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Students' Concepts‐ and Theorems‐in‐Action on a Novel Task About Similarity
Author(s) -
DeJarnette Anna Fricano,
Walczak Marissa,
González Gloriana
Publication year - 2014
Publication title -
school science and mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.135
H-Index - 2
eISSN - 1949-8594
pISSN - 0036-6803
DOI - 10.1111/ssm.12092
Subject(s) - similarity (geometry) , task (project management) , mathematics education , action (physics) , multiplicative function , construct (python library) , concept learning , mathematics , perception , proportional reasoning , analogy , computer science , epistemology , artificial intelligence , image (mathematics) , mathematical analysis , philosophy , physics , management , quantum mechanics , economics , programming language
Similarity is a fundamental concept in the middle grades. In this study, we applied V ergnaud'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.