دورية أكاديمية
Students' Concepts- and Theorems-in-Action on a Novel Task about Similarity
| العنوان: | Students' Concepts- and Theorems-in-Action on a Novel Task about Similarity |
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| اللغة: | English |
| المؤلفون: | DeJarnette, Anna Fricano, Walczak, Marissa, González, Gloriana |
| المصدر: | School Science and Mathematics. Dec 2014 114(8):405-414. |
| الإتاحة: | Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA |
| Peer Reviewed: | Y |
| Page Count: | 10 |
| تاريخ النشر: | 2014 |
| نوع الوثيقة: | Journal Articles Reports - Research |
| Education Level: | Middle Schools Secondary Education Junior High Schools |
| Descriptors: | Mathematical Concepts, Fundamental Concepts, Middle School Students, Geometric Concepts, Logical Thinking, Multiplication, Puzzles, Scaling, Problem Solving, Visual Perception, Mathematics Instruction |
| DOI: | 10.1111/ssm.12092 |
| تدمد: | 0036-6803 |
| مستخلص: | 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. |
| Abstractor: | As Provided |
| Entry Date: | 2014 |
| رقم الأكسشن: | EJ1046743 |
| قاعدة البيانات: | ERIC |
Full Text Finder | تدمد: | 0036-6803 |
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| DOI: | 10.1111/ssm.12092 |