I have a safe thats like a piggy bank. You put the money in the top then you can open it with the combo. I have been putting all my money in it and i haven't open it for years now. I went today to open and I totally forgot that I needed the combination. I tryed a lot of combo's but none worked. I know from math that there are 99,000 or about that many different 5 digit combo's. Could anyone please list all the possible 5 digit combinations?? -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > > I have a safe thats like a piggy bank. You put the money in the top > then you can open it with the combo. I have been putting all my money > in it and i haven't open it for years now. I went today to open and I > totally forgot that I needed the combination. I tryed a lot of combo's > but none worked. I know from math that there are 99,000 or about that > many different 5 digit combo's. Could anyone please list all the > possible 5 digit combinations?? Well, if you're right about there are about 99,000 of them, then I doubt that anyone will. The combinations are all the whole numbers from 00000 to 99999 of which there are clearly 100,000. -- G.C. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > I have a safe thats like a piggy bank. You put the money in the top > then you can open it with the combo. I have been putting all my money > in it and i haven't open it for years now. I went today to open and I > totally forgot that I needed the combination. I tryed a lot of combo's > but none worked. I know from math that there are 99,000 or about that > many different 5 digit combo's. Could anyone please list all the > possible 5 digit combinations?? If there are 99k combos, you aren't going to have time to input them all. Either contact the manufacturer for help (if you never changed the default combo) or contact your local locksmith. And yes, if it's a numeric keypad (0-9) and the combination is 5 digits, obviously the possible combinations are the numbers 00000-99999, 100,000 possibilities exactly. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== I hesitate to drop into this thread at this late date, but perhaps you all might consider a dissenting opinion.... > **If you look at the data, there is definitely problem with math education in > the US.** Yes, there is a major problem, there's way too much emphasis placed on it! 90 percent of the math taught in our high schools will be forgotten as soon as the student leaves high school. Try this. Randomly ask 20 strangers on the street to define Y intercept, or ask them to graph a quadratic equation. Bet you get 20 wrong answers. Now, ask these adults if they earn enough to support their families and believe themselves to be aware and concerned members of their community. Bet they would say absolutely!. > > Perhaps I haven't been clear enough. I was responding to a comment by Kevin > that there must be something seriously wrong with either the testing program or > with mathematics education in California. I think the latter is true, but that > the problem isn't merely math education, it's all public education. The public > schools in California ARE having serious trouble, especially for certain > subgroups. Some schools do well, but too large a number are struggling. > > **However, it does not make sense to cancel a test for all students, or dumb > down the general test because some speical ed students are not passing the > general test.** dumb it down????. The whole damn test is a dumb idea! First, it's multiple choice. REAL LIFE IS NOT MULTIPLE CHOICE!! Real life is a series of word problems, many without one single correct answer. Exit exam tests are multiple choice because that's the easiest type of test to score, especially with automated scoring equipment. Second, the tests DO NOT measure the skills we expect an adult to have in order to be successfully integrated into the working world, and to assume family and community responsibiliites. Thirdly, the material covered by these tests is of minimal relevance, even to the students who are going to be attending a 4 year college (a small minority of the students graduating from our high schools}. Few high school graduates major in mathematics when they go to college. Algebra is a complete waste of time and effort for any child who is not going to major in mathematics. Fourth, if truth is to be told, the primary motivation behind these tests is to raise the status (read compensation} of teachers. This is in line with the perpetually evolving jargon used by the educational establishment, the endless agonizing about highly qualified credentialed educators (what a cruel joke}, and the holding of our children as hostages to endless demands for more money for the children (BS! 85% of school non-capital expenses goes to salaries and benefits) > > Yes, I agree. Moreover I've been puzzled by the comments made by some of the > parents of special ed students that I meet in parent support groups. (My > daughter's in special ed.) They seem more concerned that their children won't > get a diploma if they can't pass the tests than they are about whether their > child has mastered the tested material -- as if the diploma alone were all that > mattered, not subject mastery. Bless these parents!!! Saints deliver us!! I hope they storm the classrooms and take over your school! They know these tests are crap, and the only thing that really matters is that damn diploma! This suggests to me the rather interesting > notion that parents may not believe the content of high school really matters > much, but the stigma of not having a diploma does, as if the knowledge in > question isn't something that's necessary for anything other than establishing > one's status after graduation. CORRECT! BTW, I've been teaching in inner city high schools for almost 3 years, and it never ceases to amaze me that more parents don't pull their kids out of the government schools. Most of them would be better off being educated by almost any adult with life experience and a basic knowledge of arithmatic and reading. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== **I hesitate to drop into this thread at this late date, but perhaps you all might consider a dissenting opinion....** You quoted me at length, but the truth is, I agree with you. I think public schools either ought to teach what they say they will or they ought to stop the pretense. And I believe that most of what is taught in k-12 schools is completely unnecessary for most people. **BTW, I've been teaching in inner city high schools for almost 3 years, and it never ceases to amaze me that more parents don't pull their kids out of the government schools.** I did. We homeschooled for several years. My daughter has only recently returned to school part-time. :) Cindy Cotter ----------------------------------------------- http://groups.yahoo.com/group/CalEdu/ Discussion about Education in California http://groups.yahoo.com/group/WildGrape/ Discussion about Los Angeles -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > I hesitate to drop into this thread at this late date, but perhaps you > all might consider a dissenting opinion.... Well I certainly will at least, since I share many of the same opinions. How d'ya like that. Support right off the bat. Betcha wasn't expecting that. > **If you look at the data, there is definitely problem with math education in >the US.