with? In my opinion, and it was my opinion more than 50 years ago, the new math made the mistake of concentrating on the cardinal representation of numbers. It is deceptively easy, but there are major difficulties, including what is a finite number. The only fully adequate "definition" of this is one which can be counted and the counting terminates. This brings in the ordinal counting process. The ordinal approach is self-contained, and the definitions are clearly definitions. One should do both; the cardinal (how many) and the ordinal (count in order) concepts describe the same finite objects, but give different ways of looking at them. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University Phone: (765)494-6054 FAX: (765)494-0558 |
#334
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Seeking straight A's, parents push for pills
Herman Rubin wrote:
In article om, laraine wrote: Herman Rubin wrote: In article . com, laraine wrote: Herman Rubin wrote: I also question the utility of English literature, unless you are going to discuss that literature. Well, discussion is the core of liberal arts, IMO. (And, as far as rigor, literary critism might be going in the direction of philosophy in its logical sense, I believe, or is trying to do so --I just saw a reference to a book on the philosophy of feminism.) But, here's another example of the utility of English literatu Dr. Rubin writes a book, non-fiction or fiction, describing a math classroom as he would like it to be taught. Perhaps he could just outline ideas, or perhaps he could write a story where an intelligent student was not able to make a difference in the world because she was not properly taught the concepts, or something like that. You are assuming that mathematics should be taught in a classroom run as the typical present elementary school classrooms are run. No, I haven't assumed that--I don't yet feel knowledgeable enough to make a judgment about it. Consider that when those who understood the concepts taught it, the original "new math" was hardly a failure, or it would never have been adopted. I think that I was taught 'new math' in elementary school in the 70's. In any case, I personally found the textbooks excellent, and I don't recall too many people having trouble with them. My recollection is that people did reasonably well until they got to algebra. The 'new math' was not as complex as what Tom Lehrer makes fun of, though, when I studied it. This was not that common; the big problem was the teachers. Many new math books had considerable use of variables. As I keep pointing out, it is the linguistic use of these which is the important one, and do not try to skimp on how many are used. Most algebra books discuss solution of one equation in one unknown, and then give many problems which should not even be tried with one unknown. Use as many as you want, and use the rule of equality to eliminate. What I didn't like was the year and a half I had in 6th and part of 7th grade when there were no math lectures, and we essentially worked independently. It would have been better, I think, if a computer could have given us each the right kinds of problems geared to our individual abilities, but we were essentially on our own (with a teacher who would privately answer questions). Also, we have evidence that strong logic can be taught in elementary school, I recall learning a lot of elementary set theory. That seems similar. No, this is merely sentential logic. Very little can be done with it; what is needed is predicate logic, with quantification only over individuals. This is definitely more complicated, but not that much, in its rules, and when it comes to using it, it is much harder. It is adequate for all of mathematics, and any question in sentential calculus can be automatically answered. and that a good proportion of high school students could handle "Euclid" geometry. In my time, in Chicago the high school enrollment was quite high. We also know that 60 years ago (and earlier) the standard high school curriculum for going to college required a good proof-oriented geometry course. It's funny--I have met people who have told me that they found geometry much easier than algebra. Now, I found algebra much easier than geometry. I don't know the reason for that. Which geometry? The "Euclid" course is rarely given now, except as an honors course. But Euclidean geometry is a totally different subject than algebra; high school level algebra essentially deals with real numbers, while geometry deals with idealized points, lines, circles, etc. It does contain some algebra, in that it uses special cases of the rule of equality. Interesting... I have never thought of algebra as dealing with real numbers--I thought that was more of a calculus issue. I always thought that the goal of algebra was to set up the problem, then solve for the unknown variable (or variables), whether they represented integers, reals, or something else. Sorry if I am woefully ignorant about the philosophical structure of mathematics. I did take a proof-oriented geometry course in high school in the late 70's. Looking at Euclid's "Elements" on the web, though, I'd have to say that my course was taught at a more basic level. Perhaps the issue with such courses now is that the homework can take quite a bit of time, and homework seems to be a no-no these days. That would be much easier and possibly more sobering to read than the many letters on this newsgroup, which, while they are quite enlightening and entertaining at times (and a sort of literature in themselves), are also repetitive, disorganized, and don't seem to lead to many clear suggestions of solutions. The existence of such books might also encourage discussion