Mathematics difficulties are widespread in US schoolchildren. However, little is known about the development of mathematical cognition in young children with mathematics disabilities (MD). To date, few studies have examined mathematics disabilities from a longitudinal perspective and many do not differentiate between children with specific MD (i.e., difficulties in mathematics but normal achievement in reading) and those with more pervasive academic weaknesses. The proposed project fills this void by examining the mathematical performance of 100 children with MD and 100 children without MD longitudinally over a 2-year period. Based on standardized achievement test scores, second grade children with CD will be divided into two groups: those with no reading difficulties and those with reading difficulties. For comparison, half of the children in the control group will have no reading and mathematics difficulties and half will have reading difficulties alone. Based on a theoretical framework of mathematical cognition, children's performance will be assessed in three domains: number facts, story problems, and multi-digit calculation. Children will be assessed a total of five times (twice in second grade and 3 times in third grade). The assessment will determine whether skills in these areas develop differentially and whether children with MD have difficulties in some domains but not in others. To examine the stability of our initial ability group classifications (e.g., mathematics difficulties-good reading) over time, each child also will be given standardized mathematics and reading achievement tests on five occasions. Growth curve modeling, a state-of-the-art statistical technique, will be used to analyze the data. The proposed project has practical as well as theoretical value. The findings will increase our knowledge of the nature and processes of mathematical thinking in children. They also will provide detailed information about children's performance on tasks that are directly applicable to teaching mathematics. Such data should provide an empirical basis for developing diagnostic tools for identification of mathematics abilities.
