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Family Forum / Parenting / Parenting / July 2008Don't Call It "Algebra"; Call It Something Warm And Fuzzy
COMMENT: Yeah, that's the ticket, call it "Yomomma," or "Slam Dunk." That should create interest in the dumbed-down set. ___________ Would name change help algebra students? Posted by Dave Murray | The Grand Rapids Press July 03, 2008 11:09AM As Shakespeare wrote, a rose by any other name would smell as sweet. But would Algebra 2 be as difficult if it were called something else? State Sen. Wayne Kuipers, R-Holland, recently told a gathering of Kent County school board members that he believes more students would pass the upper-level math course if it were called something less scary. His theory is that students have convinced themselves that algebra is too difficult and that they throw in the towel before giving it a chance. http://blog.mlive.com/grpress/2008/07/would_name_change_help_algebra.html _______ Isn't it true that you use simpler, less scary, names for illnesses and diseases? > COMMENT: Yeah, that's the ticket, call it "Yomomma," or "Slam Dunk." > That should create interest in the dumbed-down set. [quoted text clipped - 21 lines] > http://blog.mlive.com/grpress/2008/07/would_name_change_help_algebra.html > _______ Is it true that you see a school subject and disease as synonymous? >Isn't it true that you use simpler, less scary, names for illnesses >and diseases? [quoted text clipped - 24 lines] >> http://blog.mlive.com/grpress/2008/07/would_name_change_help_algebra.html >> _______ > Is it true that you see a school subject and disease as synonymous? You are unable to see the relationship between the fear of "scary, foreign names" to simpler terms whether it is a school subject or a disease. Try to expand your horizons. > On Sat, 5 Jul 2008 09:16:00 -0400, "Frank Arthur" > <Art@Arthurian.com> [quoted text clipped - 32 lines] >>> http://blog.mlive.com/grpress/2008/07/would_name_change_help_algebra.html >>> _______ >> Is it true that you see a school subject and disease as synonymous? > >You are unable to see the relationship between the fear of "scary, >foreign names" to simpler terms whether it is a school subject or a >disease. Funny how past generations didn't find algebra scary. BOO! You weenies don't seem to mind forcing them to learn Spanish with its foreign names. >Try to expand your horizons. Try to escape the world of dumbed-down left-wing classroom political correctness. Make sure they have "self-esteem, but don't torture them with readin', writin', and 'rithmetic. Heh. ______ >> On Sat, 5 Jul 2008 09:16:00 -0400, "Frank Arthur" >> <Art@Arthurian.com> [quoted text clipped - 32 lines] >>>> http://blog.mlive.com/grpress/2008/07/would_name_change_help_algebra.html >>>> _______ Yes Jack. I see your great literacy in your writing. Nothing like the "good ole days" when everything and everybody worked so well. Don't change anything Jack. And of course you will blame "dumbed-down left-wing classroom political correctness.". You left out "Leftie, Commie, Islamo-Republicrat, Fascist,elitist,Pinko, Liberal, anti-American, centrist,zionazi, child eating faggot." It's your type of contribution to the failures in America. > On Sat, 5 Jul 2008 09:27:32 -0400, "Frank Arthur" > <Art@Arthurian.com> [quoted text clipped - 68 lines] >>>>> http://blog.mlive.com/grpress/2008/07/would_name_change_help_algebra.html >>>>> _______ OK, OK, we'll call "algebra" "kwanzaa maff"! Does that work for you???? ___________ >Yes Jack. I see your great literacy in your writing. Nothing like the >"good ole days" when everything and everybody worked so well. Don't [quoted text clipped - 79 lines] >>>>>> http://blog.mlive.com/grpress/2008/07/would_name_change_help_algebra.html >>>>>> _______ >Isn't it true that you use simpler, less scary, names for illnesses >and diseases? Non-medical people use simpler, but not necessarily less scary terms. E.g., brain cancer sounds scarier than astrocytoma IV. > COMMENT: Yeah, that's the ticket, call it "Yomomma," or "Slam Dunk." > That should create interest in the dumbed-down set. [quoted text clipped - 17 lines] > http://blog.mlive.com/grpress/2008/07/would_name_change_help_algebra.... > _______ Thats about the most rediculous thing that i have ever heard.I do not see how calling algebra,algebra could posibly scare anybody at all.I guess then calling english and history is scaring students also. LOL ................. >Thats about the most rediculous thing that i have ever heard.I do not >see how calling algebra,algebra could posibly scare anybody at all.I >guess then calling english and history is scaring students also. LOL English and history are "ordinary" English words, although most of what is taught in English is not about the English language but is "literature". These subjects also scare students. The subject of algebra started out (barely) with Diophantus, but was somewhat developed by the Muslims in the Middle Ages. There were two terms used: al-muqaballah (sp?), the process of collecting terms, and al-jabr, obtaining the answer. Algebra has now advanced beyond this, starting with European developments in the 16th century, but the term remains. See my other posting in this group for the ideas (but not the details) expressed simply; it should be started very early. The details and practice can come later, and are far more likely to be understood, and as something not mysterious.  SignatureThis 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 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 >COMMENT: Yeah, that's the ticket, call it "Yomomma," or "Slam Dunk." >That should create interest in the dumbed-down set. >___________ >Would name change help algebra students? >Posted by Dave Murray | The Grand Rapids Press July 03, 2008 11:09AM >As Shakespeare wrote, a rose by any other name would smell as sweet. >But would Algebra 2 be as difficult if it were called something else? >State Sen. Wayne Kuipers, R-Holland, recently told a gathering of Kent >County school board members that he believes more students would pass >the upper-level math course if it were called something less scary. >His theory is that students have convinced themselves that algebra is >too difficult and that they throw in the towel before giving it a >chance. Students have not convinced themselves of this; teachers who do not understand algebra, and this includes most algebra teachers and an even higher proportion of elementary school teachers, think it is difficult. The following includes essentially all of algebra, except for technical terms not used at the high school level: A variable is a temporary name for something, which must maintain its meaning in a given context. The same operation performed on equal entities yields equal results. Now of course there is practice involved, and illustration but the above can be taught to those who can just read and write symbols. Translating word problems just uses the first of these; do not stint on the number of variables used. The great bulk of texts start out insisting on the use of one variable only; this is a major crime in achieving any understanding. SignatureThis 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 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 WE CALLS UM KWANZA MAFF AN sh.t >> COMMENT: Yeah, that's the ticket, call it "Yomomma," or "Slam Dunk." >> That should create interest in the dumbed-down set. [quoted text clipped - 36 lines] > use of one variable only; this is a major crime in achieving > any understanding. Signature*I AM A GAY NIGGER JANITOR AT GREYHOUND BUS STATION IN INDIANAPOLIS IND* *ALSO A REGISTERED SEX OFFENDER AND WINNER OF THE DAFN AWARD* *IN CASE OF A BATHROOM MISHAP* *ASK FOR DERRICK LAWRENCE*(*HNIC*) *OGExtremeOne@dizum.com* *have bucket,will travel* *Greyhound Bus Lines* 111 *Monument Cir* *Indianapolis, IN* 46204 *Phone*: (317) 636-6666 > In article <486f7172.10114...@news.datemas.de>, > [quoted text clipped - 16 lines] > algebra teachers and an even higher proportion of elementary > school teachers, think it is difficult. Well, whenever you post this, I ask for some peer-reviewed or other reliable studies supporting your claims that most math teachers in the United States do not understand basic mathematical concepts such as basic high school-level algebra (other than the fact that your repeated statements that this is so). Preferably, this should include information as to how NCLB has affected teacher competence with respect to math. > The following includes essentially all of algebra, except > for technical terms not used at the high school level: [quoted text clipped - 4 lines] > The same operation performed on equal entities > yields equal results. I respectfully disagree. For whatever reason, the term *algebra* has taken on some mythical status as something extremely difficult and fear-inducing. Yet without referring to it as *algebra* per se, the aforementioned concepts are introduced in most math curriculums in the 4th or 5th grade (5th grade at One's school, which uses a truly awful math curriculum). Discussion at lunch -- One's friend: *your school is so far behind ours! WE'RE learning algebra!* One *We're not even close to algebra. We're learning about variables.* Of course, the answer is not to re-name the subject. Rather, the answer is to show the students that algebra isn't that difficult. Barbara > Of course, the answer is not to re-name the subject. Rather, the > answer is to show the students that algebra isn't that difficult. My general suspicion is that the phenomenon isn't unique to 'algebra'. I suspect that the students afraid of 'algebra' are also afraid of 'physics', 'chemistry', 'literature'... etc. They are afraid of any subject that requires that they <gasp!> might have to study in order to learn. Too many are simply intellectually LAZY. On Jul 10, 12:31 pm, Barbara <mom_2_...@hotmail.com> wrote: > On Jul 10, 9:41 am, hru...