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Peer reviewed
Direct linkKoedinger, Kenneth R.; Alibali, Martha W.; Nathan, Mitchell J. – Cognitive Science, 2008
This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are…
Descriptors: Equations (Mathematics), Algebra, Problem Solving, Abstract Reasoning
Prather, Richard W.; Alibali, Martha W. – Cognitive Science, 2008
Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation.…
Descriptors: Numbers, Problem Solving, Word Problems (Mathematics), Equations (Mathematics)
McNeil, Nicole M.; Alibali, Martha W. – Cognitive Science, 2004
This study investigated the roles of problem structure and strategy use in problem encoding. Fourth-grade students solved and explained a set of typical addition problems (e.g., 5 + 4 + 9 + 5 = ?) and mathematical equivalence problems (e.g., 4 + 3 + 6 = 4 + ? or 6 + 4 + 5 = ? + 5). Next, they completed an encoding task in which they reconstructed…
Descriptors: Cognitive Processes, Arithmetic, Grade 4, Problem Solving
