TABLE 10.2 NAEP Mathematics Exam Data, by Grade/Age and Year

 

1973

1978

1982

1986

 

Average Test Score

 

 

Grade 3/age 9

219.1

218.6

219.0

221.7

Grade 7/age 13

266.0

264.1

268.6

269.0

Grade 11/age 17

304.4

300.4

298.5

302.0

 

Average Test Score Gain

 

 

 

73 to 78

78 to 82

82 to 86

 

Grades 3–7/ages 9–13

45.0

50.0

50.0

 

Grades 7–11/ages 13–17

34.4

34.4

33.4

 

 

SOURCE: Dossey et al. (1988).

previously, the assumption that slopes do not vary across schools is often a reasonable one.

Value-Added Versus Common Educational Indicators: Theory and Evidence

As discussed earlier, level indicators, such as average test scores, are frequently used to measure school performance even though they are not, in general, equivalent to either total or intrinsic performance indicators. Is the difference between level and value-added indicators substantial enough to worry about? For simplicity, consider a single-level indicator, the average test score.

The average test score, measured at a given grade level, is the product of growth in student achievement over a potentially large number of grades and years. It therefore reflects the contributions to student achievement of schools and other inputs to the learning process from multiple grades and multiple points in time. For several reasons the average test score is potentially a highly misleading indicator of how productive a school is at a given point in time. First, the average test score is, in general, contaminated by factors other than school performance, primarily the average level of student achievement prior to entering first grade and the average effects of student, family, and community characteristics on student achievement growth from first grade through the grade in which students are tested. It is likely that comparisons across schools of average test scores primarily reflect these differences rather than genuine differences in total or intrinsic school performance. Average test scores are highly biased against schools that serve disproportionately higher numbers of academically disadvantaged students.

Second, the average test score reflect information about school performance that tends to be grossly out of date. For example, the average test scores for a group of tenth-grade students reflect learning that occurred from kindergarten, roughly 10 1/2 years earlier, through the tenth grade. If the variability over time of school performance is higher in elementary school than in middle or high



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