On Mon, Oct 8, 2012 at 8:32 AM, Robert Hansen <email@example.com> wrote: > The curriculum represented by authors like Dolciani, Lawson and Forrester is > what I have been calling the golden age of high school algebra. Books like > the one I reviewed by Shute have their place, the writing is certainly > better, but I think the mix of topics and problems in the above mentioned > books are better. So do some of the asian countries that favor mathematics > because those are the books they use. That curriculum was defined in the > 60's, not recently. Today we call classes that use those books "Honors > Algebra", a phrase that wasn't in wide use till recently... >
What you say again is just more of these delusional ideas that in "the good old says" of the 1970s the masses learned much more math and much higher level math than today, never mind that fact that it's precisely the opposite - the masses learn much more math and much higher level math today than in the 1970s.
The idea that the high school Algebra I and Algebra II sequence should contain ALL of precalculus algebra, including all of analytic trigonometry, analytic geometry, matrices, vectors, and so, is a modern phenomenon that did not really get started in any widespread way until the explosion of interest in high school calculus in the 1980s, accelerated in a major way by that Jaime Escalante movie about poor high school kids learning high school calculus. Back then, one had to take at least one extra course after Algebra II to get all those extras that were not normally covered in the usual Algebra I and Algebra II sequence, on such as the binomial theorem, vectors, matrices, and analytic trigonometry and analytic geometry.
I believe that if you looked at the very first editions of all those "honors" textbooks you mentioned that first were published way back in the 1960s or 1970s, then you will find that their very first editions did NOT contain ALL of precalculus mathematics as they do now in the more modern editions. This evolution simply reflects the overall evolution that you deny, that these two one-year courses of Algebra I and Algebra II went from NOT normally being a sequence that contained ALL of precalculus algebra to being a sequence that normally does.
Side Note: By the way, these theoretically rigorous 1960s New Math texts like Dolciani, even though they in their first editions did not cover everything their modern editions cover, after being tried out briefly in the 1960s, because they were way too theoretically rigorous for the masses they were dropped like hot potatoes all over the country by districts that tried them as texts for all, and therefore were NOT widespread in the least after that in the 1970s. If they were kept at all, it was only for the gifted students. The vast majority of districts that tried them as texts for all treated them as too hot to handle and went to texts that both were much less theoretically rigorous and still did not cover all the material that modern texts do. And so the time around the 1970s was a time of low minimum standards for the masses, no higher then before the 1960s, even if they kept their higher standards only for the gifted by keeping these texts only for them. Read the history of math education, and you will read that the 1970s were considered to be a low point in minimum standards for the masses, both in terms of quality and quantity, no better than before the 1960s New Math texts coming out. (Note that the 1960s New Math experiment of theoretically rigorous math for all was a bust.)
If you read about what Escalante actually did and did not do, you will find powerful evidence of the truth of all of what I am saying. That is, at that time, since there were no off-the-shelf Algebra I and Algebra II textbook sequences that contained ALL of precalculus mathematics and that were easily and widely available, you will read that he and the teachers he worked with had to do some tweaking to get his to-be students ready for calculus by the time they were seniors. You will read that he had to have them start Algebra I in 8th grade, or if they did what they typically did then, start Algebra I in 9th grade, he had them to do some out-of-regular-class-time tutoring on all these extras that the usual Algebra I and Algebra II sequence of that time did not cover.
And if you read what some people say even now, you will find that many people still think that just two one-year courses, Algebra I and Algebra II, is NOT enough time to properly cover ALL of precalculus mathematics to be truly prepared for calculus. This is partly why we see more and more movement from the way it used to be, which is start Algebra I in 9th grade, to what it is more and more becoming, start Algebra I in 8th grade.
Finally, again: From the very beginning in this thread I have been talking about MINIMUM standards imposed on ALL, NOT other standards. Everything I have said in this thread on this is just plain fact, including the fact that because the MINIMUM standards imposed on ALL have so drastically increased from what they were in the 1970s - again recall the fact that most who graduated from high school back then had NO knowledge of algebra and gad NO knowledge of high school geometry, the AVERAGE student who graduates from high school does so with much more algebraic and geometric knowledge than was the case then in the 1970s.
And in addition, because of this explosion of interest in high school calculus that really took off in the 1980s in part because of the Escalante phenomenon becoming widespread knowledge, the percentage of the entire high school senior aged population that learns at least some calculus before graduating has tripled since the 1970s, from roughly 5% to roughly 15% (presently roughly 600,000 out of roughly 4 million, roughly 450,000 in AP Calculus), and the percentage of the entire high school senior aged population that demonstrates that they acquired and retained enough calculus knowledge and skill to pass a national AP Calculus exam has increased by an entire order of magnitude, from roughly half a percent to roughly 5 percent (presently roughly 200,000 out of roughly 4 million, where roughly a little over 300,000 take the test).
Again: This above and what I say throughout this thread is just plain fact, and you are just going to have to accept it as plain fact.
Yes, I know, your beef is something else, about "other" standards going down, but that does NOT mean that all these facts that I put forth is not fact, and it does NOT mean that therefore you can deny fact, which is what you have been trying to get away with doing all throughout this thread.
If you wish to make a beef that there is not enough attention paid to the gifted, say the roughly top couple percent or so, that there used to be more attention paid to them, then say it explicitly with respect to that type of student, and stop trying to deny fact about everyone else in the process.
By the way, on this very last point on the gifted: I have already agreed in other threads again and again that they should bring back the gifted programs they used to have in the district I grew up in and in other districts, and that in every district they should even go further than they ever used to go on this type of thing, for accelerated programs alongside the regular ones especially.