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On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations
Attaining high school diplomas with adequate levels of mathematical knowledge and reasoning to function as an informed and critical citizenry (Adelman, 1999);
Undertaking study at two-year colleges without undue fiscal burdens imposed by the need for remedial mathematics activities (Adelman, 1999);
Pursuing advanced mathematics at the research level in mathematics and science (Lutzer, 2003); and
Pursuing mathematically intensive careers in technology fields, statistics, and “client disciplines”—engineering, chemistry, and, increasingly, fields such as biology, economics, and social sciences (NRC, 2003).
In addition, concerns for preparation of all students (Campbell et al., 2002) across the spectrum of academic achievement necessitate such examination, evaluation, and critique of mathematics curricula.
Currently, too many deliberations on mathematics curricular choices lack a careful and thorough review of the evaluations of mathematics curricula. Because of the cumulative nature of mathematics topics, a weak curriculum can limit and constrain instruction beyond the K-12 years. It can discourage students from entering mathematically intensive fields or hobble the progress of those who pursue them. International studies have heightened American awareness that our mathematics performance has deteriorated, especially in the 8th and 12th grades. Even the performance of the most advanced students has suffered (Takahira et al., 1998).
The impetus for ways to examine effectiveness of curricular reform was intensified with release of the 2003 National Assessment of Educational Progress report, known as the Nation’s Report Card, which showed significant improvements in mathematics achievement as reading scores remained constant. Average 4th-grade student performance increased nine points, while 8th-grade student scores increased by five points. Closer examination shows that the percentage of students identified as below basic levels of performance declined by 12 and 5 percentage points at the 4th and 8th grades, respectively. The majority of subsequent gains occurred in the number of students identified as proficient, the second-highest level. These gains were quite evenly distributed across ethnic groups and class lines. Interpreting the scores over successive years created methodological issues, and the factors instrumental in producing these gains are not known. Determining the extent to which these gains can be attributed to curricular reform requires application of sound, sophisticated evaluation design, establishing an additional need for this report.