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INNUMERACY: Mathematical Illiteracy and Its ConsequencesAs it is, the basic elements of mathematical culture are in many cases not being communicated to our students. Vieta in 1579 began to use algebraic variables-X, Y, Z, etc.-to symbolize unknown quantities. A simple idea this, yet many high school students today can't follow this four-hundred-year-old method of reasoning: Let X be the unknown quantity, find an equation which X satisfies, and then solve it in order to find the value of the unknown. Even when the unknowns are appropriately symbolized and the relevant equation can be set up, the manipulations necessary to solve it are too often only hazily understood. I wish I had five dollars for every student who got through his or her high school algebra class only to write, on a test in freshman calculus, that (X + Y)2 = X2 + Y2. Approximately fifty years after Vieta's use of algebraic variables, Descartes devised a way of associating points on a plane with ordered pairs of real numbers and, via this association, a way of identifying algebraic equations with geometric curves ...» |
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