Tuesday, June 19, 2007

The Emperor is Naked

Perils of Modern Math Education
by Stuart Wachowicz†

“Pride in craftsmanship obligates the mathematicians of one generation to dispose of the unfinished business of their predecessors.”
-E.T. Bell, The Last Problem

"The above statement most accurately describes the legacy of one generation of mathematicians to the next. However, one might be tempted to ponder whether this will continue to be possible in North America. The discipline of mathematics, as we have known it, is clearly under threat. The threat is a consequence of allowing curriculum writers to change the centuries-old definition of mathematics and what needs to be learned based on utilitarianism, combined with the current practice of allowing unproven fads to influence pedagogy.


In a quest for utilitarian value, much of the modern mathematics curriculum in the public school system no longer seriously attempts to inculcate a deep understanding of what Newton referred to as “the language of the universe.” Lip service is paid to the goal of helping students to become more adept at problem solving, but modern curricula fail to place the emphasis on the foundation of problem solving—the mastery of number relationships and the fundamental axioms and postulates upon which mathematical
reasoning is based.
Virtually all students can and should learn these.

The second threat is that of allowing politically expedient fads to unduly influence public school pedagogy.


There is a logical fallacy at work here that few in public education seem to be willing to expose. New approaches to public school math postulate that without an ingrained knowledge base of number relationships and without fluency in calculation, symbolic manipulation and formal training in reasoning, students are still able to grasp algebraic, trigonometric, and geometric principles at a level that will enable them to become effective problem solvers in mathematics. The fact that fewer than 10% of the mathematics graduate students in our province received their early education in North American public schools may cast some doubt on this theory, which disregards the collective wisdom of centuries. The truth is that without
an appreciation for the discipline of mathematics, developed from an early age, mathematical reasoning and potential is impeded.

The new approach embraces the notion that technology is inexorably linked with the discipline of mathematics. Technology is but a consequence of mathematics. Real mathematics is in fact an independent form of technology. Today, however, technology is mindlessly driving educational philosophy, curriculum design, and assessment. Mathematical reasoning is thus impeded and held hostage to this anti-intellectual, technological imperative.

While technology may have many positive applications in education such as helping an instructor amplify a concept, its current overuse is a problem from both a financial and a pedagogical perspective. The imperative implies that because there is so much information, it is impossible to know it all. Therefore, instead of students becoming knowledge rich, they must become skilled at accessing information. This too is a logical fallacy. One may go so far as to postulate the present imperative constitutes a war on both memory skills and the establishment of a broad knowledge base. Knowledge has been, is, and always will be the raw material of reason, and without an internal knowledge base, process skills become ineffectual. Nowhere is this more true than in mathematics.

If we are to have the craftsmen to dispose of the unfinished business of our predecessors, as Bell observed, students in public schools must be given the knowledge and skills that will enable them to do just that. When the Emperor is naked there is a responsibility for those aware of his condition to have the courage to so inform him."

†Stuart Wachowicz is the Director of Curriculum for Edmonton Public Schools. During the past 25 years, he has also taught various subjects and served as a principal of a high school considered to be one of the highest achieving schools in Alberta. Stuart Wachowicz graduated with degrees in Geography and Education.

Excerpts from Perils of Modern Math Education by Stuart Wachowicz

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