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The framework design was formed by the testimony of participants in the two workshops held by the committee, and by a first reading of numerous examples of studies.
The framework’s purpose is also to provide various readers with a consistent and standard frame of reference for defining what is meant by a scientifically valid evaluation study for reviewing mathematics curriculum effectiveness.
Effectiveness can be defined in relation to the selected level of aggregation.
A single study can examine whether a curricular program is effective (at some level and in some context), using the standards of scientifically established as effective outlined in this report.
Our framework merged approaches from method-oriented evaluation (Cook and Campbell, 1979; Boruch, 1997) that focus on issues of internal and external validity, attribution of effects, and generalizability, with approaches from theory-driven evaluations that focus on how these approaches interact with practices (Chen, 1990; Weiss, 1997; Rossi et al., 1999).
This permitted us to consider the content issues of particular concern to mathematicians and mathematics educators, the implementation challenges requiring significant changes in practice associated with reform curricula, the role of professional development and teaching capacity, and the need for rigorous and precise measurement and research design.
This would be termed, “a scientifically valid study.” Meeting these standards ensures the quality of the study, but a single, well-done study is not sufficient to certify the quality of a program.
Later in this section, we discuss these issues of utility and feasibility further and suggest ways to maintain adequate scientific quality while addressing them.
In many school systems, “curriculum” is used to refer to a set of state or district standards that broadly outline expectations for the mathematical content topics to be covered at each grade level.
In contrast, at the classroom level, teachers may select curricular programs and materials from a variety of sources that address these topics and call the result the curriculum.
Many formative, as opposed to summative, assessments were not included.
The framework we proposed consists of two parts: (1) the components of curricular evaluation (Figure 3-1), and (2) evaluation design, measurement, and evidence, (Figure 3-2).
Efficacy is viewed as considering issues of cost, timeliness and resource availability relative to the measure of effectiveness.