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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
Izsak, Andrew; Caglayan, Gunhan; Olive, John – Journal of the Learning Sciences, 2009
We describe how 1 Algebra I teacher and her 8th-grade students used meta-representational knowledge when generating and evaluating equations to solve word problems. Analyzing data from a sequence of 4 lessons, we found that the teacher and her students used criteria for evaluating equations, in addition to other types of knowledge (e.g., different…
Descriptors: Word Problems (Mathematics), Equations (Mathematics), Algebra, Mathematics Instruction
Gresalfi, Melissa Sommerfeld – Journal of the Learning Sciences, 2009
This article presents an analysis of how students' dispositions toward learning shift and change over time through their engagement with particular classroom practices and identifies classroom practices that support the development of more productive dispositions. An analysis of 4 purposefully selected students from 2 different classrooms reveals…
Descriptors: Teacher Attitudes, Mathematics Instruction, Student Attitudes, Attitude Change
Jurow, A. Susan; Hall, Rogers; Ma, Jasmine Y. – Journal of the Learning Sciences, 2008
This article examines how conversations during design reviews in which 8th-grade mathematics students shared population models with visiting specialists expanded the disciplinary expertise of the classroom. "Re-contextualizing" is a conversational exchange that visiting specialists initiated to invite groups to consider their models in novel…
Descriptors: Speech Communication, Peer Evaluation, Middle School Students, Secondary School Mathematics
Moschkovich, Judit N. – Journal of the Learning Sciences, 2008
This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did…
Descriptors: Mathematics Education, Discussion (Teaching Technique), Mathematical Concepts, Concept Formation