By Stanley Ocken
Submitted to The New York Sun
Edited version was published August 29, 2002
Professor Alfred Posamentier's timely op-ed "A Mathematics Crisis in the Schools" laments the alarming shortage of both secondary school mathematics teachers and mathematics education professors who train them. He calls on university mathematics faculties to help solve these problems.
Understandably omitted from his analysis is a discussion of the relevant history of mathematics education in New York City and nationwide. Of critical import is that American graduate schools of education, for more than a decade, have been subservient to an educational philosophy whose implementation in American classrooms will likely exacerbate the current crisis.
The following verbatim citation from the preface of Constructivism, by C. T. Fosnot of the City College School of Education, outlines the reigning educational theory, a bizarre extension of the sound if unremarkable premise that students learn well, perhaps best, when working out problems on their own.
"Teachers who base their practice on constructivism reject (emphasis added) the notions that meaning can be passed on to learners via symbols or transmission, that learners can incorporate exact copies of teachers' understanding for their own use, that whole concepts can be broken into discrete sub-skills, and that concepts can be taught out of context."
Each of the rejected notions is crucial, in whole or in part, to the vision of effective mathematics instruction held by the vast majority of university mathematicians. In fact, mathematics is a symbolic language whose effective use depends on the step-by-step development of formal manipulation skills as a prerequisite to understanding and applying deep ideas.
The development of constructivist-based curricula has cost the American taxpayer nearly a billion dollars during the past decade. In New York City, District 2 has pioneered implementation of two of the worst curricula, TERC Investigations and ARISE, both of which reflect the profound anti-symbolic bias explicit in the constructivist agenda. Claims of marginally improved test results in grades K-8 omit to mention
the huge investment in outside tutoring by those parents who can afford it;
a precipitous decline in the scores of student cohorts tracked year by year in some heavily minority schools in the district; and
the modification of some testing instruments so as to exclude non-trivial but grade-appropriate questions involving basic skills.
The participation of university mathematicians sought by Professor Posamentier has already been offered but has typically been sabotaged by the reigning cadre of mathematics educators. For example, the National Science Foundation's recent Math/Science Partnership initiative explicitly called for the involvement of university scientists and mathematicians. The response in New York City: the Board of Education maneuvered to ensure that its proposal would be the only one considered on behalf of New York City schools, then contacted not a single CUNY mathematics department to solicit input for that proposal.
The call for co-operation between mathematicians and mathematics educators is welcome and long overdue. It is not too late to forge the bonds needed to develop successful programs of mathematics instruction in New York City and nationwide.
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