WASHINGTON--The best way to improve mathematics education is not to shift the emphasis of the curriculum, but to teach it better, the outgoing president of the National Council of Teachers of Mathematics argued at the group’s annual conference here this month.
Looking back on 50 years in the field--as a student, teacher, and teacher educator--F. Joe Crosswhite told his colleagues that the mathematics curriculum has often veered between emphases on “pure” and “applied” math, which he called a “false dichotomy.”
“Any school curriculum should contain a balance between those two choices,” he maintained.
“We should indeed adjust the curriculum,” Mr. Crosswhite said. “But the danger is, in a fanatic rush to incorporate a new view, we turn our back on what has been good in math for years and years.”
Thus, rather than contemplate another shift from the current emphasis on applied math, or problem-solving, to a focus on basic skills, teachers should continue to use what has been effective in both approaches, he said. Quoting another math educator, Mr. Crosswhite contended: “What is needed is not teaching better mathematics, but teaching mathematics better.”
As evidence of this need, he cited the results of the second international mathematics study, which showed the math scores of U.S. 8th and 12th graders lagging behind those of students in other industrialized nations, particularly Japan.
Graphs showing the score comparisons were published in the Education Department’s new booklet, “What Works.” (See Education Week, March 19, 1986.)
The international study’s findings, in Mr. Crosswhite’s view, point clearly to deficiencies in the methods, not the content, of math instruction in the United States.
He pointed out that, according to the study, American students actually receive more hours of math instruction per year than Japanese students, and American teachers have at least as much preparation as their Japanese counterparts.
However, U.S. math teachers spend little time on each topic, Mr. Crosswhite said, compared with Japanese teachers, who cover topics intensively.
He also cited other studies that show U.S. students trailing Japanese students in math as early as the 5th grade, suggesting that differences in teaching affects students’ performance early.
American pupils “could be falling behind quickly and playing catch-up ball,” he said.
Mr. Crosswhite’s views were echoed by Max A. Sobel, professor of mathematics education at Montclair State College and a former N.C.T.M president. Mr. Sobel said American math teachers use “an almost universal lesson plan” that devotes, at most, five minutes a day to introducing a new topic.
He quoted studies showing that Japanese students progress more rapidly than U.S. students to more advanced areas of the curriculum.
Like Mr. Crosswhite, Mr. Sobel noted that the math curriculum has too often alternated in its emphasis; he argued that educators should instead focus on “the improvement of teaching mathematics with the teacher as the main instrument.”
Role of Technology
The two former presidents differed, however, on the potential effects of technology on the future direction of the curriculum. Mr. Crosswhite said that direction is “up for grabs,” but “will surely incorporate some new technology.”
Mr. Sobel disagreed. “I don’t see” changes prompted by technology “coming about that rapidly,” he said, suggesting that teachers may be reluctant to introduce new technology into the curriculum.
As if to illustrate his point, a small group of teachers demonstrated outside the convention’s hotel in opposition to the council’s endorsement of the use of pocket calculators by math students.
Brandishing signs reading “ABG: Anything But Calculators” and “The Button’s Nothin’ Till the Brain’s Trained,” the teachers--led by an Oklahoma textbook publisher, John Saxon--said the use of calculators could weaken math education for young students.
In a policy statement adopted at the meeting that refined an earlier policy, the N.C.T.M. recommended “the integration of the calculator into the school mathematics program at all levels. ... The time gained should be spent helping students understand mathematics, develop reasoning and problem-solving strategies, and in general, use and apply mathematics.”
