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ERIC Number: EJ1046743
Record Type: Journal
Publication Date: 2014-Dec
Pages: 10
Abstractor: As Provided
ISSN: ISSN-0036-6803
Students' Concepts- and Theorems-in-Action on a Novel Task about Similarity
DeJarnette, Anna Fricano; Walczak, Marissa; González, Gloriana
School Science and Mathematics, v114 n8 p405-414 Dec 2014
Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts-in-action and theorems-in-action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric and multiplicative reasoning at the same time in order to construct similar figures? We found that students used concepts of scaling and proportional reasoning, as well as the concept of circle and theorems about similar triangles, in their work on the problem. Students relied not only on visual perception, but also on numeric reasoning. Moreover, students' use of multiplicative and proportional concepts supported their geometric constructions. Knowledge of the concepts and ideas that students have available when working on a task about similarity can inform instruction by helping to ground formal introduction of new concepts in students' informal prior experiences and knowledge.
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Publication Type: Journal Articles; Reports - Research
Education Level: Middle Schools; Secondary Education; Junior High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A