Analysis of item difficulty and change in mathematical achievement from 6th to 8th grade's longitudinal data

Abstract

Mathematics is an increasingly important aspect of education because of its central role in technology. Learning mathematics at the elementary and middle school levels forms the basis for achievement in high school and college mathematics, and for the broad range of mathematical skills used in the workplace. Especially, the middle school years (e.g., Grade 6-Grade8) are crucial to success in mathematics because students must acquire the skills needed in higher levels of mathematics and complex reasoning ability based on the developmental perspectives on cognition (e.g., Piaget, Vygotsky). The purpose of the current study was to measure and interpret the mathematical achievement growth during the middle school years using some very recent advances (confirmatory multidimensional and longitudinal models) in item response theory. It was found that the relative strength of the content areas (mathematical standards and benchmarks) shifted somewhat across grades in defining mathematical achievement. The largest growth occurred from Grade 6 to Grade 7. The specific pattern of growth varied substantially by the socio-economic status of the student but few differences emerged by gender. The implications of the results for education and for developmental theories of cognitive complexity are discussed.