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Calculations, Word Problems and Algebraic Cognition


Mathematics learning disabilities (MLD) affect 5-9% of the school-age population, leading to life-long difficulties that create financial burdens and a public health problem for society. Calculations and word problems are critical aspects of math competence beginning early and extending through adulthood. However, early calculations and word-problem skills may also be important precursors to the development of algebraic cognition, an aspect of math competence critical for later school success. The major distinction between calculations and word problems is the addition of linguistic information that requires children to construct a problem model. This seems to alter the nature of the task, and causal-comparative and correlational studies suggest that the abilities underlying these domains may differ. This raises the possibility that difficulty in these domains may be distinct; that different screening measures may be required to forecast difficulty in these domains; that intervention conducted in one domain may not transfer to the other; and that intervention in these domains may contribute differentially to students' ability to learn algebra.

In this project, the PIs recruit a large, representative sample of 2nd graders for whom they collect data on child characteristics (demographics, attention, cognitive dimensions, numerosity, reading). They randomly assign 2nd-grade classrooms to control vs. RTI calculations instruction vs. RTI word-problem instruction. RTI instruction refers to 2 tiers of research-principled instruction: classroom instruction and, as needed, small group tutoring. The PIs follow students through grade 4. At the end of grade 2, in each RTI condition, the PIs form, compare, and then follow 3 subgroups: typically-developing students, initially low-performing students who respond, and initially low-performing students who do not respond. The PIs will investigate (1) the short- and long-term efficacy of 2nd-grade RTI calculations or word-problem instruction on calculation, word-problem, and basic algebraic outcomes, assessing transfer across domains; (2) the prevalence and diagnostic stability of calculations MLD (CA-MLD) and word-problem MLD (WP-MLD) as a function of instructional condition and, within RTI condition, as a function of response to research-principled instruction; (3) child characteristics associated with development of calculations, word-problem, and algebraic skill and with CA-MLD and WPMLD; (4) child characteristics that distinguish typically developing students, initially low-performers who respond to research-principled instruction, and initially low-performers who fail to respond to research-principled instruction; and (5) how child characteristics interact with instructional condition to affect short and long-term calculations, word problems, and algebra outcomes. The PIs will assess the prevalence, child characteristics, and math profiles of MLD after eliminating inadequate instruction as the explanation for low math performance. Findings will have important implications for understanding, identifying, preventing, and treating MLD.

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