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How to lower one's expectation in teaching college algebra
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[QUOTE="mathwonk, post: 6793520, member: 13785"] I also checked online info for about 10 different local colleges and community colleges vis a vis geometry courses. about half had courses for elementary school teachers that included geometry, others had calculus courses that included analytic geometry. my impression therefore is that people think of euclidean geometry as an elementary course that is taught and learned in high school or earlier, and hence is assumed in some form in all college courses. my experience shows this is false, and that most US secondary schools offer very inadequate geometry instruction and most college students have little grasp of it. but i only learned that late in my career by teaching the geometry courses for elementary and high school teachers. at my former uni, univ of georgia, there is a very strong school of math education that coordinates with the math dept and thus there are numerous geometry courses aimed at teachers of all levels, at least elem. school, middle school, and high school. there are also courses in differential geometry, topology and algebraic geometry, as well as courses showing how modern abstract algebra (group theory and linear algebra) can be used in euclidean as well as projective geometry. the basic fact that euclidean geometry is not well taught or learned by most americans except in advanced university courses seems still somewhat ignored. As an example of this ignorance, when preparing to teach the class I read on page 8 of Hartshorne that he would use a fact he hoped was familiar to most readers: that any two angles in a circle which subtend the same arc, are equal even if their vertices are at different points of the circle, I did not myself recall that fact. And I was then a university professor and researcher specializing in (algebraic) geometry for several decades. Teaching and learning geometry from the book of Euclid, in my 60's, was one of my greatest intellectual pleasures, and I have studied thoroughly only books 1-4 and parts of 5 and 6. [/QUOTE]
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