Mathematics is an increasingly important aspect of education because of its central role in technology (Kuenzi, 2008). Mathematical achievement tests are universally applied throughout schooling in the US to assess yearly progress. The middle school years (e.g., Grade 6-Grade 8) are especially crucial to success in mathematics because students must acquire the skills needed in Algebra and higher levels of mathematics (National Mathematics Advisory Panel, 2008). The middle school years are also important developmentally because complex reasoning also emerges (e.g., Piaget, Vygotsky) and possibly at different rates for different students. According to many perspectives, the best design for studying changes in achievement and thinking in the middle school years is a longitudinal study of representative samples of children. For the current study, item responses to mathematical achievement tests administered during the middle school years were available for a randomly selected sample of 2,667 students in a Midwestern state. Until recently, however, inferences from such data were limited by the psychometric methods that were available to scale the data and provide meaningful comparisons. For the current study, some very recent advances in item response theory (IRT) were applied to provide inferences about growth. These methods consisted of confirmatory multidimensional and longitudinal models that previously were impractical to apply to large numbers of items and examinees. Growth in mathematical achievement was studied in the four major areas covered by the test (Number, Algebra, Geometry and Data) and in some specific areas that were especially consistent in definition across the grades. Differences in growth were also studied in two areas of individual differences, gender and socio-economic background, that have often been found important in careers that involve mathematics (Kuenzi, 2008). The analyses were conducted in the context of a series of hypotheses about growth and the substantive nature of differences across middle school. In Study 1, the substantive nature of change over middle school was examined by comparing the strength of the specific content areas across grades. Confirmatory multidimensional IRT models were applied to test hypotheses about concept structures in mathematics. In Study 2, growth was examined by fitting longitudinal IRT models to items from the various content areas. It was found that the relative strength of the content areas 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. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]