@odds.stat.purdue.edu (Herman Rubin) wrote: > Of course, the answer is not to re-name the subject. Rather, the > answer is to show the students that algebra isn't that difficult. My general suspicion is that the phenomenon isn't unique to 'algebra'. I suspect that the students afraid of 'algebra' are also afraid of 'physics', 'chemistry', 'literature'... etc. They are afraid of any subject that requires that they <gasp!> might have to study in order to learn. Too many are simply intellectually LAZY. --- What I find humorous is that I was in a teaching store the other day, and saw a series of books starting at 1st grade, labeled "Algebra" (which looked to me like reasonable extention activities for a child who had a good grasp on basic operations, but nothing that hasn't been taught in math classes at that age level, at least to the higher groups, for decades). So, apparently the word Algebra is considered too scary for high school kids to have on a book, but not for a 6 yr old! >On Jul 10, 12:31 pm, Barbara <mom_2_...@hotmail.com> wrote: >> On Jul 10, 9:41 am, hru...@odds.stat.purdue.edu (Herman Rubin) wrote: [quoted text clipped - 16 lines] >the word Algebra is considered too scary for high school kids to have on a >book, but not for a 6 yr old! This kinda reminds me of the town of Ossining, New York. It's the site of Sing Sing prison. Ossining used to be called "Sing Sing", hence the prison name, so Ossining changed their name to be more like the original Indian name. A decade or so ago, Sing Sing was renamed the "Ossining Correctional Institution". Heh. This renaming thing is majorly dumb. Only a non-mathematical (i.e. - verbally inclined) person woudl have thought of it. Banty > > Of course, the answer is not to re-name the subject. Rather, the > > answer is to show the students that algebra isn't that difficult. [quoted text clipped - 4 lines] > any subject that requires that they <gasp!> might have to study > in order to learn. Too many are simply intellectually LAZY. Charles Murray has said that algebra *is* hard for people with IQ's <= 100, and I think he is right: http://www.opinionjournal.com/extra/?id=110009535 What's Wrong With Vocational School? Too many Americans are going to college. by CHARLES MURRAY Wednesday, January 17, 2007 12:01 a.m. EST The topic yesterday was education and children in the lower half of the intelligence distribution. Today I turn to the upper half, people with IQs of 100 or higher. Today's simple truth is that far too many of them are going to four-year colleges. Begin with those barely into the top half, those with average intelligence. To have an IQ of 100 means that a tough high-school course pushes you about as far as your academic talents will take you. If you are average in math ability, you may struggle with algebra and probably fail a calculus course. If you are average in verbal skills, you often misinterpret complex text and make errors in logic. These are not devastating shortcomings. You are smart enough to engage in any of hundreds of occupations. You can acquire more knowledge if it is presented in a format commensurate with your intellectual skills. But a genuine college education in the arts and sciences begins where your skills leave off. In engineering and most of the natural sciences, the demarcation between high-school material and college-level material is brutally obvious. If you cannot handle the math, you cannot pass the courses. In the humanities and social sciences, the demarcation is fuzzier. It is possible for someone with an IQ of 100 to sit in the lectures of Economics 1, read the textbook, and write answers in an examination book. But students who cannot follow complex arguments accurately are not really learning economics. They are taking away a mishmash of half- understood information and outright misunderstandings that probably leave them under the illusion that they know something they do not. (A depressing research literature documents one's inability to recognize one's own incompetence.) Traditionally and properly understood, a four- year college education teaches advanced analytic skills and information at a level that exceeds the intellectual capacity of most people. >> In article <486f7172.10114...@news.datemas.de>, >> [quoted text clipped - 22 lines] >basic high school-level algebra (other than the fact that your >repeated statements that this is so). Herman doesn't consider "basic high school-level algebra" to include the "basic mathematical concepts" that he is talking about, which are theoretical and abstract. He thinks that "basic high school-level algebra" is mostly plug and chug recipes for solving problems, and rote memorization of terminology, and he considers neither of these to be real "mathematics". >> The following includes essentially all of algebra, except >> for technical terms not used at the high school level: [quoted text clipped - 8 lines] >taken on some mythical status as something extremely difficult and >fear-inducing. The reason, as I learned from raising two kids who got that attitude, is that *algebra* IS extremely difficult and fear-inducing. All other subjects (except the more mathematical sciences) use the normal English language, where words have fuzzy meanings that can be gleaned from context, and there is some overlap with the methodology that they use in solving non-academic problems. Mathematical language is first and foremost *precise*. Misspell a word and people will understand you. Fail to remember a word in most subjects, and you can talk around the word and show that you understand. But in mathematics, every step must be followed rigorously, and the most minor error means that you are totally and irrecoverably wrong, unless you notice the error and start over or backtrack. Nothing else in a kid's life works like that. Life allows for some amount of sloppiness. Mathematics does not. Teachers don't know how to teach this (if they realize that this is the essential difference) and kids see it as "difficult" and ultimately not kid-like. >Yet without referring to it as *algebra* per se, the >aforementioned concepts are introduced in most math curriculums in the [quoted text clipped - 5 lines] >Of course, the answer is not to re-name the subject. Rather, the >answer is to show the students that algebra isn't that difficult. You can't show what isn't true. Mathematics is difficult unless one first learns to appreciate precision and rigor. That may be why skilled musicians tend to do well in math - part of becoming skilled is learning that precision. But most kids don't stick with music for the same reason - hours of practice learning to produce precisely the sound you want isn't worth it to them. lojbab Bob LeChevalier - artificial linguist; genealogist lojbab@lojban.org Lojban language www.lojban.org >>> In article <486f7172.10114...@news.datemas.de>, .............. >Herman doesn't consider "basic high school-level algebra" to include >the "basic mathematical concepts" that he is talking about, which are >theoretical and abstract. He thinks that "basic high school-level >algebra" is mostly plug and chug recipes for solving problems, and >rote memorization of terminology, and he considers neither of these to >be real "mathematics". >>> The following includes essentially all of algebra, except >>> for technical terms not used at the high school level: >>> A variable is a temporary name for something, >>> which must maintain its meaning in a given context. >>> The same operation performed on equal entities >>> yields equal results. >>I respectfully disagree. For whatever reason, the term *algebra* has >>taken on some mythical status as something extremely difficult and >>fear-inducing. >The reason, as I learned from raising two kids who got that attitude, >is that *algebra* IS extremely difficult and fear-inducing. >All other subjects (except the more mathematical sciences) use the >normal English language, where words have fuzzy meanings that can be >gleaned from context, and there is some overlap with the methodology >that they use in solving non-academic problems. >Mathematical language is first and foremost *precise*. Misspell a >word and people will understand you. Fail to remember a word in most [quoted text clipped - 7 lines] >difference) and kids see it as "difficult" and ultimately not >kid-like. Unfortunately, teachers who do not know better grade on the answer. One should grade on understanding what is to be done, and as in English, errors should be corrected and pointed out to the student. Often, the teacher grades on whether the problem is done as indicated in the textbook recipe. There may be many ways about doing the problem; if the second sentence is followed, other than arithmetic errors or sloppiness, there will be no mistake made. This precision in mathematics is also needed in ALL of the sciences, and alas the public seems unable to understand that the government cannot just legislate in violation of the laws of nature, and achieve miracles. >>Yet without referring to it as *algebra* per se, the >>aforementioned concepts are introduced in most math curriculums in the >>4th or 5th grade (5th grade at One's school, which uses a truly awful >>math curriculum). Discussion at lunch -- One's friend: *your school >>is so far behind ours! WE'RE learning algebra!* One *We're not even >>close to algebra. We're learning about variables.* >>Of course, the answer is not to re-name the subject. Rather, the >>answer is to show the students that algebra isn't that difficult. >You can't show what isn't true. Mathematics is difficult unless one >first learns to appreciate precision and rigor. That may be why >skilled musicians tend to do well in math - part of becoming skilled >is learning that precision. But most kids don't stick with music for >the same reason - hours of practice learning to produce precisely the >sound you want isn't worth it to them. Teach the appreciation of precision and rigor in first grade, and that part of the problem will disappear. We CAN teach precise mathematical concepts to kids, but it is difficult to do this with adults. Stop hurting children by avoiding the rigor which adults seem unable to understand. SignatureThis 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 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 >>>> In article <486f7172.10114...