A layer framework to investigate student understanding and application of the existence and uniqueness theorems of differential equations

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Publisher: Taylor & Francis Ltd

ISSN: 1464-5211

Source: International Journal of Mathematical Education in Science and Technology, Vol.38, Iss.3, 2007-01, pp. : 367-381

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Abstract

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students' understanding of these layers construct their perception of the theorems as a whole.