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#32
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Don't Call It "Algebra"; Call It Something Warm And Fuzzy
In article ,
Larry Hewitt wrote: "Herman Rubin" wrote in message ... In article , Larry Hewitt wrote: "toto" wrote in message ... On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt" wrote: And that, as you note, geometry is the "formal" math class, requiring more rigor in answering questions? Except that in many schools in order to get kids to pass geometry, the schools are using *informal geometry* without rigorous proofs. See: http://hsfs2.ortn.edu/MYSCHOOL/WJONES/infgeom.htm Informal Geometry is a standards-based, Euclidean geometry course which meets the criteria for the state's geometry curriculum. The major difference between Informal Geometry and Geometry AB is the amount of formal proofs that are written in this curriculum. There are more hands-on activities and more real-life geometry problems versus abstract problem solving. Knowing teachers and students, the amount of formal proofs goes down to almost nothing, and the amount of it learned by students is likely to be absolute zero even if it is there. Having taught this course in a Chicago Public High School, I can tell you that it is not a college prep course and that while some of the concepts are taught, much of the course is dumbed down. There were no formal proofs with statements and reasons in our course. There were some informal proofs in paragraph form which in many ways was harder for the students to understand. My dd called this course *geometry for stones* and she called Conceptual Physics (physics without math) *physics for trees.* And I must strongly accuse the college admissions offices, in their rush to get more students, being willing to accept geometry for stones and physics for trees. These students, if the term can be used for such, lower the standards of the college courses, as good student evaluations are now needed for tenure, and often even for promotion of a tenured associate professor to full professor. I know of no distrcit where geometry is intended to be a college prep course. It was before WWII, and it should be now. This includes for those not going into mathematical subjects; it is unfortunate that our politicians and judges have no idea what a formal proof is, and what an inductive proof (NOT a proof by induction) is; the latter is what is used in decisions where the facts are in dispute. The main value of the geometry course is to give an understanding of proofs. The rest is of much less value than one would think. Nope. The main value of secondary geometry is to get students to hink spacially. This does not occur by giving names and formulas. Look, this will go nowhere. Here's achallenge for you. Got into a 9th grade calssroom. Teach the kids. If they understand English, it might still be possible. Try to get the averaage 15 yr old to understadn and comply with the rules of formal proofs. Average, average, average. Students of different ability MUST be taught differently; not accepting this is denying the well-established fact that people are different. Try to get a 16 yr old to understand number theory. This might be much easier. Or, if you'ld rather, pick a lower grade and start them off "right". I have posted here, many times, that the time to teach about variables is when they can read a little and make symbols. It is part of language; restricted to mathematics, it loses its simplicity. Let us know how it went. Do you think the educationists would let me try? -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University Phone: (765)494-6054 FAX: (765)494-0558 |
#33
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Don't Call It "Algebra"; Call It Something Warm And Fuzzy
"Herman Rubin" wrote in message ... In article , Larry Hewitt wrote: "Herman Rubin" wrote in message ... In article , Larry Hewitt wrote: "toto" wrote in message m... On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt" wrote: And that, as you note, geometry is the "formal" math class, requiring more rigor in answering questions? Except that in many schools in order to get kids to pass geometry, the schools are using *informal geometry* without rigorous proofs. See: http://hsfs2.ortn.edu/MYSCHOOL/WJONES/infgeom.htm Informal Geometry is a standards-based, Euclidean geometry course which meets the criteria for the state's geometry curriculum. The major difference between Informal Geometry and Geometry AB is the amount of formal proofs that are written in this curriculum. There are more hands-on activities and more real-life geometry problems versus abstract problem solving. Knowing teachers and students, the amount of formal proofs goes down to almost nothing, and the amount of it learned by students is likely to be absolute zero even if it is there. Having taught this course in a Chicago Public High School, I can tell you that it is not a college prep course and that while some of the concepts are taught, much of the course is dumbed down. There were no formal proofs with statements and reasons in our course. There were some informal proofs in paragraph form which in many ways was harder for the students to understand. My dd called this course *geometry for stones* and she called Conceptual Physics (physics without math) *physics for trees.* And I must strongly accuse the college admissions offices, in their rush to get more students, being willing to accept geometry for stones and physics for trees. These students, if the term can be used for such, lower the standards of the college courses, as good student evaluations are now needed for tenure, and often even for promotion of a tenured associate professor to full professor. I know of no distrcit where geometry is intended to be a college prep course. It was before WWII, and it should be now. This includes for those not going into mathematical subjects; it is unfortunate that our politicians and judges have no idea what a formal proof is, and what an inductive proof (NOT a proof by induction) is; the latter is what is used in decisions where the facts are in dispute. The main value of the geometry course is to give an understanding of proofs. The rest is of much less value than one would think. Nope. The main value of secondary geometry is to get students to hink spacially. This does not occur by giving names and formulas. Look, this will go nowhere. Here's achallenge for you. Got into a 9th grade calssroom. Teach the kids. If they understand English, it might still be possible. Try to get the averaage 15 yr old to understadn and comply with the rules of formal proofs. Average, average, average. Students of different ability MUST be taught differently; not accepting this is denying the well-established fact that people are different. Try to get a 16 yr old to understand number theory. This might be much easier. Or, if