@news.datemas.de>, > [quoted text clipped - 44 lines] > and as in English, errors should be corrected and pointed out > to the student. Nice in theiry, difficcult to imposssible in real life. How does a teacher determine, for example. whether an error in a computation with negative numbers is lack of understanding, a simple arithemtic error, or a transcription error indropping a sign whe copying from a work sheet. And should sloppiness be punished? How does a teacher determine that an incorrectly set up equation in a word problem is the result of another transcription error, a reading comprehension problem, or a misunderstanding of the underlying math? And then how does a teacher justfy what is no more than a subjective guess to angry parents and administrtors, explaining why Joey got credit and Zooey didn't?. > Often, the teacher grades on whether the problem is done as > indicated in the textbook recipe. Because this is what has been taught, and this is what a student is expected to knwo. In algebra I there is truly little mathematically correct variation from the "book recipe". There is, for example, only one way to write a linear equation in slope-intercept form, onwe way to solve a system of linear equations using hte elimination method, one way to set up a box and whiskers statistcal chart. Yes, there are other ways to "solve" the problem or display the info, but these specific algorithsm are what are being yested and knowlege of them is needed in future courses. So how would you grade a student who uses outstanfing toechnique to rpesent linear eq. in point-slope form when the question alled for the slope-intercept form? Did he just not follow instructions, and shouldn;t that be punished? Did he not knwo the correct form? Did he start out right but lose his way, either taking a wrong path or end toosoon? Further complicating the decision is a certaintity that just becaue he could do the problem correctly ont he board yesterday does not mean he could do it today. There may be many ways > about doing the problem; if the second sentence is followed, > other than arithmetic errors or sloppiness, there will be > no mistake made. But is, for exampel, a long, meadnering process that takes many more steps than needed an indication of knowledge or luck? Andisn;t effciincy an indication of understanding? So, for example, is a process that took 12 steps to combine like terms in an equation as "correct", as good an indicator of knowledge, as one that took 4 steps? > This precision in mathematics is also needed in ALL of the > sciences, and alas the public seems unable to understand that > the government cannot just legislate in violation of the laws > of nature, and achieve miracles. This would severly restrict what can be defined as a "science". Under this requirement medicine, sociology, economics, astronomy, and a whole host of disciplines crrently categorixed as "science" would fail your test. Now this may be good or bad, accurate or inaccurate, right or wrong. But it certianly would be disruptive and chaotic. >>>Yet without referring to it as *algebra* per se, the >>>aforementioned concepts are introduced in most math curriculums in the [quoted text clipped - 18 lines] > do this with adults. Stop hurting children by avoiding the > rigor which adults seem unable to understand. Current knowledge is that children of that age are mentally incapable of the rigor you want. They are incapable of understanding symbolic representation, logical sequences, cause and effect. They have limited vocabularies adn limited abilities to integrate disparate knowedge points into a whole. They are kids, after all, and have not reached adult stages of development. Some will not reach this stage until their late teens. Larry >>>>> In article <486f7172.10114...@news.datemas.de>, .............. >>>Herman doesn't consider "basic high school-level algebra" to include >>>the "basic mathematical concepts" that he is talking about, which are >>>theoretical and abstract. He thinks that "basic high school-level >>>algebra" is mostly plug and chug recipes for solving problems, and >>>rote memorization of terminology, and he considers neither of these to >>>be real "mathematics". >>>>> The following includes essentially all of algebra, except >>>>> for technical terms not used at the high school level: >>>>> A variable is a temporary name for something, >>>>> which must maintain its meaning in a given context. >>>>> The same operation performed on equal entities >>>>> yields equal results. >>>>I respectfully disagree. For whatever reason, the term *algebra* has >>>>taken on some mythical status as something extremely difficult and >>>>fear-inducing. >>>The reason, as I learned from raising two kids who got that attitude, >>>is that *algebra* IS extremely difficult and fear-inducing. >>>All other subjects (except the more mathematical sciences) use the >>>normal English language, where words have fuzzy meanings that can be >>>gleaned from context, and there is some overlap with the methodology >>>that they use in solving non-academic problems. >>>Mathematical language is first and foremost *precise*. Misspell a >>>word and people will understand you. Fail to remember a word in most [quoted text clipped - 7 lines] >>>difference) and kids see it as "difficult" and ultimately not >>>kid-like. >> Unfortunately, teachers who do not know better grade on the >> answer. One should grade on understanding what is to be done, >> and as in English, errors should be corrected and pointed out >> to the student. >Nice in theiry, difficcult to imposssible in real life. >How does a teacher determine, for example. whether an error in a >computation with negative numbers is lack of understanding, a simple >arithemtic error, or a transcription error indropping a sign whe copying >from a work sheet. By having the student put down the work, rather than just the answer. I am the "czar" of our department's qualifiers, and I can assure you that most students make errors on most of the type of problems we assign. We give partial credit, and once the faculty see how to do this, there is not much disagreement on scores. > And should sloppiness be punished? Not heavily. But someone is not going to be a good scientist, and I include the biological and psychological and economic sciences, if there is sloppiness. >How does a teacher determine that an incorrectly set up equation in a word >problem is the result of another transcription error, a reading >comprehension problem, or a misunderstanding of the underlying math? This is not as likely to be difficult as you think. >And then how does a teacher justfy what is no more than a subjective guess >to angry parents and administrtors, explaining why Joey got credit and Zooey >didn't?. The same holds for English composition. >> Often, the teacher grades on whether the problem is done as >> indicated in the textbook recipe. >Because this is what has been taught, and this is what a student is expected >to knwo. And this is NOT what should be taught. Understand what methods can be applied, and apply whichever >In algebra I there is truly little mathematically correct variation from the >"book recipe". Unfortunately. Also, at least 90% of the problems supposed to be done with one variable should not, at least by beginners. When my son was 8, and studying calculus mostly by himself from Apostol's excellent book, too hard for most, we also had him brush up on his algebra from an algebra 2 book. He was using the number of variables expected, as he usually could, but was unable to do one problem in which two variables were supposed to be used. With the bound removed, he did it with seven. Now if a genius, having really learned the subject, has difficulty using the assigned number of variables, what do you expect of the typical student? And this means that the teacher has to be able to follow the reasoning. >There is, for example, only one way to write a linear equation in >slope-intercept form, But many ways to go about getting the equation. one way to solve a system of linear equations using >hte elimination method, Where did you get that idea? If there are n equations, there are usually n! ways of doing this. one way to set up a box and whiskers statistical >chart. This is mechanical, and has no mathematical content, nor statistical content except descriptive. >Yes, there are other ways to "solve" the problem or display the info, but >these specific algorithsm are what are being yested and knowlege of them is >needed in future courses. Are they? In practice, solving systems of equations is done by computer. Understanding of the algorithms can be important, but memorization of them no. Try reducing a system of equations over the integers to row echelon form. Or more so, proving it can be done. >So how would you grade a student who uses outstanfing toechnique to rpesent >linear eq. in point-slope form when the question alled for the >slope-intercept form? >Did he just not follow instructions, and shouldn;t that be punished? I would be unlikely to ask the question. I am not even sure that I would give such, except as how to normalize the equation of a line for certain purposes, and leave it at that. Memorizing trivia is not that important. >Did he not knwo the correct form? Did he start out right but lose his way, >either taking a wrong path or end toosoon? Look at the above. It is a matter of normalization of the equation of a line and nothing more. The rule of equality covers this quite well. >Further complicating the decision is a certaintity that just becaue he could >do the problem correctly ont he board yesterday does not mean he could do it >today. STOP concentrating