Algebraic learning and cognition

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Modified Project Summary/Abstract Section Competence with algebra is the foundation for the mathematics that facilitates reasoned decision making in many aspects of day-to-day life, including medical treatment choices (Reyna et al. 2009), is demanded in high-paying technology and science fields (National Mathematics Advisory Panel 2008), and contributes to employability and wages in many blue collar occupations (Bynner 1997). Yet, only 39% of US high school graduates have the algebraic competencies needed for these endeavors. Improving the algebraic skills of US students will yield individual and wider social benefits, but this goal has been difficult to achieve. One impediment is our piecemeal understanding of algebraic learning and cognition that has resulted in both practical and theoretical costs. Practically, one student may have difficulty due to an undervaluation of the importance of mathematics, another may have poorly developed prerequisite skills, and a third may confuse current learning with prior learning (proactive inhibition). The reasons for algebraic deficits in these students are very different and consequently the interventions to address them would differ as well. No current theory exists that integrates cognitive and non-cognitive processes on algebra readiness and learning, an integration that is needed for the development of measures to better assess individual differences in algebraic learning. In this proposal we develop such a model and use it to organize a comprehensive and deep longitudinal study of individual and gender differences in readiness for algebra and the learning of specific, core algorithmic and spatial-related algebraic competencies. Carefully chosen measures of prerequisite skills, visuospatial memory and cognition, complex spatial ability, proactive interference, and inherent sensitivity to magnitude will be administered to 450 7th graders. Their attitudes about mathematics and their math anxiety, as well as their attentive behavior in mathematics and English (as a contrast) classrooms will be annually assessed in 7th to 9th grade. At the beginning and end of 9th grade, participants will be assessed using psychometric and cognitive measures of algebraic competence generally and competence with algorithmic and spatial-dependent aspects of algebra in particular. The breadth and depth of measures will enable testing of nuanced hypotheses regarding the contributions of different cognitive and memory systems to different aspects of algebraic learning; the dynamic interactions between these systems and developmental change in math attitudes and anxiety as related to engagement in the mathematics classroom and algebraic learning and cognition; and, the cognitive and non-cognitive factors that contribute to gender differences in certain aspects of algebra, specifically girls’ disadvantage in spatial aspects of algebra and their undervaluation of mathematics. The combination will significantly advance our understanding of algebraic learning and cognition, and lead to the development of better assessment measures and targeted interventions to address individual and gender differences in algebraic learning.