On Tue, Oct 9, 2012 at 6:05 AM, Robert Hansen <firstname.lastname@example.org> wrote: > > On Oct 8, 2012, at 3:34 PM, Paul Tanner <email@example.com> wrote: > > I have addressed his utterly bogus claim that minimum standards > imposed on all - students and teachers - have gone down, by showing > that it is plain fact that they have gone up. > > > Show me where I made such a claim? >
As far as I am concerned, the term "standards" means an objectively and formally given minimum floor that all are expected to be above to receive something in return (like say, a high school diploma), and so meeting a standard means meeting a minimum requirement that all are objectively and formally required to meet if they are to receive that something in return. (And so I should have said "minimum requirements" instead of "minimum standards".)
For example, think of how states use the term "standard" in their standards documents, like the CA Mathematics Content Standards: They use this term exactly as I just said.
So if you mean something else by the term "standards", then what is it? Some subjective ideal that only a small percentage of whatever group of people you are talking about ever live up to?
> > > Regarding textbooks, I have in front of me "Modern Algebra and Trigonometry, > Structure and Method, Book 2" published 1965, 1963 by Houghton Mifflin > Company. It has all of those topics you listed. Why do you insist that this > type of curriculum was a more recent invention?
Perhaps we should make distinctions between "textbooks" and "curriculums" - where the latter is more to the point as to what was actually taught in the classes.
On that particular edition of that particular *textbook* I stand corrected, but I have been going by what I've been told over the years by several "old-timer" teachers that even back in the 1960s with the New Math (that was a major bust) they never tried to stuff ALL of mathematics below calculus (after basic beginning algebra including the quadratic formula and related math, all that analytic geometry, trigonometry, vectors, matrices, and whatever else in addition to advanced treatments of polynomial, exponential, and logarithmic functions) into just two one-year high school courses, Algebra I and Algebra II. Perhaps the 1960s New Math was such a massive shock to the system back then, trying way too much way too fast in terms of *curriculum* *for the entire population* in comparison to what the system was used to at that time, that the result was the major backlash against that New Math, that major backlash that I trust you know about.
Perhaps those Harcourt Brace Jovanovich Algebra 1 and Algebra II textbooks, used at one of the high schools I taught at, published I believe first back in the 1970s and then at least through the 1980s, were part of that backlash. Again: These textbooks were exactly as I remember the textbooks used by my high school years in the 1970s. The rate of algebraic material coverage of the Algebra I and Algebra II sequence was so slow that the quadratic formula was introduced only towards the end of Algebra II. That Algebra II textbook did not contain all those things at the precalculus level needed as prerequisites for calculus, which would include advanced treatments of polynomial functions (and including such topics as the binomial theorem) and would include the transcendental functions (exponential functions, logarithmic functions, trigonometric functions), and would include such as vectors and matrices.
Back then in the 1970s, the community college for our whole county required a precalculus class at the community college as a prerequisite for calculus because of the fact that Algebra II as taught in the high schools throughout the county did not contain this extra precalculus level material that was needed for calculus and because most who went into the college did not take a precalculus-level math course in high school since it was not offered most of the time in most of the high schools back then in that county. This extra precalculus material was called "math analysis" at my high school, and again, it was not offered at my high school during my senior year. That low level Algebra II was the highest level math course offered to us during my years there.
> I wonder if that series was actually the beginning of modern high school > algebra? By modern I mean the end of Trigonometry as a subject by itself. >
Perhaps this 1960s New Math textbook Algebra I and Algebra II sequence was the first attempt at trying to stuff ALL of high school mathematics below calculus into just two one-year high school courses, but since the country was not ready for it, there was that major backlash against it resulting in the math education of the laid back 1970s, as evidenced by that Harcourt Brace Jovanovich Algebra 1 and Algebra II sequence, where at the end of the Algebra II book it had finally dealt with the quadratic formula and the math related to it.
But then there was evidently in the 1980s a backlash against the laid back 1970s, starting perhaps formally with that Nation at Risk report in 1983.
And so in terms of *curriculum* this idea that we should try to stuff ALL of mathematics below calculus into just two one-year high school courses *for the entire population* actually being accepted and implemented by the entire system *is* a modern phenomenon that was briefly tried and rejected back in the 1960s and not accepted in the 1970s, finally coming to full implementation starting around 2000 when essentially the entire country by that time required at least Algebra I and Geometry for all as a minimum requirement for graduation from high school.
This demonstrates that in fact there has been a drastic increase in standards in terms of minimum requirements for all.