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Rafferty, Anna N.; Jansen, Rachel A.; Griffiths, Thomas L. – Cognitive Science, 2020
Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how…
Descriptors: Computer Assisted Testing, Mathematics Tests, Mathematics Skills, Student Evaluation
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Anderson, John R. – Cognitive Science, 2005
This article describes the Adaptive Control of Thought-Rational (ACT-R) cognitive architecture (Anderson et al., 2004; Anderson & Lebiere, 1998) and its detailed application to the learning of algebraic symbol manipulation. The theory is applied to modeling the data from a study by Qin, Anderson, Silk, Stenger, & Carter (2004) in which children…
Descriptors: Cognitive Processes, Models, Symbols (Mathematics), Algebra
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Politzer, Guy; Van der Henst, Jean-Baptiste; Delle Luche, Claire; Noveck, Ira A. – Cognitive Science, 2006
We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expression (in the form of the Gergonne…
Descriptors: Models, Sentence Structure, Semantics, Prediction