Teaching math: That is the question

The following was circulated in the listservs, and I'd like to post it here as well:

Some Observations on Structural and Social Issues in K-12 Mathematics Education

by Arjun Janah

(A) The problem does not lie mainly with the current organization of the mathematics syllabus, but rather with structural & social issues such as:

(1) the pace at which these topics are taught, which leave little room (at least here in New York city) for confidence-building practice and for the kind of applications the authors of this article mention;

(2) the misguided attempt, noble in intention but cruel and disastrous in practice (for both students and their teachers) to try to teach all students at the same pace and to the same level of rigor, whether they are willing, prepared, able or not;

(3) the social problems arising from the cultures that permeate our communities, arising either \"naturally\" from historical and socio-economic causes, or \"artificially\" from the manipulation of youth by the media and its commercial support;

(These social pathologies, intruding into classrooms and homes, destroy focus and make the struggle that is learning impossible to carry on effectively.)

(4) undue obsession with educational methodology, its over-generalization and the imposition of methodological fads and diktats on teachers;

(5) once due, but now, belatedly (greatly exaggerated, undue and injurious) attention to results on standardized examinations.

(B) There is a reason for the abstraction that we find in mathematics. It gives it a generality and concision that is lost when we particularize it.
That said, time and energy are needed to see how the abstractions arise from the particular and concrete and can, in turn, be applied towards solving particular, concrete problems — including those of everyday life. And extended journeys into formal abstraction are best avoided with younger students, especially those in lower grades (typically below the tenth) — and with those who are unable, for a number of reasons, to comprehend these.

(C) As in other K-12 subjects, due attention needs to be restored to traditional educational subject-matter concerns. These include: purpose, choice, motivation, sequence, focus, pace (and time allocation), practice (and habituation), along with, of course, application.
Students need all of these, plus time and effort, to build familiarity and confidence and to deepen and broaden understanding.

(D) There are no substitutes for logical coherence, sequence and structure on the part of the syllabus or for focus and effort on the part of students and their teachers. Given these, the small successes and the understanding and enjoyment follow. And it is these that sustain the focus and effort, in a virtuous circle.