from educators or at least mathematicians everywhere. The books will almost entirely have to be written. So perhaps you are proposing that a new textbook needs to be written specifically for exceptionally gifted children in math. An exceptionally gifted child can use the existing books. My son did, with not that much help. In fact, for logic he used two books, with somewhat different notations, around age 6. It would not be difficult to write a logic text which could be used by average elementary school children with a good teacher; with some modifications, my late wife's book can almost do this, although it was written for juniors in college. If someone is interested in making the modifications, I would be glad to cooperate, including introductory material on variables which could be used with beginning reading. I am NOT a writer, and I know how much work is involved in writing a book. In this case, there are good templates to work from, so it will be easier. Well, one piece of advice I can give you if you decide to do this (and if you want my advice), is to do it in small pieces, and get feedback from your audience (some exceptionally gifted children) as you are working on it. I'm sure many in these newsgroups would be interested in discussing it with you too. It sounds challenging, however, to go from a junior level college text to something for early elementary school. You might want someone extra (perhaps a mathematician who has taught elementary school?) to help you. I think I have found some references to your wife's books (sorry to be nosy), so when I get a chance, I'll take a look at them just to see what it is that you are talking about. The books that my son studied to learn logic are available, but I doubt that many primary school children can handle them. The one he learned algebra from might be a possibility for someone who has already learned to read. The book which I recommend for "adults" to learn the ordinal approach to the integers was definitely written for those who were adept at using algebra and had some idea of a proof, and who were willing to see that the details could be filled in. It is not appropriate for beginning teaching, and in fact it is even inadequate in its treatment of the integers, as it does not go into positional notation. But making sense of positional notation requires ordinals. I recall learning about different bases in elementary school--it didn't seem like a big issue. Wasn't that part of the 'new math?' It is a minor part. The important aspect of this is that there are lots of representations for numbers, and it is mainly a matter of convenience which to use. I am not that familiar with the Mayan representation, but most of the representations did not use the same characters in different positions, which requires the "zero" character. It does not make that much difference, until one gets into numbers with large numbers of digits, which is relatively modern. I remember learning about the Egyptian and Roman numerals. I very much enjoyed learning history and math at the same time, though that was likely meant to be a side issue. Those who produced the new math materials did not start with a finished product. We can to some extent go back to the old structured materials we had before the idea that children should always be with their age groups was imposed, and the idea of "relevance" instead of learning for the distant future, and doing things in a manner removing repetition, were the rule. So, you mean to start more from scratch than what those who designed 'new math' started with? In my opinion, and it was my opinion more than 50 years ago, the new math made the mistake of concentrating on the cardinal representation of numbers. It is deceptively easy, but there are major difficulties, including what is a finite number. The only fully adequate "definition" of this is one which can be counted and the counting terminates. This brings in the ordinal counting process. The ordinal approach is self-contained, and the definitions are clearly definitions. One should do both; the cardinal (how many) and the ordinal (count in order) concepts describe the same finite objects, but give different ways of looking at them. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University Phone: (765)494-6054 FAX: (765)494-0558 |
#335
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Seeking straight A's, parents push for pills
"laraine" wrote in message ps.com... Perhaps the issue with such courses now is that the homework can take quite a bit of time, and homework seems to be a no-no these days. I don't know where you live, but it's so the opposite where I am. The kids are overwhelmed with homework. |
#336
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Seeking straight A's, parents push for pills
In article om,
laraine wrote: Herman Rubin wrote: In article om, laraine wrote: Herman Rubin wrote: In article . com, laraine wrote: Herman Rubin wrote: ............... No, I haven't assumed that--I don't yet feel knowledgeable enough to make a judgment about it. Consider that when those who understood the concepts taught it, the original "new math" was hardly a failure, or it would never have been adopted. I think that I was taught 'new math' in elementary school in the 70's. In any case, I personally found the textbooks excellent, and I don't recall too many people having trouble with them. My recollection is that people did reasonably well until they got to algebra. The 'new math' was not as complex as what Tom Lehrer makes fun of, though, when I studied it. This was not that common; the big problem was the teachers. Many new math books had considerable use of variables. As I keep pointing out, it is the linguistic