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On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations
conservative tests, as done in the evaluations of UCSMP, permits one to gain insight into teacher effects and to contrast test results by items included. Tests should also include content strands to aid disaggregation, at a level of major content strands (see Figure 5-11) and content-specific items relevant to the experimental curricula.
Statistical analysis should be conducted on the appropriate unit of analysis and should include more sophisticated methods of analysis such as ANOVA, ANCOVA, MACOVA, linear regression, and multiple regression analysis as appropriate.
Reports should include clear statements of the limitations to generalization of the study. These should include indications of limitations in populations sampled, sample size, unique population inclusions or exclusions, and levels of use or attrition. Data should also be disaggregated by gender, race/ethnicity, SES, and performance levels to permit readers to see comparative gains across subgroups both between and within studies.
It is useful to report effect sizes. It is also useful to present item-level data across treatment program and show when performances between the two groups are within the 10 percent confidence interval of each other. These two extremes document how crucial it is for curricula developers to garner both precise and generalizable information to inform their revisions.
Careful attention should also be given to the selection of samples of populations for participation. These samples should be representative of the populations to whom one wants to generalize the results. Studies should be clear if they are generalizing to groups who have already selected the materials (prior users) or to populations who might be interested in using the materials (demographically representative).
The control group should use an identified comparative curriculum or curricula to avoid comparisons to unstructured instruction.
In addition to these prototypical decisions to be made in the conduct of comparative studies, the committee suggests that it would be ideal for future studies to consider some of the overall effects of these curricula and to test more directly and rigorously some of the findings and alternative hypotheses. Toward this end, the committee reported the tentative findings of these studies by program type. Although these results are subject to revision, based on the potential weaknesses in design of many of the studies summarized, the form of analysis demonstrated in this chapter provides clear guidance about the kinds of knowledge claims and the level of detail that we need to be able to judge effectiveness. Until we are able to achieve an array of comparative studies that provide valid and reliable information on these issues, we will be vulnerable to decision making based excessively on opinion, limited experience, and preconceptions.