** Yes, there is a major problem, there's way too much emphasis placed on > it! 90 percent of the math taught in our high schools will be > forgotten as soon as the student leaves high school. More than 90%, if you consider all the algebra and geometry (and maybe even trig and calculus, statistics, etc.) > Try this. > Randomly ask 20 strangers on the street to define Y intercept, or ask > them to graph a quadratic equation. Bet you get 20 wrong answers. Yeah, or something very close to 20 at least. Of course, one should make sure the location in question is not the street corner directly adjacent to the mathematics department at some university or something. > Now, > ask these adults if they earn enough to support their families and > believe themselves to be aware and concerned members of their > community. Bet they would say absolutely!. Of course. Most would. Most *do*. <... > Thirdly, the material covered by these tests is of minimal relevance, > even to the students who are going to be attending a 4 year college (a > small minority of the students graduating from our high schools}. Few > high school graduates major in mathematics when they go to college. > Algebra is a complete waste of time and effort for any child who is > not going to major in mathematics. I don't agree literally with what you're saying, but I do agree in spirit. Algebra does instill logic, critical thinking, analytical, and other vital skills, so it's not a *complete* waste of time. But many of these same skills can be instilled by way of, say, a logic course, or critical thinking course, or even a philosophy course, or some such, that covers these concepts more generally that they may be applied by a larger group as opposed to, say, the group that ends up actually using algebra in the real world. Algebra (mathematics in general) is just a particular application of these concepts. Truth be told, many of the math teachers that firmly believe all this stuff actually has application in most people's lives (a common reply when asked why do I need this stuff?) create that opinion with a very strong bias. They're math teachers. The cold hard fact of the matter is, most people never go on to actualy apply most of this stuff. If they did, the number of people who could correctly answer those questions would be -->20, not -->0. That's the cold hard fact of the matter. Then, when they can't escape from that logic, they often times say that it's all the collateral benefits that make it necessary to learn al this stuff. Logical/critical thinking, etc. etc. Fact of the matter is, mathematics is must one (relatively specific) application of these necessary traits. The actual application on most's lives of thes traits, is not in appication of mathematics. Yet we seem to fool ourselves into believing we can only acquire these traits through a solid mathematics education. BS. We can acquire these traits through other means. Not only acquire them, but through means which are much more directly applicable to most's lives than mathematics. Especially with the advances in technlology. Truth is, your average Joe has less and less of a need to know anything other than basic arithmetic. For most anything involving higher mathematics than that, the reality is Joe usually resorts to some device to tell him the answer. We should focus more not on pure mathematics, but on prevailiang application of mathematics (such as, say, spreadsheet usage or really computer usage in general!) that will be much more probable to actually be needed by Joe in real life. Most people simply don't go around solving quadratic equations, taking logarithms, finding derivatives and integrals, and what not. What most people do (wrt mathematics needs) is add, subtract, multiply, and divide. That's the cold hard fact. All most people need is a four function calculator or adding machine. Come to think about it, that's all most people *have.* Why is that? Because that's all most people *need.* I like mathematics. I like tutoring people in mathematics. I don't know why, really. I suppose I always had a knack for it and I get personal satisfaction from helping others. But I never fool myself into believing that I actually *need* the vast majority of the mathematics I was taught. <... > Yes, I agree. Moreover I've been puzzled by the comments made by some of the >parents of special ed students that I meet in parent support groups. (My >daughter's in special ed.) They seem more concerned that their children won't >get a diploma if they can't pass the tests than they are about whether their >child has mastered the tested material -- as if the diploma alone were all that >mattered, not subject mastery. Bless these parents!!! Saints deliver us!! I hope they storm the > classrooms and take over your school! They know these tests are crap, > and the only thing that really matters is that damn diploma! Of course. Why do they need to master the material? Because they actually need to use the material, or because someone, somewhere, said they needed this to get a diploma? It's the latter. > This suggests to me the rather interesting >notion that parents may not believe the content of high school really matters >much, but the stigma of not having a diploma does, as if the knowledge in >question isn't something that's necessary for anything other than establishing >one's status after graduation. Now you're getting it. -- Darrell -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > Thirdly, the material covered by these tests is of minimal relevance, > even to the students who are going to be attending a 4 year college (a > small minority of the students graduating from our high schools}. Few > high school graduates major in mathematics when they go to college. > Algebra is a complete waste of time and effort for any child who is > not going to major in mathematics. While it may be true that much of what is taught in algebra classes is forgotten and of minimal relevance to many of the students, and while it is certainly true that multiple-choice tests are a poor way to test mathematical competence, I think you are underestimating the fraction that do need algebra. It is not just the math majors, but also the science majors, the engineering majors, the economic majors, ... If you look at how many students are in the majors that require algebra at a 4-year school, it usually exceeds a third of the student body. According to http://www.doe.mass.edu/infoservices/reports/hsg/96/hsg96ltr.html over 50% of high school graduates (in Massachusetts in 1996) planned to go to 4-year colleges, and over 70% planned to go to either 2-year or 4-year college. (They don't have figures on that site for what fraction actually do eventually attend college.) By these crude estimates about a fifth of the students in high school really need algebra, and we don't know at the time they are being taught which fifth they are. I think that there is room for improvement in the secondary-school math curriculum. I, for one, would like to see a lot more probability statistics, and logic, and would be willing to give up trigonometry to make room. I don't think that giving up on teaching math to kids is good for them or for society. -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Someone made a comment disapproving the highly qualified teacher designation suggesting that it is a plan that teachers are trying to use in order to make more money: Not reasonable; most teachers do NOT like that applied highly qualified teacher designation. It makes teaching something in which you're qualified, much more difficult to be allowed to do, simply because you have a bachelors degree in something else. G C -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > Someone made a comment disapproving the highly qualified teacher designation > suggesting that it is a plan that teachers are trying to use in order to make > more money: > > Not reasonable; most teachers do NOT like that applied highly qualified > teacher designation. It makes teaching something in which you're qualified, > much more difficult to be allowed to do, simply because you have a bachelors > degree in something else. > > G C n my district (Oakland), this is the most common excuse for the failure of our students to learn (math or anything else). The refrain goes: We need to give more money to schools, so we can pay the teachers more, so we can attract highly qualified credentialed teachers. The teachers union (OEA) would never tolerate performance or site-related pay incentives. They claim that ALL teachers should be paid more. The reasoning that they pitch is, our district has many emergency credentialed teachers in the classroom, and these are by definition inferior to any other fully credentialed teacher. IMHO, any deficiencies in the teaching staff has more to do with how well these people performed in their BA classes (and in their current attitudes), not in the phoney credentialling classes they took at evening school. In Oakland, we now have teachers pulling down upwards of $90K, and the poor kids are still screwed up! The establishment solution is to throw more standardized tests at the kids. Remember, You don't need a weather man to know which way the wind is blowing? Well, you sure don't need a bunch of expensive, time consuming, spirit killing JO tests to tell these kids are not getting much value out of school! And giving more money to this failed system is throwing good money after bad! God help these poor children. John -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > >Now, >ask these adults if they earn enough to support their families and >believe themselves to be aware and concerned members of their >community. Bet they would say absolutely!. > > Of course. Most would. Most *do*. > > Thinking along these lines, there is really nothing needed to be taught in school at all. Maybe we can eliminate education completely. Think of the money that can be saved! -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== I am a second year high school teacher and will be teaching Geometry for the first time. Can any experinced teacher give me some information of cooperative learning acitivities for high school geometry? Any help will be greatly appreciated. Jaffer Syed -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== My favorate part is the introduction to trig...when you get that far along education classes... > I am a second year high school teacher and will be teaching Geometry > for the first time. Can any experinced teacher give me some > information of cooperative learning acitivities for high school > geometry? Any help will be greatly appreciated. Jaffer Syed > -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Dear All, I am working at present on a math program to increase math understnading in Middle school students. I was surprised to learn that students are expected to use calculators to do minor (as small as 2+2) calculations. If any people in here have studied math they will recognise mathematics is about understanding concepts and knowing concepts. It involves a lot of hard work, conceptual understanding which is totally missing in today's reform or hand-onor for that matter inquiry based mathematics curiculum. We forget that Mathematics and Sciences are conceptual subjects and need repeated practice. They are not liberal arts or philosophy which are inquiry based. No pun intended on liberal arts supporters but mathematics and sciences cannot be taught the same way other subjects might be. They are just different and need to be tackled accordingly. National science foundation has spent billions on trying to come out with one size-fits all curriculum but have repeatedly failed. The math programs which are successful have been employed in sub-urban schools and do not meet the needs of urban schools. I think it is time for us to learn from Japan and India which have excellent mathematics curriculum. It involves concepts, inquiry and most important of all practise and testing of mathmatical concepts.And these are the reasons they have superior technical man power. > mathematics increased by almost half between 1995 and 2001, university > officials said. If this is accurate, it would provide more evidence > that the promotion of reform math, in which Connecticut has been in > forefront since 1989, has been another massive failure. It is > unfortunate that Robert Frahm did not expose the staggering amounts of > money, time and effort that have been wasted on this latest educational > scam. Dom Rosa > ------------------ http://www.ctnow.com/news/local/hc-remedial0717jul17.story CSU Tightens Remedial Rules By ROBERT A. FRAHM > Courant Staff Writer > Connecticut State University students who cannot do college-level math > or English no longer will be given unlimited time to make up the > deficiencies, university officials decided Wednesday. CSU trustees voted to set a time limit for completing remedial classes > starting in 2004, saying students must finish the classes within their > first 24 credits - in effect, by the end of their freshman year. At least one-fourth, and possibly as many as one-third, of those taking > remedial courses are sophomores, juniors or seniors, according to a CSU > report. We are convinced the sooner a student takes and completes his remedial > courses, the better he will do, said John A. Doyle, chairman of the > academic affairs committee of the board of trustees. The committee recommended the policy change after a lengthy study of a > problem that vexes colleges and universities across the nation: a > substantial number of students unprepared for college-level work. A report last year by the Association of American Colleges and > Universities said that 40 percent of students in four-year colleges, and > 53 percent overall, take remedial courses. Less than one-half of high school graduates complete even a minimally > defined college preparatory curriculum in high school, the report said. At CSU, officials last fall recommended that 40 percent of new freshmen > take remedial math and 15 percent take remedial English, but the actual > remedial enrollments were lower: 27 percent in math and 7 percent in > English. The number of students in remedial mathematics increased by > almost half between 1995 and 2001, university officials said. The trustees Wednesday asked for continued review of the university's > policy, including a study of the standards by which students are > recommended for remedial work. Some trustees, however, raised doubts about the approach. One said it > fails to address fundamental questions about the degree to which the > university should be responsible for providing remedial help. Why aren't [students] taking it before they come in the door? Why > aren't they doing it in the summer? asked Joseph A. Mengacci, who voted > against the new policy. In many states, remedial education is the > responsibility of two-year community colleges instead of four-year > colleges, he said. Lawrence D. McHugh, the board chairman, said he agrees with the new time > limit for completing remedial work, but added that CSU should continue > to offer the classes. Some of the reason we've had success with a lot of students ... is > because of these courses, he said. I want to give these students every > opportunity to succeed. > -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Well, there are several things wrong with your point of view. First, have you ever actually read the NSF documents regarding science and math education? If anything, they take the OPPOSITE approach to one-size-fits-all. Yes, students should still learn multiplication tables, how to divide, handle fractions, etc. But graphing calculators also allow complex concepts to be learned much more quickly. How much time would it take, for example, to do what-if discovery of polynomials using pencil and graph paper? In the Workshop Physics approach, an extremely strong conceptual approach to physics, is heavily dependent on technology. You can't think about and play with concepts if most of your time is used with rote data collection and manual calculation. Doing things the hard way is not a virtue. The scam of reform is nonsense in most cases. Yeah, there is some garbage out there, the cultural diversity of arithmetic answers comes to mind. But if anyone really believes that the old lecture to an auditorium is the best way to teach science and math, that person is uninformed and/or just too lazy to be a teacher. The same weeping and wailing occurred when I was young. There, however, the problem was the use of slide rules in the classroom. Nothing really changes. John > Dear All, > I am working at present on a math program to increase math understnading in > Middle school students. I was surprised to learn that students are expected > to use calculators to do minor (as small as 2+2) calculations. If any people > in here have studied math they will recognise mathematics is about > understanding concepts and knowing concepts. It involves a lot of hard work, > conceptual understanding which is totally missing in today's reform or > hand-onor for that matter inquiry based mathematics curiculum. > We forget that Mathematics and Sciences are conceptual subjects and need > repeated practice. They are not liberal arts or philosophy which are inquiry > based. No pun intended on liberal arts supporters but mathematics and > sciences cannot be taught the same way other subjects might be. They are > just different and need to be tackled accordingly. National science foundation has spent billions on trying to come out with > one size-fits all curriculum but have repeatedly failed. The math programs > which are successful have been employed in sub-urban schools and do not meet > the needs of urban schools. I think it is time for us to learn from Japan and India which have excellent > mathematics curriculum. It involves concepts, inquiry and most important of > all practise and testing of