He's definitely talking about the "you HAVE to finish calculus in high school" track as representing "rigor" and some kind of badge of smartness/worthiness in high school students. That's not at all the same thing as a student who legitimately takes a very rigorous approach to mathematics but simply does it FASTER than most learners can. Those students are somewhat rare. That's what he's getting at; undermining the prestige of "advanced in mathematics" for its own sake, and a return to rigorous learning-- for ITS own sake.
Many scientists, engineers, and economists will use calculus and other math as a tool. I wonder how much rigor they need. I don't see how a year of geometry with proofs helped me in my academic or working career. A benefit of acceleration through calculus is that it enables you to study physics, statistics, economics, and other subjects at a higher level.
Well, speaking to
chemistry there, it was of NO use to come into chemistry (as a major) having already gone through a calculus sequence in high school, because most major's tracks have you taking general physics as a sophomore undergraduate, anyway, and you only need VERY good algebraic skills and the rigor taught by the study of geometric proofs (IMO and my DH's) in order to really learn gen-chem well.
HOWEVER-- those students who do NOT have good geometry backgrounds often find themselves at sea when it comes to molecular geometry (and all that comes with it), and truthfully, that "sense" of spatial intuition comes only with a great mastery of the subject. It's part of what
makes chemists-- chemists, and not biologists, statisticians or pharmacologists. This makes organic chemistry in particular a NIGHTMARE for those students, many of whom change majors to either biology or physics at that point. (It also makes instrumental analysis, molecular spectroscopy, and inorganic chemistry far, far more difficult than they should be.)
So while I respect that most people feel that they have "never used" the geometry that they learned so arduously, I disagree. That deeply embedded understanding, and the diligent practice of logic applied to proofs is unmistakably preparation of the very best sort for some STEM fields.
Also true that as a chemist, having advanced skills in mathematics isn't really very useful (beyond calculus) until you get into distinctly graduate level topics. Stat Mech, instrumentation design, etc. Better to have had Statistics early and well, IMO, than calculus in high school (where it is often taught very BADLY-- by people who don't really understand it well conceptually).
So I think that what the university professors in mathematics are really saying is two-fold, but the second part of it is mumbled a bit so as not to offend those that they hope will go along with CCSSM:
a) students are NOT really "advantaged" significantly by taking very high-level mathematics topics earlier and earlier, and some of them may be "rushed" if this is encouraged; and
b) most high school teachers have no business teaching anything past trigonometry anyway, so they should leave the advanced math topics to those who DO understand them.
