Graduate Thesis Or Dissertation

The development and validation of an instrument to assess cognitive domain status of preservice and inservice elementary teachers in the division of rational numbers

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  • The purpose of this study was to develop a valid and reliable instrument to determine cognitive domain status of preservice and inservice elementary teachers in the operation of division with rational numbers in the context of Wilson's (1971) taxonomy. The domain was defined with the cooperation of a panel of content specialists recruited nationwide. The panel first established a list of tasks considered representative of the domain of interest. Objectives were selected to match the tasks and items were chosen or constructed to test the objectives. A panel of preservice teachers rated each of the items for clarity. Analysis of reliability and validity began by administering two 40- item forms of the test to 79 students enrolled in mathematics education courses for elementary teachers at Eastern Washington University, Gonzaga University, and Washington State University during the Fall term of 1988. Using statistics generated by these first two forms, a third form with 64 items was constructed. The third form was administered to 81 students enrolled in mathematics and mathematics education courses at Eastern Washington and Gonzaga Universities during the Fall term of 1989. Included were students from a foundations of mathematics course which has a calculus prerequisite. Based upon the statistics accumulated on the third form, the final 48-item version of the instrument was assembled and the statistics reviewed to establish evidence of reliability and validity. The reliability of the test results was established by various reliability coefficients which ranged from 0.872 to 0.886. The standard error of measurement ranged from 2.778 to 2.946. Content-related evidence of validity was established through the definition of the domain by content specialists and the table of specifications assigning the relative importance of each of the related objectives. Construct-related evidence of validity based upon the hierarchical structure of the domain was significant at [alpha] = 0.01. A factor analysis yielding a single factor furnished further evidence of this structure. Construct-related evidence for validity based upon known groups was significant at [alpha] = 0.005.
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