mathmatical concepts.And these are the reasons > they have superior technical man power. >mathematics increased by almost half between 1995 and 2001, university >officials said. If this is accurate, it would provide more evidence >that the promotion of reform math, in which Connecticut has been in >forefront since 1989, has been another massive failure. It is >unfortunate that Robert Frahm did not expose the staggering amounts of >money, time and effort that have been wasted on this latest educational >scam. > > Dom Rosa >------------------ > > http://www.ctnow.com/news/local/hc-remedial0717jul17.story > > CSU Tightens Remedial Rules > > By ROBERT A. FRAHM >Courant Staff Writer > > Connecticut State University students who cannot do college-level math >or English no longer will be given unlimited time to make up the >deficiencies, university officials decided Wednesday. > > CSU trustees voted to set a time limit for completing remedial classes >starting in 2004, saying students must finish the classes within their >first 24 credits - in effect, by the end of their freshman year. > > At least one-fourth, and possibly as many as one-third, of those taking >remedial courses are sophomores, juniors or seniors, according to a CSU >report. > > We are convinced the sooner a student takes and completes his remedial >courses, the better he will do, said John A. Doyle, chairman of the >academic affairs committee of the board of trustees. > > The committee recommended the policy change after a lengthy study of a >problem that vexes colleges and universities across the nation: a >substantial number of students unprepared for college-level work. > > A report last year by the Association of American Colleges and >Universities said that 40 percent of students in four-year colleges, and >53 percent overall, take remedial courses. > > Less than one-half of high school graduates complete even a minimally >defined college preparatory curriculum in high school, the report said. > > At CSU, officials last fall recommended that 40 percent of new freshmen >take remedial math and 15 percent take remedial English, but the actual >remedial enrollments were lower: 27 percent in math and 7 percent in >English. The number of students in remedial mathematics increased by >almost half between 1995 and 2001, university officials said. > > The trustees Wednesday asked for continued review of the university's >policy, including a study of the standards by which students are >recommended for remedial work. > > Some trustees, however, raised doubts about the approach. One said it >fails to address fundamental questions about the degree to which the >university should be responsible for providing remedial help. > > Why aren't [students] taking it before they come in the door? Why >aren't they doing it in the summer? asked Joseph A. Mengacci, who voted >against the new policy. In many states, remedial education is the >responsibility of two-year community colleges instead of four-year >colleges, he said. > > Lawrence D. McHugh, the board chairman, said he agrees with the new time >limit for completing remedial work, but added that CSU should continue >to offer the classes. > > Some of the reason we've had success with a lot of students ... is >because of these courses, he said. I want to give these students every >opportunity to succeed. > -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > You can't think about and play >with concepts if most of your time is used with rote data collection and >manual calculation. That, data collection and calculation, is fundamental to the study of any hard science. It should never be abbreviated in the initial learning process. G C -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== >The same weeping and wailing occurred when I was young. There, however, the >problem was the use of slide rules in the classroom. Nothing really changes. John We had to learn our arithmetic in Pennsylvania before we could be promoted to the next grade. We did use slide rules, but very rarely. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== No. The training for most students should be concepts, not busy work. There is NO value for students to sit there for an hour plotting 100 points on a piece of graph paper. These rote activities reinforces the notion that science is a dull and mindless exercise in drudgery. I'd rather have them spend the time actually learning concepts. For science and engineering students should learn concepts as well as how to do the work the way it is done in the real world. Have you worked in research labs? Do you spend days chunking away with pencil and paper? Of course not. You are using computers, sensors, probes, LabPro, MatLab, Mathematica, calculators, etc. J >You can't think about and play >with concepts if most of your time is used with rote data collection and >manual calculation. That, data collection and calculation, is fundamental to the study of any hard > science. It should never be abbreviated in the initial learning process. G C > -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== >NO value for students to sit there for an hour plotting 100 points on a >piece of graph paper. These rote activities reinforces the notion that >science is a dull and mindless exercise in drudgery. That drudgery work is part of the value of math and science. It is part of the skills. I'd rather have them >spend the time actually learning concepts The skills and the concepts are both important. G C -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Now this part is written, too: >For science and engineering students should learn concepts as well as how to >do the work the way it is done in the real world. Have you worked in >research labs? Yes. Absolutely yes. Do you spend days chunking away with pencil and paper? Of >course not. That part of the work did not require days. It was still very important. You are using computers, sensors, probes, LabPro, MatLab, >Mathematica, calculators, etc. You MUST be kidding! About the only practical convenience available was a scientific calculator. I bought my own. Computers and software...? Hey, sometimes the real world can disappoint you. G -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > The training for most students should be concepts, not busy work. There is > NO value for students to sit there for an hour plotting 100 points on a > piece of graph paper. These rote activities reinforces the notion that > science is a dull and mindless exercise in drudgery. I'd rather have them > spend the time actually learning concepts. Plotting 100 points certainly busy work, but having young students plot 5 or 6 points certainly helps them undertand the notion of a a graph and a coordinate system. It does them no good to have graphs produced for them magically, if they have no idea what the graphs mean. Creating small graphs manually helps increase their chances of understanding them. > For science and engineering students should learn concepts as well as how to > do the work the way it is done in the real world. Have you worked in > research labs? Do you spend days chunking away with pencil and paper? Of > course not. You are using computers, sensors, probes, LabPro, MatLab, > Mathematica, calculators, etc. I work in a research lab. Although I do most of my data plotting on a computer (it's much too hard to plot a scatter diagram of half a million points by hand, just to see if there is some obvious relationship between two values), I still see value in being able to sketch out a relationship or a probability distribution on the whiteboard and talking about it without needing to pin down all the parameters and run a computer program. Although CAD tools have replaced most hand drafting of mechanical drawings, they certainly haven't replaced sketching, which still takes a lot of practice to do well. Students need to be able to sketch mathematical functions, not just use CAD tools to crank out already well-understood functions. Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== >>NO value for students to sit there for an hour plotting 100 points on >>a piece of graph paper. These rote activities reinforces the notion >>that science is a dull and mindless exercise in drudgery. > > That drudgery work is part of the value of math and science. It is > part of the skills. > This is a joke, right? Practice may reinforce skills, but does it have to be drudgery? Are we suggesting that school mathematics should be a survival game -- only those who can survive the drudgery should be able to enter the field. It is exactly this attitude that promulgates the utter hatred of mathematics as a discipline that seems to exist. > I'd rather have them >>spend the time actually learning concepts > > The skills and the concepts are both important. Absolutely. But why then do too many teachers stress skills through drikk and kill drusgery rather than embedding skills in activities that reinforce concepts? Aeron -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== I agree that busy work of the sort that requires plotting 100 points on a piece of graph paper is unproductive, and that use of technology in this situation may be preferred. However, it is important to separate the purpose of schooling (process oriented, learning) from research (product, results of learning). It is ok to do something by hand in order to learn and/or practice something that might be done by a computer in a research the students understand the process that is being eased by use of technology is not always helpful. Science students need to first learn fundamentals, initially with manual tools on problems that show mastery of concepts. This need not involved excessive busy work. For example, graphing of 15 data points by hand should not involve excessive drudgery, and allows the instructor to verify that the students can (1) choose an appropriate type of graph for the question asked and the data available, (2) choose an appropriate scale for the axes, and (3) label the graph appropriately. My own research involves heavy use of computers. However, I never allow my students to use a computer until they have first shown that they understand the concepts, as demonstrated in part through manual computations. Of course, to do this I have had to develop and find teaching examples for which manual steps are not too hard. One rule of thumb that I try to follow is to avoid teaching too many concepts with one activity. However, it can still be extremely difficult to strike the right balance between use of spiffy technology and boring manual drudgery. ************************************************************************ Ellen M. Wijsman COURIER DELIVERY ADDRESS ONLY: Research Professor Ellen M. Wijsman Div. of Medical Genetics and 1914 N 34th St., suite 209 Dept. Biostatistics Seattle, WA 98103 BOX 357720, University of Washington (Note: Use this address Seattle, WA 98195-7720 EXACTLY as given above, and phone: (206) 543-8987 use ONLY for courier delivery!!!) web page: http://faculty.washington.edu/wijsman ************************************************************************* > No. The training for most students should be concepts, not busy work. There is > NO value for students to sit there for an hour plotting 100 points on a > piece of graph paper. These rote activities reinforces the notion that > science is a dull and mindless exercise in drudgery. I'd rather have them > spend the time actually learning concepts. For science and engineering students should learn concepts as well as how to > do the work the way it is done in the real world. Have you worked in > research labs? Do you spend days chunking away with pencil and paper? Of > course not. You are using computers, sensors, probes, LabPro, MatLab, > Mathematica, calculators, etc. > J >You can't think about and play >>with concepts if most of your time is used with rote data collection and >>manual calculation. > > That, data collection and calculation, is fundamental to the study of any > hard >science. It should never be abbreviated in the initial learning process. > > G C > -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== It depends upon what is meant by young students. The Colorado CSAP exams for 8th grade science assumes a very good knowledge of topics including graphing, estimation, calculation, even the basics of experimental design. Some have complained that the test is too hard for 8th graders yet most students do well. They have the basics when they enter 9th grade. I haven't looked at the CSAP for mathematics at this level but I'd bet they cover many of the other concerns some people have about learning the basics. As for those people in industry who are still doing their work with pencil and paper, I feel sorry for you. It is the same waste of productivity you'd get if expected to go back to an O26 keypunch. The guy (gal?) who even had to buy their own personal calculator, well, time to move on as soon as (if) the economy ever recovers. Once again, you do not have to revert to the manual techniques of 30-40 years ago to teach students the basic concepts of science and math. If your students are not learning the basics, it is most likely YOUR fault, not the lack of manual labor. J. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== I'd suggest you take a really good look at approaches such as Workshop Physics (mostly college) and Studio Physics (high school and college). These methods make very heavy use of technology and do a better job of teaching concepts than other teaching methods. There is a huge amount of data to back this up, easy to find if you are interested. Manual labor does not translate to learning the basics. I have used Workshop Physics in a college environment and was amazed at the results. Yes, it is costly for the initial setup. Yes, it takes a huge amount of teacher preparation. But pre/post assessment testing shows fantastic results. The difference here is using technology to achieve a goal rather than making technology itself the goal. As I mentioned before, the argument that raged when I was in high school was the use of slide rules. Almost identical arguments were presented to support the banning of their use, especially while learning basic concepts. It was silly then, it is silly now. J. > I agree that busy work of the sort that requires plotting 100 points on a > piece of graph paper is unproductive, and that use of technology in this > situation may be preferred. However, it is important to separate the > purpose of schooling (process oriented, learning) from research (product, > results of learning). It is ok to do something by hand in order to learn > and/or practice something that might be done by a computer in a research > the students understand the process that is being eased by use of > technology is not always helpful. Science students need to first learn > fundamentals, initially with manual tools on problems that show mastery of > concepts. This need not involved excessive busy work. For example, > graphing of 15 data points by hand should not involve excessive drudgery, > and allows the instructor to verify that the students can (1) choose an > appropriate type of graph for the question asked and the data available, > (2) choose an appropriate scale for the axes, and (3) label the graph > appropriately. My own research involves heavy use of computers. However, I never allow > my students to use a computer until they have first shown that they > understand the concepts, as demonstrated in part through manual > computations. Of course, to do this I have had to develop and find > teaching examples for which manual steps are not too hard. One rule of > thumb that I try to follow is to avoid teaching too many concepts with one > activity. However, it can still be extremely difficult to strike the > right balance between use of spiffy technology and boring manual drudgery. ************************************************************************ > Ellen M. Wijsman COURIER DELIVERY ADDRESS ONLY: > Research Professor Ellen M. Wijsman > Div. of Medical Genetics and 1914 N 34th St., suite 209 > Dept. Biostatistics Seattle, WA 98103 > BOX 357720, University of Washington (Note: Use this address > Seattle, WA 98195-7720 EXACTLY as given above, and > phone: (206) 543-8987 use ONLY for courier delivery!!!) > web page: http://faculty.washington.edu/wijsman > ************************************************************************* >No. > > The training for most students should be concepts, not busy work. There is >NO value for students to sit there for an hour plotting 100 points on a >piece of graph paper. These rote activities reinforces the notion that >science is a dull and mindless exercise in drudgery. I'd rather have them >spend the time actually learning concepts. > > For science and engineering students should learn concepts as well as how to >do the work the way