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Adding + It Up: Helping Children Learn Mathematics
Since the early 1970s, a series of national and international assessments have provided a reasonably consistent picture of U.S. students’ achievement in mathematics. As one analysis of these assessments puts it, the results “evoke both a sense of despair and of hope.”96 The despair comes from the generally low level of performance, the hope from signs that performance in some areas of mathematics and by some groups of students has been improving over the last decade.
The many mathematics assessments conducted since 1973 by NAEP demonstrate that student performance at each of the grade levels assessed is considerably below what mathematics teachers and the public would prefer. Since 1990, NAEP has included two separate components for mathematics: main NAEP and long-term trend NAEP. The long-term trend assessments use the same sets of questions first used in 1973, allowing comparison across time. The main assessments reflect more contemporary educational objectives and are used to collect both national and state data, including contextual data such as teaching practices, some of which are reported earlier in this chapter.97 Except when we refer explicitly to the long-term trend assessments, the data reported here are from the main assessments.
In the 1996 mathematics assessment—the most recent main assessment to be thoroughly analyzed—across grades 4, 8, and 12, roughly 35% of the students were below the basic level of achievement and another 45% or so were at that level, which is defined as denoting “partial mastery of knowledge and skills that are fundamental for proficient work.” In the same assessment, 21% of fourth graders and 24% of eighth graders were at or above the “proficient” level, where proficiency is defined as students having “demonstrated competency over challenging subject matter” and being “well prepared for the next level of schooling.” Only 2% and 4% of fourth-grade and eighth-grade students, respectively, were doing advanced work significantly “beyond proficient grade-level mastery.”98
Although overall levels of achievement are low, the main NAEP assessments in the 1990s revealed significant gains.99 The gains between 1990 and 1996 have been estimated to be about one grade level.100 According to the NAEP long-term trend, mathematics achievement improved between 1973 and 1996 at both the fourth-grade and eighth-grade levels.101 Performance improved even more sharply from 1973 to 1996 among black and Hispanic students.102 Although the gap between black students and white students had narrowed through the 1980s, it widened between 1990 and 1999, especially among students of the best-educated parents.103 This disparity repre-