Academic journal article Education Next

The New, A-Maze-Ing Approach to Math: A Mathematician with a Child Learns Some Politics

Academic journal article Education Next

The New, A-Maze-Ing Approach to Math: A Mathematician with a Child Learns Some Politics

Article excerpt

I am not a mathematics teacher, but I have a degree in mathematics and an intense interest in how the subject is taught. When I retire, I would like to teach math, which is why I started tutoring high school students in my spare time three years ago. My first student was a 9th grader having difficulty with geometry. He stated his problem succinctly: "I don't know how to do proofs." Confronted with what I thought could be a common problem, I was still unaware that what I was really seeing was a national crisis in mathematics education.

Here's some of what I would soon learn:

-- Only 55 percent of 8th graders taking the National Assessment of Educational Progress (NAEP) exam in math correctly answered the question, "How many pieces of string will you have if you divide 3/4 yard of string into pieces each 1/8 yard long?"

-- In an international math test taken by students worldwide in 1995 (the Third International Mathematics and Science Study, or TIMSS), U.S. student math proficiency for 8th graders fell below the international average (28th out of 41 countries). For 12th grade, U.S. math performance was among the lowest (18th of the 21 countries participating).

-- In 1989 the National Council of Teachers of Mathematics (NCTM) published its Curriculum and Evaluation Standards for School Mathematics--an extensive set of mathematics standards for grades K-12 which de-emphasized memorization of number facts, the learning of proofs, and algebraic skills, but encouraged the use of calculators and "discovery learning."

-- The National Science Foundation (NSF) promoted the NCTM standards beginning in 1991 and awarded millions of dollars in grant money for the writing of math texts that embraced them and to state boards of education whose math standards aligned with them (see Figure 1).

Not knowing about these significant events (all of them before last December's release of the Program for International Student Assessment report ranking American 15-year-olds 24th out of 29 in math among industrial countries (see Figure 2)), I had no idea that our children were being deprived of a math education, thanks in no small part to a dubious education theory, watered-down standards, and a well-meaning but intellectually bankrupt federally subsidized program of math illiteracy.

What I did know was that my 9th grader didn't know how to do proofs.

I looked through his textbook, one of whose authors was a recent president of NCTM, and I was surprised to find very few proofs of anything. More troubling, most theorems in the book were stated as postulates--that is, propositions stated without proof--and students were told to memorize them. The problems at the end of the chapter required students to do only a few simple proofs.

Proofs in geometry class have been a mainstay of mathematics. In fact, proofs were always considered an essential part of high school geometry, not only because of their importance in higher math, but because learning the rules of logical argument and reasoning has applications in science, law, political science, and writing. To see proofs being shortchanged in a geometry textbook was shocking.

Algebra texts were in no better condition, in terms of presentation and content--or, rather, their lack of content. Even if you accept the argument that geometry in general, and proofs in particular, are unnecessary for students to learn, at least algebra should be taught properly, since algebra is the common language of, and gateway to, all of higher math. The absence of clear explanation and logical development left students I later tutored in algebra as lost as my geometry student. Their textbooks (and, probably, their teachers too) encouraged them to use a graphing calculator. Operations with algebraic fractions, like a/b + c/d, were given little attention, to say nothing of quadratic equations, once the pinnacle of any first-year algebra course. …

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