it is done in the real world. Have you worked in >research labs? Do you spend days chunking away with pencil and paper? Of >course not. You are using computers, sensors, probes, LabPro, MatLab, >Mathematica, calculators, etc. > > J > >> You can't think about and play >>with concepts if most of your time is used with rote data collection and >>manual calculation. >That, data collection and calculation, is fundamental to the study of any >hard >> science. It should never be abbreviated in the initial learning process. >G C -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Jhon I might be wasting my time replying to this but as I understand there is a slight misunderstanding that needs to be cleared and certain points that need to be clarified. > Well, there are several things wrong with your point of view. First, have > you ever actually read the NSF documents regarding science and math > education? If anything, they take the OPPOSITE approach to > one-size-fits-all. Yes I have read the documents. What you say is almost correct. However my point is have you seen the number of curriculum developed by various agencies based on funds from NSF? I would really suggest that you look at those if you haven't. If you are a teacher and that to in an urban inner city school then I would love to talk to you on how you teach math to kids. If you are a sub-urban teacher all I can say is that you are in a good position. > Yes, students should still learn multiplication tables, how to divide, > handle fractions, etc. But graphing calculators also allow complex concepts > to be learned much more quickly. How much time would it take, for example, > to do what-if discovery of polynomials using pencil and graph paper? In > the Workshop Physics approach, an extremely strong conceptual approach to > physics, is heavily dependent on technology. You can't think about and play > with concepts if most of your time is used with rote data collection and > manual calculation. But how about handling a calculator to a 6th grader to do 2+2? as for working with polynomials I have seen fourth year engineering students unable to solve a 3x3 matrix with pencil and paper when the computers dont work. How do you propose to teach them the process without paper and pencil practice? Basics are not learnt through computers in math and my dear friend I have seen students struggling even to solve a simple mixed fraction problem in college. Technology is good to assist when u know the concepts but is a bane when u dont even know what the things are all about. As far as Physics is concerned it can be learnt using technology ...cause if you have any knowledge of sciences and mathematics you will realise that they are interdependent yet quite different. > Doing things the hard way is not a virtue. The scam of reform is nonsense > in most cases. Yeah, there is some garbage out there, the cultural > diversity of arithmetic answers comes to mind. But if anyone really > believes that the old lecture to an auditorium is the best way to teach > science and math, that person is uninformed and/or just too lazy to be a > teacher. I agree doing things the hard way is not a virtue. How about not knowing that 2+2= 4 (just an example) and not 2+2=3? How about a 14 year old using fingers to count because they are lost without calculators. Lectures dont work , I agree with that. However that doesnt mean that technology does me who's lazy a person who can do simple mathmetics in his/her head or someone who cant add without a calculator.Technology is to assist us, not for us to be dependent on it. -- Girish Behal -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== I am writing a program for land surveyors and in it I need to find the azimuth of a line. I have the northings and eastings of two points on the line and now need to convert that to an azimuth. I am trying to convert a formula someone was nice enough to give me which finds an angle given the northing and easting. Here is the formula angle = tan^-1 ((delta northing) / (delta easting)) I'm embarresed to say I don't remember what delta means, if I ever knew. Can someone demonstrate to me what delta means? Can I use this formula to find the azimuth of a line? Any help would be great! -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Delta means the change in, the difference between two readings. I am writing a program for land surveyors and in it I need to find the > azimuth of a line. I have the northings and eastings of two points on > the line and now need to convert that to an azimuth. I am trying to convert a formula someone was nice enough to give me > which finds an angle given the northing and easting. Here is the formula angle = tan^-1 ((delta northing) / (delta easting)) I'm embarresed to say I don't remember what delta means, if I ever > knew. Can someone demonstrate to me what delta means? Can I use this formula to find the azimuth of a line? Any help would be great! -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > Can someone demonstrate to me what delta means? A capital Greek Delta (which looks like a triangle) is often used to indicate a difference, so that Delta x would mean the difference between two x values. -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== >Can someone demonstrate to me what delta means? > > A capital Greek Delta (which looks like a triangle) is often used to > indicate a difference, so that Delta x would mean the difference > between two x values. > > -- > Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus > life member (LAB, Adventure Cycling, American Youth Hostels) > Effective Cycling Instructor #218-ck (lapsed) > Professor of Computer Engineering, University of California, Santa Cruz > Undergraduate and Graduate Director, Bioinformatics > Affiliations for identification only. (slap the forhead!) ;-) -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Can the distance formula be applied to determine equational forms for anything in ADDITION TO conic sections, or is it only possible to create the conic section type equations and nothing more? Any other possibilities? G C -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== If x is divided by a, the remainder is b. y is divided by a, and the remainder is 4b. how can i use Euclid's algorithm to find this? a and b's HCF is 1. i don't want to know the answer, but can anyone direct me to some sites or give me some hints? -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== >If x is divided by a, the remainder is b. y is divided by a, and the >remainder is 4b. how can i use Euclid's algorithm to find this? a and >b's HCF is 1. i don't want to know the answer, but can anyone direct >me to some sites or give me some hints? Not sure what it is you're trying to find. x and y? To say a divides x with a remainder of b is to say: x = n*a + b To say y divided by a leaves a remainder of 4b is to say: y = m*a + 4*b where m,n are any two positive integers (or 0). To say HCF of a,b is 1 is to assert they have no common factors i.e. they're coprime. So if you have: x = n*a + b y = m*a + 4*b it's easy enough to just pick a,b,m,n out of thin air, where b Can anyone help me to solve this problem: > I have the unknown variables H and F and I dont'd know wich way to go. 12.100 + 27.000F = 200H > 22.960 + 40H = 90.000F The solution should be F=0,3 and H=101! But why??? please help!!! > And my response is: Two ways to solve this are by substitution or elimination. Let's do both: SUBSTITUTION We want to substitute one variable for another. Let's say we want to substitute H into F. So we need to change one of the equations so that H is by itself. REMEMBER: Whatever you do to one side of the equation you MUST do to the other! If we use the first equation: 12.100 + 27.000F = 200H So to isolate H, we need to divide both sides of the equation by 200 (the coefficient of H): (12.100 / 200) + (27.000F / 200) = (200H / 200) 0.0605 + 0.135F = H ----> since 200 / 200 = 1 and 1*H = H Now we can plug this equation into the opposite equation that we first used. We used the first equation the first time, so now we'll use the second equation. If we plug it into equation 2, we get: 22.960 + 40H = 90.000F 22.960 + 40 ( 0.0605 + 0.135F ) = 90.000F 22.960 + 2.42 + 5.4F = 90.000F Now we need to get F on one side of the equation. So we'll subtract 5.4F from BOTH sides: 22.960 + 2.42 + 5.4F - 5.4F = 90.000F - 5.4F Now simplify: 25.38 = 84.6F Divide both sides by 84.6 to isolate F: 25.38 / 84.6 = 84.6F / 84.6 0.3 = F So far we have solved for F. Now we need to solve for H. We can plug our solution of F = 0.3 into EITHER of our first 2 equations to solve for H. Let's plug F=0.3 into equation 1: 12.100 + 27.000F = 200H 12.100 + 27.000 ( 0.3) = 200H 12.100 + 8.1 = 200H Simplify: 20.200 = 200H Divide both sides by 200 to isolate H: 20.200 / 200 = 200H / 200 0.101 = H So our solution is H = 0.101 and F = 0.3. To check we plug both values into both equations. If the left side = right side, then we know we have the right answer: Equation 1: 12.100 + 27.000F = 200H 12.100 + 27.000 ( 0.3) = 200 ( 0.101 ) 12.100 + 8.1 = 20.2 20.200 = 20.2 the left equals the right ... so far so good Equation 2: 22.960 + 40H = 90.000F 22.960 + 40 ( 0.101 ) = 90.000 (0.3) 22.960 + 4.04 = 27 27.000 = 27 the left equals the right in BOTH equations therefore we know our solution is correct!! ELIMINATION We want to eliminate one variable by making the coefficients for that variable equal to each other. Let's say we want to eliminate H. So we need to make both coefficients equal. Let's make them both 200. 