on memorization and routine. Minimize them. > There may be many ways >> about doing the problem; if the second sentence is followed, >> other than arithmetic errors or sloppiness, there will be >> no mistake made. > But is, for exampel, a long, meadnering process that takes many more steps >than needed an indication of knowledge or luck? Andisn;t effciincy an >indication of understanding? Possibly and possibly not. >So, for example, is a process that took 12 steps to combine like terms in an >equation as "correct", as good an indicator of knowledge, as one that took 4 >steps? I do not expect a student to find a short method, especially on a test. I would rather a student figure out a method from basic principles, no matter how clumsy, than memorize a trick. >> This precision in mathematics is also needed in ALL of the >> sciences, and alas the public seems unable to understand that >> the government cannot just legislate in violation of the laws >> of nature, and achieve miracles. >This would severly restrict what can be defined as a "science". >Under this requirement medicine, sociology, economics, astronomy, and a >whole host of disciplines crrently categorixed as "science" would fail your >test. Now this may be good or bad, accurate or inaccurate, right or wrong. >But it certianly would be disruptive and chaotic. Wrong. Randomness is subject to mathematical precision, as is the more complicated quantum mechanics. It is just that there is no simple correct deterministic process. For many purposes, one can neglect the differences, just as we can neglect the effect of cosmic dust on the Earth-Mars trajectory. >>>>Yet without referring to it as *algebra* per se, the >>>>aforementioned concepts are introduced in most math curriculums in the >>>>4th or 5th grade (5th grade at One's school, which uses a truly awful >>>>math curriculum). Discussion at lunch -- One's friend: *your school >>>>is so far behind ours! WE'RE learning algebra!* One *We're not even >>>>close to algebra. We're learning about variables.* >>>>Of course, the answer is not to re-name the subject. Rather, the >>>>answer is to show the students that algebra isn't that difficult. The important part should be taught as soon as the student can read and produce symbols. >>>You can't show what isn't true. Mathematics is difficult unless one >>>first learns to appreciate precision and rigor. That may be why >>>skilled musicians tend to do well in math - part of becoming skilled >>>is learning that precision. But most kids don't stick with music for >>>the same reason - hours of practice learning to produce precisely the >>>sound you want isn't worth it to them. >> Teach the appreciation of precision and rigor in first grade, >> and that part of the problem will disappear. We CAN teach >> precise mathematical concepts to kids, but it is difficult to >> do this with adults. Stop hurting children by avoiding the >> rigor which adults seem unable to understand. >Current knowledge is that children of that age are mentally incapable of the >rigor you want. Are they? The game _WFF N PROOF_ was marketed to such children. They are capable of the rigor if you present it to them as such, and not try to lead them up to it. The same holds for other concepts; an abstract concept is NOT an abstraction of more concrete ones. Going from general to special is easy; going from special to general requires unlearning, which is always difficult. They are incapable of understanding symbolic representation, This is utter baloney. >logical sequences, They understand rules of a simple game. This is what formal logical sequences are. Now this is not what inductive inference is. Inductive inference should be done as statistical decision theory, which is simple to state, but not at all easy to carry out. I will not go further into this here. cause and effect. You are raising a full garbage can of worms here. Often, to understand cause and effect, one needs to use precise mathematics. This definitely applies to disease risk factors, including a disease I have. My conclusions, from reading the studies, do not agree with those of physicians, who seem unable to distinguish between correlation and causation. This effect was, AFAIK, first noticed by a biologist in 1919. Once pointed out mathematically, it becomes obvious to one who can think precisely. I wish our politicians could understand this instead of their misunderstandings of cause and effect, what can be done instead of what they want to legislate. They have limited vocabularies and >limited abilities to integrate disparate knowedge points into a whole. I do not see the abilities of adults who cannot handle precision as that great. >They are kids, after all, and have not reached adult stages of development. >Some will not reach this stage until their late teens. My son, at age 6, was a high school student in mathematics, and at the college level in logic. Learning to think precisely may even get more difficult with increasing age; I would not want to try to teach most of today's teachers, even high school mathematics teachers. My late wife had much experience here, and it rarely made her feel good. The original "new math" was tested on tens of thousands of children; when taught by those who understood, it worked. But the teachers could not learn it; they could not understand. It is my opinion, based on decades of experience and discussion with others, that teaching facts and methods before understanding does not help with understanding, but those who understand can use the facts and know what the methods are doing and WHY. SignatureThis 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 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 >>Because this is what has been taught, and this is what a student is expected >>to knwo. > >And this is NOT what should be taught. That is what the state standards expect him to know. If you don't teach it, you get fired. >>So how would you grade a student who uses outstanfing toechnique to rpesent >>linear eq. in point-slope form when the question alled for the [quoted text clipped - 3 lines] > >I would be unlikely to ask the question. The state test will ask the question, and you as the teacher will be blamed if he cannot solve it in the required manner. >I am not even sure >that I would give such, except as how to normalize the equation >of a line for certain purposes, and leave it at that. Memorizing >trivia is not that important. It is, when the state tests ask questions about trivia. Which they do. >Look at the above. It is a matter of normalization of the >equation of a line and nothing more. The rule of equality [quoted text clipped - 5 lines] > >STOP concentrating on memorization and routine. Minimize them. Memorization and routine lead to automatization, which is required on a timed test. lojbab Bob LeChevalier - artificial linguist; genealogist lojbab@lojban.org Lojban language www.lojban.org >>>Because this is what has been taught, and this is what a student is expected >>>to knwo. >>And this is NOT what should be taught. >That is what the state standards expect him to know. If you don't >teach it, you get fired. We are having considerable discussion on the effect of this kind of state standard. We cannot have good education if the educationists, who ONLY know memorization and routine, make up the tests. >>>So how would you grade a student who uses outstanfing toechnique to rpesent >>>linear eq. in point-slope form when the question alled for the >>>slope-intercept form? >>>Did he just not follow instructions, and shouldn;t that be punished? >>I would be unlikely to ask the question. >The state test will ask the question, and you as the teacher will be >blamed if he cannot solve it in the required manner. I repeat what I have said above. There even are may teachers who complain about the students not learning what is important because of teaching to the test. This continues in college, and the colleges are not willing to back up their professors who would teach the more important parts. >>I am not even sure >>that I would give such, except as how to normalize the equation >>of a line for certain purposes, and leave it at that. Memorizing >>trivia is not that important. >It is, when the state tests ask questions about trivia. Which they >do. How many times have I said that the only way the public schools can be improved is to have affordable private schools, however it is done? One can destroy the quality of a school quickly. It is a major problem to even improve it, let alone restore it. Until we have the attitude that a school should educate each student as if he or she were the only student, and there were no such things as being in certain grades, we can only have the present bad turnout from the high schools, the universities, and even the graduate schools. >>Look at the above. It is a matter of normalization of the >>equation of a line and nothing more. The rule of equality >>covers this quite well. >>>Further complicating the decision is a certaintity that just becaue he could >>>do the problem correctly ont he board yesterday does not mean he could do it >>>today. >>STOP concentrating on memorization and routine. Minimize them. >Memorization and routine lead to automatization, which is required on >a timed test. You continue to stress the trivia. You seem unable to tell the difference between education and training; memorization and routine is training. This destroys the ability to be educated later. Education gives the ability to use the concepts, and reconstruct the methodology when needed. SignatureThis 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 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 >>>>Because this is what has been taught, and this is what a student is expected >>>>to knwo. [quoted text clipped - 8 lines] >if the educationists, who ONLY know memorization and routine, >make up the tests. The public wants the tests, and furthermore, they want kids to learn the mathematics (i.e. algorithmic arithmetic) that they learned as kids. And they seem likely to vote out of office anyone who tells them "no". >>The state test will ask the question, and you as the teacher will be >>blamed if he cannot solve it in the required manner. > >I repeat what I have said above. There even are may >teachers who complain about the students not learning >what is important because of teaching to the test. Yep, and yet the tests aren't going away. This should tell you something. We can hope that maybe NCLB goes away, which will reduce SOME of the pressure of teaching to the test, but the tests themselves are almost certainly here to stay, and indeed are likely to expand to cover all grades and not just the ones under the federal mandate. >This continues in college, and the colleges are not >willing to back up their professors who would teach >the more important parts. Which also should teach you something about social reality. He who pays the piper calls the tune. >>It is, when the state tests ask questions about trivia. Which they >>do. > >How many times have I said that the only way the public >schools can be improved is to have affordable private schools, >however it is done? It can't be done, without making them into public schools. >>>>Further complicating the decision is a certaintity that just becaue he could >>>>do the problem correctly ont he board yesterday does not mean he could do it [quoted text clipped - 8 lines] >the difference between education and training; memorization >and routine is training. And "We the people" want the animals (children) to be trained into useful and self-supporting members of society. I suspect that this is far more important to most people than any idealized concept of "education", which is why the system has evolved in the direction that it has. lojbab Bob LeChevalier - artificial linguist; genealogist lojbab@lojban.org Lojban language www.lojban.org .............. >>>Memorization and routine lead to automatization, which is required on >>>a timed test. >>You continue to stress the trivia. You seem unable to tell >>the difference between education and training; memorization >>and routine is training. >And "We the people" want the animals (children) to be trained into >useful and self-supporting members of society. I suspect that this is >far more important to most people than any idealized concept of >"education", which is why the system has evolved in the direction that >it has. And this is why we need to import graduate students in the sciences, and people to teach college and graduate science, to do non-trivial programming, etc. Sure, we can turn out clerks, assembly line workers, and the like, but not those who can use their brains and innovate. The US has consistently led the world in CS, but it has not produced many Americans in that; that many of the imports have become Americans is to the good. When "we the people" attempt to decide things involving the nature of the universe, only bad things can result. In the 19th century, there was curriculum, and while understanding has never been directly taught, some was introduced. "We the people" did not interfere when Johnny had to repeat a grade, and did not ask a teacher to lower the level of a course to accommodate the weak students. Nor did they object when Jane was skipped a grade, unless they though Joe was smarter, and usually not even then. SignatureThis 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 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 > .............. > [quoted text clipped - 16 lines] > clerks, assembly line workers, and the like, but not those > who can use their brains and innovate. We do not import workers becaue US citizens cannot perform the work, we import workers because they are willing to work for far less than the prevailing wages. According to the US BLS the unemploymern rate for college graduates is currently about 60% higher than it was in the last decade of the last century. They also report that the number of college graduates working outside of their major is more than twice what it was in that period. IOW, there are thousands of US citizens with degrees in math, engineering, chemistry, computer science, and other technical fields not working in those fields beccuse of a shortage of jobs _or_ depressed salary levels mking non-tecnical (esp finance) jbs more attractive. Larry > The US has consistently led the world in CS, but it has not > produced many Americans in that; that many of the imports [quoted text clipped - 9 lines] > when Jane was skipped a grade, unless they though Joe was > smarter, and usually not even then. >>>>Because this is what has been taught, and this is what a student is >>>>expected [quoted text clipped - 9 lines] > if the educationists, who ONLY know memorization and routine, > make up the tests. Using perjorative, made up labels to describe opponents is exactly what you are complaining abut --- eliminating the need to tkink fro yoruself. My state's laws are made up by lawyers, aprents, teachers, and politicians. They are accepted by the voters, meeting their desires. YOU are teh "educationist", insisting that you know better than the rest of the world. larry >>>>So how would you grade a student who uses outstanfing toechnique to >>>>rpesent [quoted text clipped - 55 lines] > educated later. Education gives the ability to use the > concepts, and reconstruct the methodology when needed. .............. >>Look at the above. It is a matter of normalization of the >>equation of a line and nothing more. The rule of equality >>covers this quite well. >>>Further complicating the decision is a certaintity that just becaue he could >>>do the problem correctly ont he board yesterday does not mean he could do it >>>today. One of my former colleagues told me of a student in a graduate course complaining about a B. On one problem, the student started correctly, but did not finish. The colleague then told him of this and asked how he would proceed. The student then answered that the course was over two weeks before, and he had forgotten that. This happens frequently when there is too much memorization. >>STOP concentrating on memorization and routine. Minimize them. >Memorization and routine lead to automatization, which is required on >a timed test. And even if the automation is retained, it cannot be used for anything other than that explicit type of problem. Understanding may not give quick answers, but it enables students to put things together when the case has not been covered. If we want clerks or assembly line workers, training may be appropriate. If we want any better, start educating early; training will even come more quickly. SignatureThis 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 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 >>>>>> In article <486f7172.10114...@news.datemas.de>, > [quoted text clipped - 58 lines] > credit, and once the faculty see how to do this, there is > not much disagreement on scores. This is relatively easy to do at the college level, but in 8th grade forget it Many problens, for ex., require only a few steps, too few to really develop a cluie to te student's thinking. Not to mention the difficulty in getting the kids to separate out relatively smple operations, like a two step addition, into separate steps. Yes, partial credit can be given, and often is. But then we have to address what is really being taught. How do you handle an error that develops but all of the stpes were not written down? How do you handle a correct answer wtthout the steps? Do you fail a student who got all ofthe correct answeres but failed to show her work (usually the more intelleginet students)? Or do you enforce the requirement arbitrarily? >> And should sloppiness be punished? > > Not heavily. But someone is not going to be a good scientist, > and I include the biological and psychological and economic > sciences, if there is sloppiness. First, very few of my students wee going to be scientists. A girl with her heart set on being a beautician or a boy who want to be a mason souldn't care less. And how much is a little? 10%? 5%? Bear in mind that, for some inexplicable reason, my state legislature has decided that 7 points separate grades, no 10%. so a refusal to follow directions, or even a charitable misunderstannd if instrsuction, can mean a letter grade difference. Also beasr in mind that in my state, and others, there is a minimum grade for 8th grade students to get academic credit for algebra. That is, (over teh strenuous objections of teachers) 8th graders must score a minimum 85% to get credit for completing algebra I (they get credit for graduating 8th grade, but must retake algebra in 9th grade for an 84% or less). Politics. Blah. >>How does a teacher determine that an incorrectly set up equation in a word >>problem is the result of another transcription error, a reading >>comprehension problem, or a misunderstanding of the underlying math? > > This is not as likely to be difficult as you think. This is far more difficualt than you assume, given the many reading comprehension problems of many 8th graders. >>And then how does a teacher justfy what is no more than a subjective guess >>to angry parents and administrtors, explaining why Joey got credit and >>Zooey >>didn't?. > > The same holds for English composition. As noted above, in many states there are elevated grade requirements for algebra I in middle school. And to be perfectly honest, mu English peers moved away from subjective grading, too, using purely objective measures like counting spelling and grammar errors. The logic is that we are not training novelists so content are less important. After all, in public school we are teaching what our legislature has told us to teach, the rules and structure of our subjects. >>> Often, the teacher grades on whether the problem is done as >>> indicated in the textbook recipe. [quoted text clipped - 5 lines] > And this is NOT what should be taught. Understand