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ERIC Number: EJ891125
Record Type: Journal
Publication Date: 2010
Pages: 6
Abstractor: As Provided
Reference Count: 21
ISSN: ISSN-1744-2710
Towards the Development of an Automated Learning Assistant for Vector Calculus: Integration over Planar Regions
Yaacob, Yuzita; Wester, Michael; Steinberg, Stanly
International Journal for Technology in Mathematics Education, v17 n2 p81-86 2010
This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a problem into a form that Mathematica can understand and then choose the correct solution technique. ILMEV is designed to help students with this process. The typical presentation of this material in textbooks is not easily adapted to an interactive interface, so we developed a model of vector integration that allows ILMEV to present a structured overview of this material that helps students choose a correct solution method. Mathematica can solve the translated problem using its cylindrical algebraic decomposition (CAD) algorithm, but does not provide any explanation of what is being done. To overcome this, we implemented a simplified CAD algorithm which is used to reduce integrals appearing in vector calculus to sums of iterated integrals which Mathematica can then compute. This allows students to interactively compute closed form solutions to many two dimensional textbook examples using the ILMEV interface. ILMEV is built on important pedagogical guiding principles - interactivity, visualisation, experimentation, White and Black Box Principle, multiple representations and step-by-step technique with explanations. The user interface was critical for the implementation of the guiding principles. (Contains 7 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A