1. To extend scientific knowledge of the underlying cognitive processes that contribute to learning difficulties in mathematics with the goal of identifying new approaches for intervening and providing more effective instruction for students with learning difficulties in mathematics. 2. To utilize cognitive science to develop innovative approaches for improving instruction for students with learning difficulties in mathematics. A secondary goal is to work cooperatively with the Institute to formulate and carry out supplemental research studies that are responsive to the needs of special education practitioners and policy makers.
The aim of the small-scale experimental studies is to enhance understanding of the cognitive processes that underlie magnitude representations of fractions and use of the those representations in operations with fractions. The purpose of the longitudinal study is to examine growth and achievement of students with and without math difficulties between grades 3-6 with particular emphasis on development of early fractions concepts and operations. The goal is to identify component processes and skills that predict or underlie learning difficulties with fractions. Findings from the experimental studies and longitudinal study will be used to inform the development of intervention for improving conceptual understanding of fractional magnitudes, by working on concepts and procedures involved in common fractions and decimal equivalents. An intervention component will be developed each year. The intervention components to be developed include linking division and measurement situations, multiplicative relations, multiple representations, use of common fractions to represent relations within word problems, and use of ratios and proportions within word problems. The interventions are conceptualized for use within an RTI framework that provides Tier 2 small-group instruction. The intervention will be implemented 3 times weekly for 10 weeks, 30 min per session to determine feasibility and potential promise. |