An investigation of dimensionality across grade levels and effects on vertical linking for elementary grade mathematics achievement tests

摘要

It is a widely held belief that mathematical content strands reflect different constructs which produce multidimensionality in mathematical achievement tests for Grade 3-8. This study analyzes the dimensional structure of mathematical achievement tests aligned to NCTM content strands using four different methods for assessing dimensionality. The effect of including off-grade linking items as a potential source of dimensionality was also considered. The results indicate that although mathematical achievement tests for Grades 3-8 are complex and exhibit some multidimensionality, the sources of dimensionality are not related to the content strands or the inclusion of several off-grade linking items. The complexity of the data structure along with the known overlap of mathematical skills suggest that mathematical achievement tests could represent a fundamentally unidimensional construct. Refining the definition of dimensionality to include "detectable dimensionality" is discussed.