use of these which is the important one, and do not try to skimp on how many are used. Most algebra books discuss solution of one equation in one unknown, and then give many problems which should not even be tried with one unknown. Use as many as you want, and use the rule of equality to eliminate. What I didn't like was the year and a half I had in 6th and part of 7th grade when there were no math lectures, and we essentially worked independently. It would have been better, I think, if a computer could have given us each the right kinds of problems geared to our individual abilities, but we were essentially on our own (with a teacher who would privately answer questions). Also, we have evidence that strong logic can be taught in elementary school, I recall learning a lot of elementary set theory. That seems similar. No, this is merely sentential logic. Very little can be done with it; what is needed is predicate logic, with quantification only over individuals. This is definitely more complicated, but not that much, in its rules, and when it comes to using it, it is much harder. It is adequate for all of mathematics, and any question in sentential calculus can be automatically answered. and that a good proportion of high school students could handle "Euclid" geometry. In my time, in Chicago the high school enrollment was quite high. We also know that 60 years ago (and earlier) the standard high school curriculum for going to college required a good proof-oriented geometry course. It's funny--I have met people who have told me that they found geometry much easier than algebra. Now, I found algebra much easier than geometry. I don't know the reason for that. Which geometry? The "Euclid" course is rarely given now, except as an honors course. But Euclidean geometry is a totally different subject than algebra; high school level algebra essentially deals with real numbers, while geometry deals with idealized points, lines, circles, etc. It does contain some algebra, in that it uses special cases of the rule of equality. Interesting... I have never thought of algebra as dealing with real numbers--I thought that was more of a calculus issue. I always thought that the goal of algebra was to set up the problem, then solve for the unknown variable (or variables), whether they represented integers, reals, or something else. Sorry if I am woefully ignorant about the philosophical structure of mathematics. If this was what you got, it was better than what most ended up with. But as for details, the only kinds of numbers you had were real, until you got to a small amount of complex. Integers and rational numbers are types of real numbers, and mostly one stays within them. The problem with most students in algebra, and the courses and what they learn reflects this, is that the emphasis is on solving formulated problems, using only routine methods. I have seen an outline which has quite a few rules for handling equations, all of which are special cases of the rule of equality, and the students memorize them one at a time. One of my colleagues told me about a bright minority student who was in danger of flunking out; nobody had told him that he could formulate word problems. I said a bright student; for such, it is that it has not been taught, not that it was not learned. I did take a proof-oriented geometry course in high school in the late 70's. Looking at Euclid's "Elements" on the web, though, I'd have to say that my course was taught at a more basic level. Perhaps the issue with such courses now is that the homework can take quite a bit of time, and homework seems to be a no-no these days. That would be much easier and possibly more sobering to read than the many letters on this newsgroup, which, while they are quite enlightening and entertaining at times (and a sort of literature in themselves), are also repetitive, disorganized, and don't seem to lead to many clear suggestions of solutions. The existence of such books might also encourage discussion from educators or at least mathematicians everywhere. The books will almost entirely have to be written. So perhaps you are proposing that a new textbook needs to be written specifically for exceptionally gifted children in math. An exceptionally gifted child can use the existing books. My son did, with not that much help. In fact, for logic he used two books, with somewhat different notations, around age 6. It would not be difficult to write a logic text which could be used by average elementary school children with a good teacher; with some modifications, my late wife's book can almost do this, although it was written for juniors in college. If someone is interested in making the modifications, I would be glad to cooperate, including introductory material on variables which could be used with beginning reading. I am NOT a writer, and I know how much work is involved in writing a book. In this case, there are good templates to work from, so it will be easier. Well, one piece of advice I can give you if you decide to do this (and if you want my advice), is to do it in small pieces, and get feedback from your audience (some exceptionally gifted children) as you are working on it. I'm sure many in these newsgroups would be interested in discussing it with you too. The pieces cannot be too small, and that has been considered. It sounds challenging, however, to go from a junior level college text to something for early elementary school. You might want someone extra (perhaps a mathematician who has taught elementary school?) to help you. I do not think it harder than the ones which have been taught at the elementary school level, except that the applications, which are not in those other books, may involve unknown