"The algorithm comes first, and understanding comes later. Mathematics simply is. It cannot be negotiated." -- John Armstrong, The Unapologetic Mathematician
The Unapologetic Mathematician's rant about Everyday Math:
The authors of Everyday Mathematics do not believe it is worth students’ time and effort to fully develop highly efficient paper-and-pencil algorithms for all possible whole-number, fraction, and decimal division problems. Mastery of the intricacies of such algorithms is a huge endeavor, one that experience tells us is doomed to failure for many students. It is simply counter-productive to invest many hours of precious class time on such algorithms. The mathematical payoff is not worth the cost, particularly because quotients can be found quickly and accurately with a calculator. (Everyday Math Teacher’s Reference manual for 4-6, page 136)
"I’ll grant you that most people will never have to long-divide even a polynomial in their “everyday” lives. But without this ability, and the comfort with mathematical algorithms it acts as a marker of, students will never achieve in mathematics, science, or engineering. What the authors are really saying in the above quote is, “we don’t think most of your kids are ever going to do much of anything in science or engineering, so we’re going to cripple all of them — even those who might otherwise have done.”
"And here’s another point: you don’t always have a calculator. To indulge a bit of hyperbole, there’s a reason that a naval submarine carries paper copies of its own schematics rather than a CD-ROM of them. Jim Lovell didn’t have a calculator when things went wrong on Apollo 13. Pencils and paper never get shorted out, never run out of batteries, never have hardware glitches. In a mission-critical situation, having the ability to do without a calculator or computer is essential. Yes, most people will never be slingshotted around the dark side of the moon in a tin can, but the authors of these curricula are saying they have no problem with preventing that being your child on the first manned spaceflight to Mars."
"I know that what I’m about to say is horribly politically incorrect (”counter-revolutionary”?), but the most basic mathematical methods must be taught — they cannot be discovered without mastery of the basic algorithms. I know I’m more interested in “why” than in “how” in higher mathematics, but this is simply not how people lay the foundations of familiarity with mathematics. It’s just not how human beings learn to think mathematically."
"You want to know how people learn mathematics? There’s actually a movie about it, though you might not have recognized it as such at the time: The Karate Kid. Mr. Miyagi starts by making Daniel wax his car, paint his fence, sand his deck, and so on. Daniel doesn’t understand why he’s supposed to go through these motions, but Mr. Miyagi knows that the understanding will come only after mastery of the basic techniques, not before."
Excerpts from More Math Education, The Unapologetic Mathematician, John Armstrong, PhD, Mathematics, Yale