On Oct 9, 2012, at 11:59 AM, Paul Tanner <email@example.com> wrote:
> For instance, on Algebra I courses - do you really want raise the > minimum floor such that only the gifted can get above it, making it so > that only the gifted could ever be expected to pass even just a > general Algebra I course? If so, I would think that those who wrote or > who are in favor of such as the CA Mathematics Content Standards would > disagree with you, since they wrote those standards for the whole > population. Are you aware that Wayne Bishop was part of that movement > that created these CA standards - this minimum floor - for all?
If CA wrote those standards for the "whole" population then they didn't do a good job since only 25% of the "whole" population passes. What if we defined music instruction for the "whole" population? What does that get us? A whole population that knows a little bit about music but none able to make it a profession? Let's recall how algebra became important in the first place. It typified the college bound student, probably along with Geometry, Latin, literature and some science (Chemistry/Biology). If you really wanted to "give" that to other students, then you why would you change the standards at all? What sense is it to prescribe college bound courses to students and then cut the legs off those courses?
I think many of our students are capable of a lot more. Not all of them, probably not most of them, but many more than just a select few. As it stands now, only a select few even have the opportunity because the vast majority are exposed to a substandard form of mathematics. And I am not talking about gifted students. We do not have to label anyone. All you have to do is when you offer a course titled Algebra, offer the real thing. The students will know if they are ready or not.
Thus far, the best idea I have seen is to increase or decrease the pace of the course, but not the coverage. Some students might very well have the same algebra book for 3 or 4 years. After the remarks by Dave and yourself, I paged through my Dolciani text last night and realized just how much was in there. I could see using that book for 2 or even 3 years. But the students better be mastering the pieces. And some students will not have any algebra book, they will have some other manual geared towards their interests and aspirations. Also, last night, as I paged through the book and tried to transport myself back in time to those days, I realized that the book was like an operational manual for your head and all the neat things it can do. Very personal. Each chapter was like the next neat feature, not of math, of my mind. All books dealing with an artful skill are probably like that.