12.100 + 27.000F = 200H 22.960 + 40H = 90.000F We can turn 40H into 200H by multiplying by 5, but in order to do that we must remember that whatever we do to one side of the equation we MUST do to the other. So, 5 ( 22.960 + 40H ) = 5 ( 90.000F ) 5 ( 22.960 ) + 5 ( 40H ) = 450.000F 114.8 + 200H = 450.000F So now our 2 equations are: 12.100 + 27.000F = 200H 114.8 + 200H = 450.000F Let's get 200H on the right side of both equations. So for equation 2 we'll subtract 200H from both sides: 114.8 + 200H - 200H = 450.000F - 200H 114.8 = 450.000F - 200H Now we'll subtract 450.000F from both sides: 114.8 - 450.000F = 450.000F - 450.000F - 200H 114.8 - 450.000F = ( - 200H ) So now our 2 equations are: 12.100 + 27.000F = 200H 114.8 - 450.000F = ( - 200H ) So to eliminate H, we can add the 2 equations together: 12.100 + 27.000F = 200H + 114.8 - 450.000F = ( - 200H ) ___________________________ 126.900 - 423F = 0 We want to isolate F, so we subtract 126.900 from both sides: 126.900 - 126.900 - 423F = 0 - 126.900 ( - 423F ) = ( - 126.900 ) Now we can multiply both sides by ( - 1 ): ( - 1 )( - 423F ) = ( - 1 )( - 126.900 ) 423F = 126.900 And divide both sides by 423: 423F / 423 = 126.900 / 423 F = 0.3 So far we have solved for F. Now we need to solve for H. We can plug our solution of F = 0.3 into EITHER of our first 2 equations to solve for H. Let's plug F= 0.3 into equation 2: 22.960 + 40H = 90.000F 22.960 + 40H = 90.000 ( 0.3 ) 22.960 + 40H = 27 Since we want to isolate H, we need to get it on either side of the equation by itself. So we can subtract 22.960 from both sides: 22.960 - 22.960 + 40H = 27 - 22.960 Simplify: 40H = 4.04 Divide both sides by 40 to isolate H: 40H / 40 = 4.04 / 40 H = 0.101 So our solution is H = 0.101 and F = 0.3. To check we plug both values into both equations. If the left side = right side, then we know we have the right answer: Equation 1: 12.100 + 27.000F = 200H 12.100 + 27.000 ( 0.3) = 200 ( 0.101 ) 12.100 + 8.1 = 20.2 20.200 = 20.2 the left equals the right ... so far so good Equation 2: 22.960 + 40H = 90.000F 22.960 + 40 ( 0.101 ) = 90.000 (0.3) 22.960 + 4.04 = 27 27.000 = 27 the left equals the right in BOTH equations therefore we know our solution is correct!! -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== geomitry ???plz....... thanks -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > > geomitry ???plz....... > thanks Try this: http://www.bymath.com/studyguide/geo/geo14.htm For me it worked in Internet Explorer but not Netscape. Or this: http://mathworld.wolfram.com/DihedralAngle.html And others... Googling helps. -- G.C. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== I assume you mean dihedral angle -- angels might be a bit off-topic. Multiple sites on google search, some below (might want to skip references to chemistry) : http://mathworld.wolfram.com/DihedralAngle.html http://www.cem.msu.edu/~cem251/F96/alkane_conformations/ANGLE1.html http://www.bartleby.com/61/imagepages/A4dihedr.html http://sinai.mech.fukui-u.ac.jp/gcj/software/Dihed/ http://www.olympus.net/personal/mortenson/preview/definitionsd/dihedralangle ..html http://josephfusco.org/Articles/Dihedral/Dihedral.html http://www.homoexcelsior.com/omega.db/datum/aerospace_engineering/dihedral_a ngle/5728 http://www.it-c.dk/bibliotek/encyclopedia/math/d/d207.htm http://www.ics.uci.edu/~eppstein/junkyard/tetraqual.html > geomitry ???plz....... > thanks > -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > geomitry ???plz....... Someone suggested skipping all the chemsitry papers. Actually, that may be a bad idea. I had absolutely no use for dihedral angles until I started doing protein-structure prediction in my 40s---the dihedral angles of protein backbones give a very concrete visualization of the angles, and are absolutely critical to understanding protein shapes. -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== By definition, a linear transformation T from vector space V to W is one that satisfies 1. T (x+y) = T(x) + T(y), and 2. T (kx) = kT(x) for any x, y in V, and scalar k. Can anybody give a simple example of a non-linear transformation F which satisfies condition 2 but not 1? -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > > By definition, a linear transformation T from vector space V to W is > one that satisfies > 1. T (x+y) = T(x) + T(y), and > 2. T (kx) = kT(x) > for any x, y in V, and scalar k. > > Can anybody give a simple example of a non-linear transformation F > which satisfies condition 2 but not 1? consider T: RxR -> R T((x,y)) = { x if y=0 { 0 otherwise T((kx,ky)) = { kx if ky=0 { 0 otherwise = { kx if y=0 { 0 if k=0 { 0 otherwise = k T((x,y)) T((1,-1)) =0 T((1,1)) = 0 T( (1,1) + (1,-1) ) = T((2,0)) = 2 -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Math is not politically connected. Please do not math to teach about cultural diversity. Math does not belong to any culture or a single community and everybody learns same mathematical concepts. If you think that math is sensitive subject to people from some communities ... i would like to know how.. cause being not math is a sensitive subject and not math itself. Please dont teach math subjectively because it cannot be taught subjectively.It is cold hearted and strsight subject. Teaching it subjectively will only confuse a lot of students. Carol what you are trying to do is appreciable but imagine for example saying that community X adds 2+2=3.... I think you have more sense than that.. Instead you would do much better trying to use geometrical figures rather than algebra to get across your point about difference in thinking. I am looking for ideas as to how I might teach the subject of > mathematics in my classroom, while at the same time recognizing and > showing appreciation to the many diverse cultures that are present. In > general, I try to avoid the subject of mathematics, since it is a very > sensitive topic for many students of other cultures. However, it is > also required by the school board that at least an hour of mathematics > be taught each day. In general, to avoid hurt feelings or notions of > cultural intolerance, I try to teach math in a very subjective manner. > For example, rather than teaching that 2+2=4, and there is no other > correct answer, I try to prepare my students to tolerate other ways of > thinking by asking them ''how do you feel about the equation 2+2?'' If > a student were to answer that 2+2=3, I would not reprimand him or her. > Rather, I would introduce his/her answer as a different point of view, > and try to show the rest of the class how different people and > different cultures think in diverse ways. At any rate, I was wondering if anyone else has had similar > experiences balancing math with cultural diversity. I would be > interested to know how others have dealt with the issue. Respectfully, > Carol Andrews -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== >> Please do not math to teach about cultural diversity. Exactly! This type of nonsense introduce [2+2=3] his/her answer as a different point of view, and try to show the rest of the class how different people and different cultures think in diverse ways is insulting and condescending. It does more to set people apart than it does to bring them together. Too bad this particular math teacher chooses talk down to the students instead of teaching