what methods > can be applied, and apply whichever Wrong. We are thaching hte methods. We cannot allow a student to choose on particular method that he has become comfortable with, ignoring all others. First, we are mandated to teach and assess his ability on _all_ methods. Second, a studnet is incapable of stermining whter or not the method he ignores will be nedded in later courses. Third, this isentirely contrary to your desire to teach an understadning of underlying conceepts. The ability to contrast and compare different operations, and to determine which is most efficient/accurate/easiest/reliable in a given situation is basic. If a student does not use an alternative technifue how do we determine if it is lack of knowledge, lack of comprehension, lack of logical ability, or just plain orneriness? >>In algebra I there is truly little mathematically correct variation from >>the [quoted text clipped - 9 lines] > unable to do one problem in which two variables were supposed > to be used. With the bound removed, he did it with seven. I have no idea what you are trying to say here. I'm talking algegra I here, and none of what I think yoiu said is relevant. > Now if a genius, having really learned the subject, has difficulty > using the assigned number of variables, what do you expect of the > typical student? And this means that the teacher has to be able > to follow the reasoning. Algebra I does not have problems like this. Algebra I is simplfy 3e + 5t - 6y = 8y -2e >>There is, for example, only one way to write a linear equation in >>slope-intercept form, > > But many ways to go about getting the equation. But only one optimal way. And my point is that that writing the equation in that form is what is being assessed, anot to write the equatoin in simplist form, a common error in algebra I So do you reward the rote math f simplifying despite the fact that the student did not answer the question asked? . > one way to solve a system of linear equations using >>hte elimination method, > > Where did you get that idea? If there are n equations, > there are usually n! ways of doing this. I meant the technique is fixed. The order of opertion _may_ be commutable, but the technique is fixed, and it isthe technique that is being assessed. And again, os a process that takes 12 steps as good as one that tkes 4? Not according to our standards--- efficiency is an important assessement of ability. > one way to set up a box and whiskers statistical >>chart. > > This is mechanical, and has no mathematical content, nor > statistical content except descriptive. Wrong. There are calculations to determine quartiles, and an assessment of understanding of statistical concepts. This chart is an important foundation for further study of statistics. In fact, my first college stat class mentioned it as a quick and easy way to demonstrate skewed data. >>Yes, there are other ways to "solve" the problem or display the info, but >>these specific algorithsm are what are being yested and knowlege of them [quoted text clipped - 4 lines] > done by computer. Understanding of the algorithms can > be important, but memorization of them no. Yes, they are. In linear algebra, for ex, being able to determine the most efficient way to solve a systme of linear equations is important. If you haven;t learned them in algebra, you are at a disadvantage. > Try reducing a system of equations over the integers to > row echelon form. Or more so, proving it can be done. A subject not taught until college linear algebra. I has 2 weeks to teach my entire course content on linear algebra, starting with the definition of a linear equation. Matrices had not yet been taught and matrix operations used to get the matrix in row echelon form were what was taught. >>So how would you grade a student who uses outstanfing toechnique to >>rpesent [quoted text clipped - 7 lines] > of a line for certain purposes, and leave it at that. Memorizing > trivia is not that important. My legislature demands that I teach this, failure to do so will result in my termination. And, quite frankly, it is an important consept used in later courses. You pooh pooh memorization, but retention is required and testing that retention is the name of the game. >>Did he not knwo the correct form? Did he start out right but lose his >>way, [quoted text clipped - 3 lines] > equation of a line and nothing more. The rule of equality > covers this quite well. Wrong. It is a question of writing the equation in a format such that the student can, by examination alone, determine certain characteristcs of the line. It also prepares the equation for further evaluation or calculation, such as graphing, a subject we teach. >>Further complicating the decision is a certaintity that just becaue he >>could [quoted text clipped - 3 lines] > > STOP concentrating on memorization and routine. Minimize them. That is what I taught. Despite your experience with a genius child and genius college students, the kids I teach need to concentrate on th algorithm, on the methods. I _try_ to impart a little underlying theory, but snores ripple through the room in moments, and I really do not ahve time to stray far. Understand , computation is a challenge for some of the students. My first week of algebra i class was a review of calcualtions with negative numbers. I agree with you, to a point. Math needs to be taken more seriously, is far more important than the way it is treated. But also understand that eeven most college graduates do not take more than 1 or 2 math courses, one of them calculus for the humanities student. A "D" is all they need to graduate, adn they aim for the "D". I put myself through college turoring amth to business students, and some took two or three tries to pass. Not because of how they were taught, but because oftheir attitude. Soem even were forced to delay graduatoin for one omre summer schools ession because they kept blowing off the work. I deal with what I am given. And when, as I said, I am dealt a student body who's)and their parent's) life expectations for math is balancing a check book, I deal with it. I cannot force a student to learn what he does not want to learn. >> There may be many ways >>> about doing the problem; if the second sentence is followed, [quoted text clipped - 7 lines] > > Possibly and possibly not. Exactly. SO how do you assess what you cannot determine? >>So, for example, is a process that took 12 steps to combine like terms in >>an [quoted text clipped - 5 lines] > a test. I would rather a student figure out a method from basic > principles, no matter how clumsy, than memorize a trick. I do. I have found that wandering, meandering processes are indiciative of a lack of knowedge. OOne of the things I am required to assess is the ability to accomplish a list of taks in a certain time frome. College even requires this ---- you have a fixed time period to compelte te assessment, no more. >>> This precision in mathematics is also needed in ALL of the >>> sciences, and alas the public seems unable to understand that [quoted text clipped - 14 lines] > one can neglect the differences, just as we can neglect the > effect of cosmic dust on the Earth-Mars trajectory. I am not tlking randomness, O am referong to your reference of precision. The subjects I listed are inherently incapable of achieving the level of precision required in math, physics, etc. >>>>>Yet without referring to it as *algebra* per se, the >>>>>aforementioned concepts are introduced in most math curriculums in the [quoted text clipped - 8 lines] > The important part should be taught as soon as the student > can read and produce symbols. How does one assess that for for the 112 students I typically taugh? Does not hte assessment of development become a major distraction? Tell me how I can get a taxophobic electorate to pay for the assessments. Tell me how I can convince parents who think that what I am teaching is a bunch of unecessary hooey that their child will never need to push the legislature to implement this testing. >>>>You can't show what isn't true. Mathematics is difficult unless one >>>>first learns to appreciate precision and rigor. That may be why [quoted text clipped - 20 lines] > Going from general to special is easy; going from special to general > requires unlearning, which is always difficult. Wrong. Generalization requires biological advancement. > They are incapable of understanding symbolic representation, > > This is utter baloney. Nope. It is current understanding of hiuman development. I do not intend to be offensive to anyone, but you _really_ need to get dwon into the trensches. You seem to be dealiing with the top few percent of intellects. I deal with the masses, and what you propose is impossible. >>logical sequences, > > They understand rules of a simple game. This is what formal logical > sequences are. But the rules are not immutable. In fact, chaging hte rules is the rule, not the exception. Watch kids payng a ganm, they cahnge the rules to meet circumstance. Their worlds are flexible, fungible, variable. They modify the rules to meet cricumstances or to intensify enjoyment. How many kids do you know that don;t add house rules to Monopoly, don;t argue over the rules for hide-'n-go-seek, amke up crd games rather than play the staid old maid or war? Strict adherence to rules is an impediment to early childhood development, not a goal. They are experimenting, experiencing, evaluating, learning. Rigorous attention to rule shuts down this process. Larry > Now this is not what inductive inference is. Inductive inference > should be done as statistical decision theory, which is simple to [quoted text clipped - 40 lines] > does not help with understanding, but those who understand can > use the facts and know what the methods are doing and WHY. >> This is mechanical, and has no mathematical content, nor >> statistical content except descriptive. [quoted text clipped - 7 lines] >fact, my first college stat class mentioned it