There has been a profound change in mathematics education in the years indicated, and the author of the submitted article is on to something. One of my favorite authors on mathematics, Professor John Stillwell, writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998):

"What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus; and the calculus now taught is, sadly, much less than it used to be. Little by little, calculus has been deprived of the algebra, geometry, and logic it needs to sustain it, until many institutions have had to put it on high-tech life-support systems. A subject struggling to survive is hardly a good introduction to the vigor of real mathematics.

". . . . In the current situation, we need to revive not only calculus, but also algebra, geometry, and the whole idea that mathematics is a rigorous, cumulative discipline in which each mathematician stands on the shoulders of giants.

"The best way to teach real mathematics, I believe, is to start deeper down, with the elementary ideas of number and space. Everyone concedes that these are fundamental, but they have been scandalously neglected, perhaps in the naive belief that anyone learning calculus has outgrown them. In fact, arithmetic, algebra, and geometry can never be outgrown, and the most rewarding path to higher mathematics sustains their development alongside the 'advanced' branches such as calculus. Also, by maintaining ties between these disciplines, it is possible to present a more unified view of mathematics, yet at the same time to include more spice and variety."

Stillwell demonstrates what he means about the interconnectedness and depth of "elementary" topics in the rest of his book, which is a delight to read and full of thought-provoking problems.

http://www.amazon.com/gp/product/0387982892/

I have a collection of analytic geometry and calculus books, accumulated as used books from various readers, that includes the books used by my late father in his higher education as a chemistry major during the Truman administration, followed by books from other previous owners reflecting "new math," "back to basics," and "reform" approaches to mathematics education. Plainly today's secondary and tertiary students of mathematics need to take advantage of current technology so that they can devote more time to THINKING about the mathematics they learn and less time to what even any mathematician would call "tedious calculation." But too few students have ever been guided to through the kind of insight-producing problems in which the tedious steps themselves and the false starts while struggling with the problem produce deep understanding. Stillwell gives examples of such problems in his books, and the minority of students who participate in math contexts or who voluntarily work the "challenge" problems not assigned in their textbooks may gain such insight, but most school textbook problems of all eras are mere exercises, and too few students do enough of those thoughtfully to have hope of learning mathematical concepts.

See "Basic skills versus conceptual understanding: A bogus dichotomy in mathematics education," American Educator, Fall 1999, Vol. 23, No. 3, pp. 14-19, 50-52 for additional commentary on mathematics education,

http://www.aft.org/newspubs/periodicals/ae/fall1999/index.cf...

and see an earlier HN comment

http://news.ycombinator.com/item?id=2515796

for a FAQ on the distinction between problems and exercises in mathematics education.