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Ottmar, Erin; Landy, David – Journal of the Learning Sciences, 2017
Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…
Descriptors: Mathematics Instruction, Algebra, Outcomes of Education, Learning Processes
Kapur, Manu – Journal of the Learning Sciences, 2014
A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…
Descriptors: Foreign Countries, Grade 8, Mathematics Instruction, Failure
Alibali, Martha W.; Nathan, Mitchell J. – Journal of the Learning Sciences, 2012
Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based…
Descriptors: Mathematics Education, Mathematical Concepts, Physical Environment, Mathematics Instruction
Lobato, Joanne; Rhodehamel, Bohdan; Hohensee, Charles – Journal of the Learning Sciences, 2012
As transfer researchers have begun to investigate a broader range of phenomena, they have correspondingly put forward new processes to provide explanatory accounts for the occurrence of transfer. This move coincides with a call to acknowledge the contribution of social interactions, language, cultural artifacts, and normed practices to the…
Descriptors: Transfer of Training, Mathematics Instruction, Cognitive Processes, Interpersonal Communication
Abrahamson, Dor – Journal of the Learning Sciences, 2012
Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…
Descriptors: Teaching Methods, Mathematics Instruction, Middle School Students, Thinking Skills