On Thu, 3 Apr 1997, Michael Paul Goldenberg wrote: > > Drill and practice on computation skills has its place. So does seeing the > beauty of mathematics. But so do developing the ability to question why > procedures work, how to solve non-routine problems, how to communicate > one's mathematical conjectures, and a host of other things raised by the > Standards (and generally decried by counter-reformers.
"Counter-reformers"? Nobody admits to that title, I think. Counter-*Standards*, perhaps, but not on the grounds that all is well today. See what Goldenberg says below:
> There is reason to > believe that some folks have gone to the other extreme (throwing out any > and all parts of traditional math pedagogy entirely), but I haven't met or > spoken with a single one. On the other hand, I sit in mathematics > classrooms every single week at various schools (grades 6-12) in > southeastern Michigan
*where the instruction is indistinguishable from that > of my own education some 35 years ago. How much impact have the Standards > really had, I wonder.* [my emphases, RAR]
This is the question. 35 years ago was the apogee of the New Math, which was also supposed to have been a reform, though it was not as monolithic as the Standards in its Writs. I have heard it said by veterans that The New Math (by whatever definition you like) affected something like 10% of K-8 students, though other reforms, only loosely connected to all that about sets, logic, Boole and base-n for small children, did affect grades 9-12, especially for the college bound. The reasons for the lack of penetration of these two reform movements, however, seem to me to have been different. In the case of the most touted of the newmath reforms, it was a simple unwillingness across the country for teachers, school boards and parents to learn what was intended (not that the Writ carried out the intentions very well), all this backed up by a publishing industry that, after an enthusiastic beginning, gradually adjusted itself to the true (not lipservice) demands of the market. In the case of the Standards I believe, though I know much less about it, that the length, language and vagueness of the document are important in its lack of success in changing anything for the better. In the small, in a given paragraph, it doesn't *sound* vague, but in the large? As messages to this list and others show, *everyone's* philosophy of education has found a place in the Standards. Thus every teacher, every publisher, every School Board, can find solace in the Standards; and the lessons go on as they did not only 35 years ago, as in the case of Mr. Goldenberg, but 60 years ago, as in my case. (Again, I except 9-12 for the college-bound, which is a more complicated matter.) Standards are a good idea, likewise Frameworks, Syllabi and Guidelines. But they must be simple enough to provide a single vision, and not justification for whatever it is that anyone wants to do.