you'ld rather, pick a lower grade and start them off "right". I have posted here, many times, that the time to teach about variables is when they can read a little and make symbols. It is part of language; restricted to mathematics, it loses its simplicity. Let us know how it went. Do you think the educationists would let me try? Set up a lab program in the math department, say on Saturday mornings, for interested parents to enroll their child in. Such programs are common in Schools of Music (and in other fine arts areas). Music teachers aren't trained by education departments, but by music departments, so such programs serve multiple purposes. They provide hands-on experience to college professors, who then are teaching actual children, as opposed to just hypothesizing about how things will work with children. They provide a research laboratory to test and try out new programs, which then become common, and they provide observation and practicum experiences for students who are going through music training, before they ever begin any significant training in pedagogy. (Music pedagogy is typically a 5th or even 6th year program, completed after the music requirements are satisfied. Specialist training in Orff, Kodaly, or Dalcroze isn't even availble until after a teacher has a baccalaureate degree in music). My university was the first to begin Orff-Schelwerk in the USA, in a lab program between the university and the local schools. Other similar programs have done the same with Kodaly and Dalcroze, and Edwin Gordon has taken his research as well. The result is that all of these tested methodologies have found their place in the elementary school music curriculum, and, in areas where elementary school music is actually taught by trained music specialists, the quality of music instruction K-12 is much, much higher than it was 30+ years ago (finances have eliminated or cut back music from so many districts that unfortunately it is relatively rare for a child to get regular classes in the elementary years-and then, such districts wonder why the secondary music programs fall apart). Even when there is no trained music teacher, if a district actually purchases and uses a music textbook series, which are designed for classroom teachers, many of the principles which have been shown to be effective will be applied, and the students will STILL get a higher quality music education than was available in most schools 30+ years ago. There is absolutely no reason why other academic departments couldn't do likewise. If you want to teach children, train teachers, and change education, the first step is doing it yourself, locally, in a situation under your control. Prove what you do works, and eventually, what works will be adopted. Given that over half my preschool music students this year were enrolled in Kumon math (which is simply drill and memorization, at a very high price tag), I don't think you'd have any trouble getting students. |
#34
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Don't Call It "Algebra"; Call It Something Warm And Fuzzy
"Herman Rubin" wrote in message ... In article , Larry Hewitt wrote: "Herman Rubin" wrote in message ... In article , Larry Hewitt wrote: "toto" wrote in message m... On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt" wrote: And that, as you note, geometry is the "formal" math class, requiring more rigor in answering questions? Except that in many schools in order to get kids to pass geometry, the schools are using *informal geometry* without rigorous proofs. See: http://hsfs2.ortn.edu/MYSCHOOL/WJONES/infgeom.htm Informal Geometry is a standards-based, Euclidean geometry course which meets the criteria for the state's geometry curriculum. The major difference between Informal Geometry and Geometry AB is the amount of formal proofs that are written in this curriculum. There are more hands-on activities and more real-life geometry problems versus abstract problem solving. Knowing teachers and students, the amount of formal proofs goes down to almost nothing, and the amount of it learned by students is likely to be absolute zero even if it is there. Having taught this course in a Chicago Public High School, I can tell you that it is not a college prep course and that while some of the concepts are taught, much of the course is dumbed down. There were no formal proofs with statements and reasons in our course. There were some informal proofs in paragraph form which in many ways was harder for the students to understand. My dd called this course *geometry for stones* and she called Conceptual Physics (physics without math) *physics for trees.* And I must strongly accuse the college admissions offices, in their rush to get more students, being willing to accept geometry for stones and physics for trees. These students, if the term can be used for such, lower the standards of the college courses, as good student evaluations are now needed for tenure, and often even for promotion of a tenured associate professor to full professor. I know of no distrcit where geometry is intended to be a college prep course. It was before WWII, and it should be now. This includes for those not going into mathematical subjects; it is unfortunate that our politicians and judges have no idea what a formal proof is, and what an inductive proof (NOT a proof by induction) is; the latter is what is used in decisions where the facts are in dispute. The main value of the geometry course is to give an understanding of proofs. The rest is of much less value than one would think. Nope. The main value of secondary geometry is to get students to hink spacially. This does not occur by giving names and formulas. Look, this will go nowhere. Here's achallenge for you. Got into a 9th grade calssroom. Teach the kids. If they understand English, it might still be possible. Try to get the averaage 15 yr old to understadn and comply with the rules of formal proofs. Average, average, average. Students of different ability MUST be taught differently; not accepting this is denying the well-established fact that people are different. Try to get a 16 yr old to understand number theory. This might be much easier. Or, if you'ld rather, pick a lower grade and start them off "right". I have posted here, many times, that the time to teach about variables is when they can read a little and make symbols. It is part of language; restricted to mathematics, it loses its simplicity. Let us know how it went. Do you think the educationists would let me try? Absolutely. No question. YOu have impeccable credentials, and there are enough experimental programs, charter schools, private schools, and the like _begging_ for teachers you would be snapped up in a heartbeat. Larry -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University Phone: (765)494-6054 FAX: (765)494-0558 |
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