Book ChapterDOI
Perspectives on representation in mathematical learning and problem solving
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The article was published on 2008-06-19. It has received 108 citations till now. The article focuses on the topics: Representation (systemics).read more
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Journal ArticleDOI
Designing for Productive Failure
Manu Kapur,Katerine Bielaczyc +1 more
TL;DR: The design principles undergirding productive failure (PF) are described and findings from an ongoing program of research on PF in mathematical problem solving in 3 Singapore public schools with significantly different mathematical ability profiles, ranging from average to lower ability.
Journal ArticleDOI
A further study of productive failure in mathematical problem solving: unpacking the design components
TL;DR: Kapur et al. as discussed by the authors showed that despite seemingly failing in their collective and individual problem-solving efforts, PF students significantly outperformed their counterparts in the other two conditions on both the well-structured and higher-order application problems on the post-test, and demonstrated greater representation flexibility in working with graphical representations.
Journal ArticleDOI
Modeling in Engineering: The Role of Representational Fluency in Students' Conceptual Understanding
TL;DR: The authors investigated the role that representations and representational fluency play in conceptual understanding during a complex modeling task related to heat transfer and found that students who are learning to model often use a variety of representations to express, test, revise, and communicate their own thinking.
Book ChapterDOI
Encyclopedia of mathematics education
TL;DR: A taxonomy of mathematics education can be found in this paper, where Bloom's Taxonomy of Mathematics Education is used to describe the main issues in mathematics education, including the following: "Actions, Processes, Projects, Schema (APOS) in Mathematics Education."
Journal ArticleDOI
Geometrical representations in the learning of two-variable functions
TL;DR: In this paper, the authors investigate the relationship between students' notion of subsets of Cartesian three-dimensional space and the understanding of graphs of two-variable functions, and find that students' understanding can be related to the structure of their schema for R3 and to their flexibility in the use of different representations.