Evidence That They Cannot Apply Those Skills to Solve Everyday Problems

According to Everybody Counts: A Report to the Nation on the Future of Mathematics Education (Board on Mathematical Sciences and Mathematical Sciences Education Board, National Research Council, 1989), American children have mathematical skills that are insufficient for problem solving in the workplace and for mathematics literacy at the college level. The report states, "Current mathematical achievement of U.S. students is nowhere near what is required to sustain our nation's leadership in a global technological society" (p.1).

The National Center for Education Statistics (1991) confirms this idea. For more than 20 years, National Center for Education Statistics has used the National Assessment of Educational Progress (NAEP) to monitor the educational achievement of American students and the changes in that achievement across time. The level of mathematics proficiency is determined for students in grades 4, 8, and 12. Proficiency levels are:

• Level 200: simple additive reasoning and problem solving with whole numbers.

• Level 250: simple multiplicative reasoning and two-step problem solving.

• Level 300: reasoning and problem solving involving fractions, decimals, percents, elementary geometry, and simple algebra.

• Level 350: reasoning and problem solving involving geometry, algebra, and beginning statistics and probability.

Results of the 1990 NAEP (National Center for Education Statistics, 1991) show that:

"Virtually all the eighth graders performed at or above Level 200, but only two-thirds of these students performed at or above Level 250, indicating success in using all four numerical operations with whole numbers. Fourteen percent demonstrated some mathematical understanding beyond whole numbers, but none in this group showed breadth in their understanding." (p. 58)

"Most twelfth graders (91 percent) performed at or above Level 250, indicating some facility in problem solving with whole numbers. However, less than half (46 percent) demonstrated consistent success with problems involving fractions, decimals, percents, and simple algebra. Only 5 percent demonstrated a breadth of mathematical understanding that included problem solving involving geometric relationships, algebraic equations, and elementary statistics." (p. 58)

"Students performing at Level 300 showed knowledge of a broader range of mathematical concepts and procedures. For example, they could operate with rational numbers, find areas and perimeters, were developing some working familiarity with geometric terms, and could perform simple manipulations involving algebraic expressions." (p. 68)

"However, some of these concepts, such as fractions, decimals, and percents, are often introduced as early as the fourth or fifth grade. The measurement and geometry concepts, and even the simple algebra concepts, would be introduced for most students by the end of the middle-school curriculum. The majority of the content covered by the anchor questions at Level 300 would typically have been covered by the seventh grade. Yet only 14 percent of the eighth graders and less than half the high school seniors performed at or above this level." (p. 68)

Results of the 1992 NAEP (National Center for Education Statistics, 1994) show that the scores of twelfth graders at or above Level 250 increased to 97 percent; those scoring at Level 300 increased to 59 percent; and those scoring at Level 350 increased, but only to 7 percent.

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