as a quick and easy way to >demonstrate skewed data. Herman is a statistics professor of significant repute, and he seems not to consider that sort of stat class to be proper statistics. "Cookbook" statistical algorithms are frequently used without understanding, leading to misleading results (sometimes intentionally misleading). >>>So how would you grade a student who uses outstanfing toechnique to >>>rpesent [quoted text clipped - 10 lines] >My legislature demands that I teach this, failure to do so will result in my >termination. Herman doesn't think that legislatures should have the right to decide curriculum - only subject matter academicians. >Strict adherence to rules is an impediment to early childhood development, >not a goal. They are experimenting, experiencing, evaluating, learning. >Rigorous attention to rule shuts down this process. But in mathematics, such rigor is mandatory for real understanding. Which is why I think it is so hard to improve mathematical education. Other countries that outperform us in science and math tests are also noted for being envious of American initiative and creativity. It could very well be that there is a tradeoff between rigor and creativity for all but the most intelligent (and maybe even them). lojbab Bob LeChevalier - artificial linguist; genealogist lojbab@lojban.org Lojban language www.lojban.org >>> This is mechanical, and has no mathematical content, nor >>> statistical content except descriptive. [quoted text clipped - 13 lines] > understanding, leading to misleading results (sometimes intentionally > misleading). I understand . But that does not negate teh , admittedly slight, benefit of these structures for conveying understanding and meaning. >>>>So how would you grade a student who uses outstanfing toechnique to >>>>rpesent [quoted text clipped - 26 lines] > could very well be that there is a tradeoff between rigor and > creativity for all but the most intelligent (and maybe even them). I understand both sides of the coin. AS a mathematician myself, and as a math teacher, under Ideal circumstances I would prefer to impart more rigor into my classes. But, despite Herman's and others opinions, and as you note, I am paid to provide a specific product. And failure to provide that product means I don;t get paid. I have considerable qualms about the product I provide. I would much, much prefer to provide a more rigorous, more thorough treatment of my subject. But, not tooting my own horn, I and thousands of others went through a public education to successfully graduate with BS's and MS's adn PHD's in math. But i cannot decide whther or not such rigor is truly needed. AS in the stated case above, the closest most of my students will ever get to a statsistical analysis is an election poll. I am friends with people in a wide variety of careers and professions, from doctors to self-employed media consultants, to construction worlers to retail clerks. And truth to tell, beyond an ability to understand money they have no need to understand math, yet are still successful, some greatly so. So the eye surgeon doesn;t need to know how to calculate rates of decay of he meds he gives to patients, he just needs to knwo what a rate of decay is and how to read the literature. my self employed friends need to know how to read their accountants reports, not write them, and so on. Perversely, my construction friends may use more math than the others. But there are tools ranging from specialized calculators to scales on squares and rules to do most of the work. In any event, who am I to say what parents consider to be best for their kids, and who am I to say what each person will need in the future. ALl my job is is to impart enough basic knowledge so that when the student's future clarifies he can succeed in those later classes. It just won;t happen that a lesson in, say rudimentary probability, will be remembered in detail 6 yrs later in college, whether it is a rigorous analysis or rote calculation of odds. Heck, I'd be delighted if the kids remembered for the next year! Larry > lojbab > Bob LeChevalier - artificial linguist; genealogist > lojbab@lojban.org Lojban language www.lojban.org > Herman is a statistics professor of significant repute, and he seems > not to consider that sort of stat class to be proper statistics. [quoted text clipped - 7 lines] > Herman doesn't think that legislatures should have the right to decide > curriculum - only subject matter academicians. And he is correct. The idea that the legislature, who knows nothing abouth math, chemistry, physics, literature, sociology, etc. should decide course content is absurd.... The inmates are running the asylum. > Other countries that outperform us in science and math tests are also > noted for being envious of American initiative and creativity. It > could very well be that there is a tradeoff between rigor and > creativity for all but the most intelligent (and maybe even them). However, it is precisely the "most intelligent" who are responsible for the creativity. And creativity in math/science DEMANDS rigor. We have the 3rd largest population in the world. And the most of any *developed* country. (China & India are getting there. I expect China to overtake the U.S. in science and technology during this century). It is not surprising that we would have more creative people than most other countries. Perhaps what we need to do (this is VERY politically incorrect) is to separate those who can from those who can not very early on in school. Provide training (in the sense under discussion) for those who can't, and provide education (in the sense under discussion) for those who can. It is my understanding that at least some countries already do this (e.g. Germany). One might argue that this will lead to a 2- tiered society, but I would argue that this is what we already have. The widening income gap in this country is driven by (IMO) the gap in education between the poor and the economically well-to-do. The poor are poor precisely because they have below average intelligence and hence get "training" instead of "education". >> >My legislature demands that I teach this, failure to do so will result in my >> >termination. [quoted text clipped - 6 lines] >decide course content is absurd.... The inmates are running the >asylum. Democracy - the worst form of government - except for all the rest. >> Other countries that outperform us in science and math tests are also >> noted for being envious of American initiative and creativity. It [quoted text clipped - 3 lines] >However, it is precisely the "most intelligent" who are responsible >for the creativity. That is questionable. In any event, in other countries, the most intelligent don't have so much creativity. >We have the 3rd largest population in the world. And the most of any >*developed* country. (China & India are getting there. I expect >China to overtake the U.S. in science and technology during this century). They may have a larger economy, but we will likely still be the innovators, because China does not reward innovation, and indeed often punishes it. >It is not surprising that we would have more creative people than most >other countries. China has more "most intelligent" people than we do, by a factor of 4, unless you assume that their population has a significantly different bell curve. So if creativity is just another word for high intelligence, they would have more creative people. But they don't. >Perhaps what we need to do (this is VERY politically incorrect) >is to separate those who can from those who can not very early on >in school. The United States is not that sort of country. If that is what we "need" to do, we will find a different way, or choose a different goal, because to do as you suggest would fundamentally violate our cultural identity. >Provide training (in the sense under discussion) for those >who can't, and provide education (in the sense under discussion) for >those who can. Many who "can" don't *want*. And many of their parents don't "want", either. >It is my understanding that at least some countries already >do this (e.g. Germany). And Germany doesn't have nearly the innovation levels that we do. They have some superb craftsmen, though, because they value that sort of thing. >One might argue that this will lead to a 2-tiered >society, but I would argue that this is what we already have. Not legally. >The widening income gap in this country is driven by (IMO) the gap in education >between the poor and the economically well-to-do. The poor are poor >precisely because they have below average intelligence and hence get "training" instead >of "education". George Bush was economically well off. What's your explanation for him? Those Asian immigrants who come over tend to arrive fairly poor. What is your explanation for their success? Clearly socioeconomics does provide benefits and handicaps. It does in Germany and in that ultimate meritocracy Singapore. But the pride of our system is our social mobility. Bill Clinton, whatever you think of his politics, went from broken family poverty to the highest office in the land. Obama likewise started rather low on the socioeconomic totem pole. It's a little harder to find such examples in the sciences, but one of the 2006 Physics Nobelists was the son of a traveling salesman. Robert Grubbs, one of the 2005 Chemistry Nobelist, grew up in rural Kentucky. lojbab Bob LeChevalier - artificial linguist; genealogist lojbab@lojban.org Lojban language www.lojban.org >>> >My legislature demands that I teach this, failure to do so will result in my >>> >termination. >>> Herman doesn't think that legislatures should have the right to decide >>> curriculum - only subject matter academicians. >>And he is correct. The idea that the legislature, who knows nothing >>abouth math, chemistry, physics, literature, sociology, etc. should >>decide course content is absurd.... The inmates are running the >>asylum. >Democracy - the worst form of government - except for all the rest. Thousands of laws people have spoken, A handful the Creator sent. The former are frequently broken, The latter can't even be bent. If our representatives legislate in contradiction to the laws of nature, which laws will be observed? Congress can legislate a bound of 3 dollars a gallon for gasoline, but this will not change the price of oil, and nobody will get gasoline. Congress can legislate that everyone will get good health care, and that will mean that some bureaucrat will decide who gets what; the resources are not there. I have been in various medical facilities now for the last 5 weeks, and these are considered good facilities, but today I had to wait 15 minutes for a nurse to respond; an assistant would have been adequate. If everyone had the medical attention Ted Kennedy had, assuming it could be done, it would cost several times the GDP. The inmates are running the asylum. They assume that everyone can learn a good amount at the same rate in homogeneous classes, and that the bright and gifted can learn it "deeper". In mathematics, this cannot be done except by concentrating on trivia. The mathematical equivalent of writing paragraphs is the formulation of word problems; the economists I worked with, even those with not too great a mathematical background, could do this, even including calculus. It is more important that the engineer formulates the problem correctly than that he is able to solve it in closed form. >>> Other countries that outperform us in science and math tests are also >>> noted for being envious of American initiative and creativity. It >>> could very well be that there is a tradeoff between rigor and >>> creativity for all but the most intelligent (and maybe even them). >>However, it is precisely the "most intelligent" who are responsible >>for the creativity. >That is questionable. It is, because many have had their ability to use their intelligence, or even their intelligence, weakened by the (expletive deleted) schools. >In any event, in other countries, the most intelligent don't have so >much creativity. Many are converted to religion and other forms of philosophy. Zen does not prove theorems. >>We have the 3rd largest population in the world. And the most of any >>*developed* country. (China & India are getting there. I expect >>China to overtake the U.S. in science and technology during this century). >They may have a larger economy, but we will likely still be the >innovators, because China does not reward innovation, and indeed often >punishes it. >>It is not surprising that we would have more creative people than most >>other countries. >China has more "most intelligent" people than we do, by a factor of 4, >unless you assume that their population has a significantly different >bell curve. So if creativity is just another word for high >intelligence, they would have more creative people. But they don't. Many of their best come to the US and other western countries. Japan, which used to be highly creative, has lost it. Israel, a small country, is highly creative. >>Perhaps what we need to do (this is VERY politically incorrect) >>is to separate those who can from those who can not very early on >>in school. >The United States is not that sort of country. If that is what we >"need" to do, we will find a different way, or choose a different >goal, because to do as you suggest would fundamentally violate our >cultural identity. Nonsense. It was the policy in the 19th century, and lasted mainly to WWII. >>Provide training (in the sense under discussion) for those >>who can't, and provide education (in the sense under discussion) for >>those who can. There were the three tier high school programs when I went. College preparative, shop, and "general". Many who could have taken the college preparative program did not because they did not think they could get into college or afford it; these were the GIs who raised standards after WWII in the colleges. This program was put in under democracy. >Many who "can" don't *want*. And many of their parents don't "want", >either. This can be a problem. What do you propose to do about it? Is depriving those who can and want an answer? >>It is my understanding that at least some countries already >>do this (e.g. Germany). >And Germany doesn't have nearly the innovation levels that we do. They >have some superb craftsmen, though, because they value that sort of >thing. Because a large number of top Germans came to the US. Also Chinese; there are five Zhang's in our department. Before WWII, Germany was number 1 in science, with France and England behind, and the US possibly ahead of those. This with the US doctoral program starting in 1876. >>One might argue that this will lead to a 2-tiered >>society, but I would argue that this is what we already have. >Not legally. >>The widening income gap in this country is driven by (IMO) the gap in education >>between the poor and the economically well-to-do. The poor are poor >>precisely because they have below average intelligence and hence get "training" instead >>of "education". >George Bush was economically well off. What's your explanation for >him? What is the problem? I have seen his IQ estimated at 128. >Those Asian immigrants who come over tend to arrive fairly poor. What >is your explanation for their success? They believe in education, in learning more and better. This is in contrast to many Americans, who at most believe in grades. >Clearly socioeconomics does provide benefits and handicaps. It does >in Germany and in that ultimate meritocracy Singapore. But the pride >of our system is our social mobility. Bill Clinton, whatever you >think of his politics, went from broken family poverty to the highest >office in the land. Obama likewise started rather low on the >socioeconomic totem pole. I was not from a broken family, but from poverty. I was taught to read very early, but taught little more; I believe arithmetic. I did learn in the schools, but not from the teachers. It was not until just before I got to high school that I learned anything about matheamtics, and it was the first principle of algebra; this is all I needed to take off. How many years earlier could I have done that? Before, I was mainly reading biography, history, and geography; the science section available to grade school students was of poor quality. >It's a little harder to find such examples in the sciences, but one of >the 2006 Physics Nobelists was the son of a traveling salesman. Robert Grubbs, one of the 2005 Chemistry Nobelist, grew up in rural Kentucky. My father became unemployed when I was 3, and I was 12 when my parents progressed to opening a mom-and-pop delicatessen, and later they sold it and opened a grocery. My father must have been a genius, but had no education. We need to search out and encourage these, not bury them in a heterogeneous class. SignatureThis 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 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 >The inmates are running the asylum. They assume >that everyone can learn a good amount at the same >rate in homogeneous classes, and that the bright >and gifted can learn it "deeper". No. They DEFINE "a good amount" as what most kids manage to pick up of the subject, REQUIRE that teachers attempt to teach that amount to all students, and figure that WHATEVER the kids who are gifted can learn above what is REQUIRED is more or less of equal importance, so they don't much care if it is more or deeper or different, as long as it doesn't cost too much. >>>However, it is precisely the "most intelligent" who are responsible >>>for the creativity. [quoted text clipped - 4 lines] >their intelligence, or even their intelligence, >weakened by the (expletive deleted) schools. If that were really the case, then home-schooled kids, and those educated at the few "academic private schools" would be showing up their peers of comparable IQ who attend the public schools. I haven't seen the evidence. >>>It is not surprising that we would have more creative people than most >>>other countries. [quoted text clipped - 5 lines] > >Many of their best come to the US and other western countries. Even if you count all of those, they don't have more creative people. And remember that China controls who gets to leave. >Japan, which used to be highly creative, has lost it. Japan was NEVER highly creative in technical fields. They built their economy by copying western technology and producing it cheaply efficiently. >>>Perhaps what we need to do (this is VERY politically incorrect) >>>is to separate those who can from those who can not very early on [quoted text clipped - 7 lines] >Nonsense. It was the policy in the 19th century, and lasted >mainly to WWII. In the 19th century almost no one attended secondary education OR college, regardless of their IQ. It was money and location that determined access to education, not intelligence. >>Many who "can" don't *want*. And many of their parents don't "want", >>either. > >This can be a problem. What do you propose to do about it? Not much. Individual and parental rights are paramount in our culture. >Is depriving those who can and want an answer? Those who can and want, in our culture can usually find a way. Maybe not while they are kids. But society really doesn't place much of a priority of meeting what kids want. Money still rules, and kids generally don't have any. >>>The widening income gap in this country is driven by (IMO) the gap in education >>>between the poor and the economically well-to-do. The poor are poor [quoted text clipped - 5 lines] > >What is the problem? I have seen his IQ estimated at 128. And despite all his money, he has demonstrated that his education was worthless. He comes across as neither well-educated NOR well-trained. >>Those Asian immigrants who come over tend to arrive fairly poor. What >>is your explanation for their success? > >They believe in educati |
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