Why I Support Reform:
The Good Old Days Never Were

Larry Sowder, San Diego State University

A mathematics curriculum and its implementation might be judged by its results, as is the case in most fields. Good results would suggest keeping things the way they are; poor results would indicate that change of some sort is in order.

How well have we been doing with the traditional mathematics curriculum and its implementations? Here are some results:

In 1931 Schorling, studying over 200,000 students in grades 5-12, found that only 20 percent of the twelfth-grade students could compute 2.1 percent of 60. In 1937 Taylor studied more than 2000 freshmen in teachers' colleges and found that more than half could not divide 175 by .35. In 1942 Admiral Nimitz reported that 68 percent of 4200 freshmen at 27 United States universities and colleges were unable to pass the arithmetical-reasoning portion of the examination for entering the Naval Reserve Officers' Training Corps. In 1943 Brueckner, conducting a national survey, found that the arithmetical competence throughout the country was even worse than the Nimitz report indicated. (Johnson & Rising, 1967, p. 22)

Note that in those pre-calculator days, computational skill was extremely important and the focus of schooling in mathematics; nonetheless, the computational skills of the students were poor. These reports were also from times when far fewer students went to college or even finished high school than is now the case. The students in those reports were, presumably, the best ones. In most fields, results like these would not be tolerated; the curriculum and implementation leading to them would be changed.

Did the results improve in later times? Sadly, they did not. We continued to have years of experience dealing with a curriculum that made calculation the "star" of the show...with abysmal results, judging from results from the National Assesssment of Educational Progress (1983, p. 26). The pre-reform curriculum of the late 1970s and early 1980s and its implementation resulted in 60% of the 13-year-olds being able to multiply two fractions--that is, 2 out of every 5 could not multiply two fractions, at a time when such computation was still the dominant part of the curriculum. At the same time, only 17% of the 13-year-olds could do a simple "story" problem that involved only multiplying two fractions--that is, 5 out of 6 could not! Thus, not only was computational skill poor, performance on the conceptual side of fraction multiplication was even worse.

Most people would say that a curriculum and implementation leading to such results must be changed! Large-scale curriculum and implementation revisions necessarily involve unknowns that breath-takingly successful small-scale changes do not reveal. For example, leaders of one forward-looking reform group in California were astonished when they visited classrooms to find that too many of the teachers were misinterpreting their training in the use of small group problem solving to mean that all work in mathematics was to be in small groups, without teacher input, intervention, and summary. So there have been errors of implementation in some reform projects, and no doubt there will be similar misrenderings of the intent of reform--witness the interpretation of "decreased attention" to mean "omit" with the 1989 NCTM Standards. But to continue with a curriculum and implementation that has failed so many children for so long is inexcusable.

References

Johnson, D., & Rising, G. (1967). Guidelines for Teaching Mathematics. Belmont, CA: Wadsworth Pub. Co.

National Assessment of Educational Progress. (1983). The third national mathematics assessment: Results, trends, issues. Report No. 13-MA-01. Denver: Education Commission of the States.

Dr. Larry Sowder is a professor in the Department of Mathematics and Computer Science at San Diego State University.