Abstract:
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.
