Student Understanding of Directional Derivatives of Functions of Two Variables / Rafael Martn̕ez-Planell, Maria Trigueros Gaisman and Daniel McGee.
Action-Process-Object-Schema (APOS) Theory is applied to study student understanding of directional derivatives of functions of two variables. A conjecture of the main mental constructions that students may do in order to come to understand directional derivatives is proposed and is tested by conduc...
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| Main Authors: | , , |
| Format: | eBook |
| Language: | English |
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2015.
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| Summary: | Action-Process-Object-Schema (APOS) Theory is applied to study student understanding of directional derivatives of functions of two variables. A conjecture of the main mental constructions that students may do in order to come to understand directional derivatives is proposed and is tested by conducting semi-structured interviews with 26 students who had just taken multivariable calculus. The interviews explored the specific constructions of the genetic decomposition that student are able to do and also the ones they have difficulty doing. The conjecture, called a genetic decomposition, is largely based on the elementary notion of slope and on a development of the concept of tangent plane. The results of the empirical study suggest the importance of constructing coordinations of plane, tangent plane, and vertical change processes in order for students to conceptually understand directional derivatives. [For the complete proceedings, see ED583989.] |
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| Item Description: | Availability: North American Chapter of the International Group for the Psychology of Mathematics Education. e-mail: pmena.steeringcommittee@gmail.com; Web site: http://www.pmena.org/. Abstractor: As Provided. |
| Physical Description: | 1 online resource (1 online resource (8 pages)) |
| Type of Computer File or Data Note: | Text (Speeches/Meeting Papers) Text (Reports, Research) |
| Preferred Citation of Described Materials Note: | North American Chapter of the International Group for the Psychology of Mathematics Education, Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (37th, East Lansing, MI, Nov 5-8, 2015). |