mswaine wrote: > > Guy, > Thank you for that clarification. By it, can I infer that one could use > Saxon in conjunction with other constructivist text to provide a > balanced math course. I ask this because I have seen that my son and his > fellow students score lower in computational skill on SAT9 tests. My > general experience is that "Traditional Schools" score much higher on > SAT9 tests in our area (Phoenix). Do you have any thoughts on this dichotomy.
I don't know any of the facts about the Phoenix area performance, so any thoughts on my part would be pure speculation. I am not convinced that the SAT9 (which we use here in DC) is all that great a test.
> I find that word problems alone do not seem to provide the variety of > permutations of a given algorithm for the student to become proficient. > I agree with you that teaching the context of math in the real world is > more difficult, and I find many of the word problems my son brings home > rather open ended or incomplete with many possible (or impossible) > answers depending on how the question is interpreted.
Sometimes textbooks don't do a good job of coming up with real world problems. We have to balance the overwhelming open-endedness, fuzziness, and incompleteness of the real world with students' need to have some clarity and closure. Not an easy job to balance the two. Traditional word problems in traditional textbooks could be translated almost word-by-word into an equation. But the real world is a lot trickier than that. At the same time, we shouldn't overwhelm and confuse the students too much.
> Sometimes I feel we are trying to teach too much math in middle grades. > I was not introduced to algebra until high school. I see my son will be > into algebra in his advanced 6th grade math this next fall/spring.
Interesting complaint. Most other developed countries in the world actually do teach some algebra in the 5th and 6th grade. On the other hand, they do not have a single year-long course labeled "algebra", followed by a single year-long course labeled "geometry", and so on. What they do is the following: there is a standard, national curriculum. Each year certain topics are introduced, others are reviewed and plumbed in more depth, and others are essentially only used for further topics. The textbooks are rather small by US standards, because the publishers are not faced with the anarchic situation we have here in the US where there are 50 states that attempt to set their own standards and curricula, more or less, followed by thousands (maybe tens of thousands) of local, autonomous school boards attempting to set their own standards and curricula, and in those school districts, many individual schools and many individual teachers are free to 'do their own thing' and make up their own curricula. The result is that textbook publishers in this country have to anticipate the desires of thousands of different school districts -- and thus they have to include virtually EVERY conceivable topic that anybody might be interested in teaching that grade level, and they have to be very attractive visually so as to appeal to overworked, harried committees that are in charge of choosing the next textbook series in those thousands of school districts and hundreds of thousands of local schools. Thus, many of the books are about 500 to 700 pages long and are guaranteed to have the latest buzz words. The common complaint is that the American math and science curricula are a mile wide and an inch deep.
> I > find myself looking to a tutor to see if he can bring his computational > skills up sufficiently.