material. A small amount of the vocabulary may need to be changed, but not much. I think I have found some references to your wife's books (sorry to be nosy), so when I get a chance, I'll take a look at them just to see what it is that you are talking about. You are likely to have GREAT difficulty with any of the others. They are written for people with considerable mathematical knowledge, while this one, despite it being junior level, has no real prerequisites. The books that my son studied to learn logic are available, but I doubt that many primary school children can handle them. The one he learned algebra from might be a possibility for someone who has already learned to read. The book which I recommend for "adults" to learn the ordinal approach to the integers was definitely written for those who were adept at using algebra and had some idea of a proof, and who were willing to see that the details could be filled in. It is not appropriate for beginning teaching, and in fact it is even inadequate in its treatment of the integers, as it does not go into positional notation. But making sense of positional notation requires ordinals. I recall learning about different bases in elementary school--it didn't seem like a big issue. Wasn't that part of the 'new math?' It is a minor part. The important aspect of this is that there are lots of representations for numbers, and it is mainly a matter of convenience which to use. I am not that familiar with the Mayan representation, but most of the representations did not use the same characters in different positions, which requires the "zero" character. It does not make that much difference, until one gets into numbers with large numbers of digits, which is relatively modern. I remember learning about the Egyptian and Roman numerals. I very much enjoyed learning history and math at the same time, though that was likely meant to be a side issue. Those who produced the new math materials did not start with a finished product. We can to some extent go back to the old structured materials we had before the idea that children should always be with their age groups was imposed, and the idea of "relevance" instead of learning for the distant future, and doing things in a manner removing repetition, were the rule. So, you mean to start more from scratch than what those who designed 'new math' started with? Not really. We do have the theoretical materials in a pedagogical form. The only problems are to combine it all, extend where necessary, produce exercises, and figure out how fast to do it. Find one person willing to work on this with me, as I am not a good writer, and a "self-paced" program without enough exercises can be produced in a few months. In my opinion, and it was my opinion more than 50 years ago, the new math made the mistake of concentrating on the cardinal representation of numbers. It is deceptively easy, but there are major difficulties, including what is a finite number. The only fully adequate "definition" of this is one which can be counted and the counting terminates. This brings in the ordinal counting process. The ordinal approach is self-contained, and the definitions are clearly definitions. One should do both; the cardinal (how many) and the ordinal (count in order) concepts describe the same finite objects, but give different ways of looking at them. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University Phone: (765)494-6054 FAX: (765)494-0558 |
#337
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Seeking straight A's, parents push for pills
On 28 Sep 2006 21:52:37 -0700, "laraine" wrote:
Perhaps the issue with such courses now is that the homework can take quite a bit of time, and homework seems to be a no-no these days. Huh? Most people are claiming their kids have a lot of homework, so I can't see how you can say it's a no-no. -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits |
#338
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Seeking straight A's, parents push for pills
toypup wrote:
"laraine" wrote in message ps.com... Perhaps the issue with such courses now is that the homework can take quite a bit of time, and homework seems to be a no-no these days. I don't know where you live, but it's so the opposite where I am. The kids are overwhelmed with homework. toto wrote: Huh? Most people are claiming their kids have a lot of homework, so I can't see how you can say it's a no-no. I wasn't referring to the current situation in schools, but rather to what I perceive to be the attitude towards homework, particularly busy work, by some on these newsgroups. I realize the discussions about homework go back a few years, so I hope I am not overgeneralizing. The reason I particularly noticed those comments was because I have always been a big fan of homework. I have a fairly poor memory as well as a somewhat short attention span in class, even when I am trying very hard, so doing homework helped me a lot. It gave me time on my own to sift out important concepts and details, and I found repetition to be an advantage for me. But, of course, others might not be like me at all. In any case, if students are assigned a lot of homework these days (and I too have heard that), to expect them to spend a lot more time on proof geometry, advanced physics, etc., if they are not doing so already, is asking a lot, though some of that is helpful for later success if they desire a technical career. C. |
#339
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Seeking straight A's, parents push for pills
Herman Rubin wrote:
