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Arithmetical and Cognitive Antecedents and Concomitants of Algebraic Skill


This is an Institute for Educational Sciences (IES) research project for an Education Research Grant under the National Center for Education Research (NCER) RFA. The topic is Cognition and Student Learning (CASL), and this is a Goal 1 identification study. In line with Goal 1 objectives, the proposed study aims to (1) experimentally evaluate the degree to which algebraic conceptual and procedural knowledge are separable, (2) evaluate associations between malleable factors (arithmetical knowledge and skills) that are predictive of algebra achievement, and (3) identify factors (cognitive resources) that directly affect algebra learning and/or mediate or moderate relations between arithmetical knowledge and skills and algebra achievement. To do so, we propose experimental and descriptive studies rely on an extant database as well as primary data collection on arithmetical, algebraic, and cognitive data on students over two cohorts just prior to and at the end of their first course in algebra (8th or 9th grade). A key advantage of this project is a window of opportunity to capitalize on a wealth of cognitive and arithmetical data from earlier grades (3, 4, 5) available on a portion of the proposed student sample from a prior grant (NIH R01 HD46154). The proposed study will provide empirical evidence as to the specific knowledge and skills that are predictive of algebra achievement and address how early such predictors are evident. Our general hypotheses are that (a) algebraic proficiency comprises both procedural skill and conceptual knowledge which are separate and measureable, though related; and (b) these types of abilities have overlapping yet different sets of immediate and earlier predictors. Identifying these predictors and their relative strength in the context of one another will be useful in the design of interventions that directly improve the relevant arithmetical skills or that develop compensatory strategies for students with specific cognitive deficits.