The authors essentially capsulate "the math wars" as being a dispute between competing values held for two differing kinds of instructional outcomes: (1) "traditionally", students' abilities to perform calculations of kinds needed in specific STEM encounters, and (2) "progressively", student's personal powers for thinking their own way through mathematical challenges.
The authors attempt to bridge that gap by pointing out some underlying connections between mathematical thinking and effective use of algorithms ... and their claims that students' struggles and experiences with prescribed algorithms nurtures the development of thinking powers. Unfortunately, their philosophic musings badly fail to pave a way for resolving "the math war" so as to provide nationwide benefits to the masses.
[So far, only a small (and too, too small) percentage survive "traditional" instruction long enough to enter STEM-specific higher education programs. So far, "progressive" curricula have largely failed to salvage the rest ... most of whom are early trained to avoid curricular mathematics, as much as possible within the sights of their respective aspirations.]
In truth, "the math war" is a straw man created through defenses of entrenched and innovative instructional orientations. The true silliness of the dispute ... and the professional stupidity of both sides ... comes through near-universal failure of the competing professors to clinically study how humans most naturally learn K-calculus mathematics.
It now is clinically certain that each of the (K-calculus) THEOREMS that the authors call algorithms can be common-sensibly concluded by any normal human ... given a natural-learning evolution. [Any serious, qualified investigator can re-confirm that claim. Private dialog on the specifics of "how to" is welcome.]
K-12 algorithms which are personally concluded by the learners are more easily mastered, more efficiently retained, and more effectively invoked. Meanwhile, such learning can be guided to progress through creative, analytic, systematic, gratifying, and empowering instructional modes.
When the science of psychomathematics is so-used as a lens, it is seen the there is no essential conflict between the two sides of "the math war." Rather, the "war" results from the nationwide failure of American professors to educate the profession in how to teach algorithms in ways that develop students' personal rational powers for mathematical thinking.
- -------------------------------------------------- From: "Joe Niederberger" <email@example.com> Sent: Monday, June 17, 2013 9:28 AM To: <firstname.lastname@example.org> Subject: Math Wars Philosophizing in the NY Times