The problem with most students in algebra, and the courses and what they learn reflects this, is that the emphasis is on solving formulated problems, using only routine methods. I have seen an outline which has quite a few rules for handling equations, all of which are special cases of the rule of equality, and the students memorize them one at a time. One of my colleagues told me about a bright minority student who was in danger of flunking out; nobody had told him that he could formulate word problems. I said a bright student; for such, it is that it has not been taught, not that it was not learned. An exceptionally gifted child can use the c existing books. My son did, with not that much help. In fact, for logic he used two books, with somewhat different notations, around age 6. It would not be difficult to write a logic text which could be used by average elementary school children with a good teacher; with some modifications, my late wife's book can almost do this, although it was written for juniors in college. If someone is interested in making the modifications, I would be glad to cooperate, including introductory material on variables which could be used with beginning reading. I am NOT a writer, and I know how much work is involved in writing a book. In this case, there are good templates to work from, so it will be easier. Well, one piece of advice I can give you if you decide to do this (and if you want my advice), is to do it in small pieces, and get feedback from your audience (some exceptionally gifted children) as you are working on it. I'm sure many in these newsgroups would be interested in discussing it with you too. The pieces cannot be too small, and that has been considered. It sounds challenging, however, to go from a junior level college text to something for early elementary school. You might want someone extra (perhaps a mathematician who has taught elementary school?) to help you. I do not think it harder than the ones which have been taught at the elementary school level, except that the applications, which are not in those other books, may involve unknown material. A small amount of the vocabulary may need to be changed, but not much. I think I have found some references to your wife's books (sorry to be nosy), so when I get a chance, I'll take a look at them just to see what it is that you are talking about. You are likely to have GREAT difficulty with any of the others. They are written for people with considerable mathematical knowledge, while this one, despite it being junior level, has no real prerequisites. Yes, I definitely want to look at the appropriate text. Are you thinking of 'Set Theory for the Mathematician?' There is at least one mo 'Mathematical Logic Applications and Theory' The books that my son studied to learn logic are available, but I doubt that many primary school children can handle them. The one he learned algebra from might be a possibility for someone who has already learned to read. The book which I recommend for "adults" to learn the ordinal approach to the integers was definitely written for those who were adept at using algebra and had some idea of a proof, and who were willing to see that the details could be filled in. It is not appropriate for beginning teaching, and in fact it is even inadequate in its treatment of the integers, as it does not go into positional notation. But making sense of positional notation requires ordinals. Those additional texts you mention would probably also be useful to look at, if your idea is implemented. Those who produced the new math materials did not start with a finished product. We can to some extent go back to the old structured materials we had before the idea that children should always be with their age groups was imposed, and the idea of "relevance" instead of learning for the distant future, and doing things in a manner removing repetition, were the rule. So, you mean to start more from scratch than what those who designed 'new math' started with? Not really. We do have the theoretical materials in a pedagogical form. The only problems are to combine it all, extend where necessary, produce exercises, and figure out how fast to do it. Find one person willing to work on this with me, as I am not a good writer, and a "self-paced" program without enough exercises can be produced in a few months. It sounds like a possibility, and I have some ideas of whom I could contact for initial advice and information, but I also want to look at the book you mentioned before saying more. I can probably give you a better response in the next five weeks or so. Would you require the writer to work with you at Purdue, for at least some of the time, and would the initial six months of work be a full or part-time task for the writer? C. |
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Seeking straight A's, parents push for pills
In article . com,
laraine wrote: Herman Rubin wrote: ................. I think I have found some references to your wife's books (sorry to be nosy), so when I get a chance, I'll take a look at them just to see what it is that you are talking about. You are likely to have GREAT difficulty with any of the others. They are written for people with considerable mathematical knowledge, while this one, despite it being junior level, has no real prerequisites. Yes, I definitely want to look at the appropriate text. Are you thinking of 'Set Theory for the Mathematician?' No; this is written for graduate students in mathematics, and is fairly difficult. There is at least one mo 'Mathematical Logic Applications and Theory' This is the one. It would take little revision to make this accessible to elementary school children, and possibly primary school. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University Phone: (765)494-6054 FAX: (765)494-0558 |
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