them that 2+2=4 regardless of culture. John > Math is not politically connected. Please do not math to teach about > cultural diversity. > Math does not belong to any culture or a single community and everybody > learns same mathematical concepts. > If you think that math is sensitive subject to people from some communities > ... i would like to know how.. cause being not math is a sensitive subject > and not math itself. > Please dont teach math subjectively because it cannot be taught > subjectively.It is cold hearted and strsight subject. Teaching it > subjectively will only confuse a lot of students. Carol what you are trying to do is appreciable but imagine for example > saying that community X adds 2+2=3.... > I think you have more sense than that.. Instead you would do much better trying to use geometrical figures rather > than algebra to get across your point about difference in thinking. > > I am looking for ideas as to how I might teach the subject of >mathematics in my classroom, while at the same time recognizing and >showing appreciation to the many diverse cultures that are present. In >general, I try to avoid the subject of mathematics, since it is a very >sensitive topic for many students of other cultures. However, it is >also required by the school board that at least an hour of mathematics >be taught each day. In general, to avoid hurt feelings or notions of >cultural intolerance, I try to teach math in a very subjective manner. >For example, rather than teaching that 2+2=4, and there is no other >correct answer, I try to prepare my students to tolerate other ways of >thinking by asking them ''how do you feel about the equation 2+2?'' If >a student were to answer that 2+2=3, I would not reprimand him or her. >Rather, I would introduce his/her answer as a different point of view, >and try to show the rest of the class how different people and >different cultures think in diverse ways. > > At any rate, I was wondering if anyone else has had similar >experiences balancing math with cultural diversity. I would be >interested to know how others have dealt with the issue. > > Respectfully, >Carol Andrews > -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Greetings, years old son, to help him with math. Seeing noticeable improvement of his math skills within few days after playing with this game I started thinking to give it a spin as a commercial product. I am seeking a second opinion. I would appreciate comments from both teachers and parents. If you would like to give it a try it is available for download from the link below: http://pjwalczak.com/mninja/mnsetup.exe The intended platform is MS Windows, preferable configuration is sound, and color display. Piotr J. Walczak -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== I am wondering if anyone knows of a program I can download to give me all possible 5 number combinations from the numbers 0 through to 9??? thanks -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > I am wondering if anyone knows of a program I can download to give me > all possible 5 number combinations from the numbers 0 through to 9??? > thanks Do you mean 5 digit combinations, ie, all numbers of the form XXXXX? If so, just count from 0 (or 1000 if you want to be picky) to 9999. If you don't want to duplicate numbers (ie each digit only used once) then something like the following: (C++; code snippet is sloppy and inefficient but easy to type and understand) for (int i=0; i<10) for (int j=0; j<10) for (int k=0; j<10) for (int l=0; j<10) { if ((i !=j) && (i!=k) && (i!=l) && (j!=k) && (j!=l) && (k!=l)) { cout << i << j << k << l << endl; } } That will output all of the combinations. Stick it into a program with the appropriate header files and pipe the output to a file for use. If you have no idea what that last paragraph said, post again and I'll simplify :-) -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== What is the angle of each side of a perfect octagon? -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Use this formula: [180(n-2)]/n n = sides Good Luck John > What is the angle of each side of a perfect octagon? > -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== >What is the angle of each side of a perfect octagon? Interior or exterior angle? Either way, you can work it out yourself. Imagine going all round the octagon; you will have to turn a total of 360 degrees. Since there are 8 angles, 360/8 will be important in your answer. -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com Fortunately, I live in the United States of America, where we are gradually coming to understand that nothing we do is ever our fault, especially if it is really stupid. --Dave Barry -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > What is the angle of each side of a perfect octagon? I assume that by perfect you mean regular -- i.e., that all angles are equal and all side lengths are equal. A regular triangle has 60 degrees in each angle. Starting with that, mathematical induction will prove a nice formula for any regular polygon. Good luck and enjoy. Michael Hamm BA scl Math, PBK, NYU msh210@math.wustl.edu Note new URL: http://www.math.wustl.edu/~msh210/ -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > What is the angle of each side of a perfect octagon? Do you know the formula for the sum of the measures of the interior angles of an n-gon? That would be a good first step. Also, when you say perfect octagon I assume that you actually mean a regular octagon? A regular n-gon is a polygon where all n sides have equal lengths and all n angles have the same measures. Rich -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > What is the angle of each side of a perfect octagon? To solve this problem, think about a turtle moving along the edges of the polygon. The turtle turns a bit at each corner (the amount it turns is sometimes called the exterior angle of the polygon). When it has gone all the way around the polygon, it is facing the same way as it started. How much as it turned in total? How many times very easy to get the interior angles you are looking for. -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== > > What is the angle of each side of a perfect octagon? > Sides don't have angles. Adjacent sides have angles between them. Imagine yourself walking along the sides of a _regular_ octagon. At each vertex you must turn through 45 degrees because 8*45 degrees = 360 and you must have turned through a total of 360 degrees when you get back to where you started since you will then facing in the same direction as when you set out. Had you not turned at a vertex you would have made an angle of 180 degrees at that vertex, so the interior angle at each vertex is (180 - 45) degrees = 135 degrees. Draw a picture. -- G.C. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== >>I am stuck on the following three problems. Any help would be greatly >>appreciated. I started writing a list of hints and questions for each one. But it >all boils down to: What _specifically_ did you try? Students tend to give up over any >problem that is not entirely straightforward. Yet the first and >third at least are pretty standard problems, and you should expect >similar problems on your exam -- where you will have to solve them >without assistance. It's okay to ask for help, but you need to build >up your own mental muscles by getting as far as you can on your own. >very often a student will find that simply looking at the problem a >second time is all it takes. I'll be happy to help you over a particular rough spot, but simply >doing the problems for you to look at the solutions is really no >service to you. -- >Stan Brown, Oak Road Systems, Cortland County, New York, USA > http://OakRoadSystems.com >Fortunately, I live in the United States of America, where we are >gradually coming to understand that nothing we do is ever our >fault, especially if it is really stupid. --Dave Barry > > > I'll try each some more and if I still don't get them I'll post back Ya, i was making stupid mistakes on them, and was able to get 1+3, and got 2 after realizing cos(105) wasn't a variable(duh!). > Scott Eliason -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== MathLove in S Korea has a broad range of materials, including GrafEq and Poly in Korean language interfaces. http://www.mathlove.or.kr/ Gary Tupper Pedagoguery Software Inc. -- newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html