The average mathematical competence of U.S. students lags far behind that of peers in East Asia and much of Europe.  Few U.S. students possess the knowledge of mathematics needed to pursue careers in STEM disciplines. Many lack even the basic competence needed to succeed in most jobs in a modern economy.  Moreover, a large gap separates the mathematical knowledge of children from rich and poor backgrounds and from differing racial and ethnic groups; differences are already present in preschool and increase over the course of schooling. The goal of the Center for Improving Learning of  Fractions (CILF) is to apply theories, methods, and empirical findings from cognitive science research on the acquisition of mathematical knowledge to better understand the problems that children with mathematics difficulties (MD) have with a crucial component of mathematical knowledge – rational numbers – and to develop effective interventions to remedy those problems.

   The Center research program comprises three strands. In Strand 1, we are conducting relatively small-scale experimental studies to enhance understanding of the cognitive processes that underlie magnitude representations of rational numbers and use of those representations in operations with rational numbers. In Strand 2, we are conducting short- and long-term longitudinal studies of students with and without MD to examine how numerical magnitude representations, proficiency with whole number operations, working memory for numbers, inhibitory processes, attentive behavior, and strategic behavior contribute to the ability to understand and operate with rational numbers. As results from research conducted within Strands 1 and 2 emerge, they are informing the design of the instructional innovations, which are the focus of Strand 3. In Strand 3, our major focus is on building a solid foundation of conceptual understanding of fractional magnitudes by working on concepts and procedures involved in common fractions and decimal equivalents. Each year in Years 1-5, we develop an intervention component, integrate it into the overall intervention package, and conduct research to develop an evidence-based fidelity of implementation tool and assess its feasibility. This also provides us with data for estimating the effects of each year’s component on conceptual understanding and procedural skill with fractional quantities and for assessing whether effects differ as a function of MD severity; these data are used to inform the next year’s development work.