and pedagogical approaches might show that they have acquired the intended knowledge and skills, and that the teachers are attempting to realize these ideas in their teaching. Assuming a well-designed investigation into teachers’ participation in standards-oriented professional development and the outcomes of that participation (including direct observations in their classrooms), it would be reasonable to infer that ITEA content standards had contributed to changes in those teachers’ thinking and practice. (Establishing this particular claim does not necessarily imply that students learned more; that inference would require a different study, or an additional component to this investigation.) Once again, comparisons with other school sites less invested in standards-related content would help to establish the claim.

Note that the Framework helps to establish the conceptual soundness of research inferences by highlighting elements of the domain that, through a reasonable chain of evidence and inference, link national standards to classroom outcomes.

By contrast, the following hypothetical examples involve unwarranted conceptual leaps in their reported conclusions:

  • Analysis of student achievement gains in states that align their mathematics standards with NCTM standards. Impressive student achievement gains in states that apparently embrace national mathematics standards invite the possible conclusion that the standards contributed to the improvements in student performance. But even assuming a technically sound analysis of test score trends that took into account known correlates of student achievement scores (e.g., student socioeconomic status), the inference is weak at best, or even fallacious, if the analysis did not consider other components highlighted by the Framework. Those conditions include alignment of the mathematics achievement measures with the standards, local interpretation of state and national curricular guidance, and the extent of standards-based classroom practice. In

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