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ERIC Number: EJ1091422
Record Type: Journal
Publication Date: 2014
Pages: 19
Abstractor: As Provided
ISSN: ISSN-1479-4802
Generalising Calculus Ideas from Two Dimensions to Three: How Multivariable Calculus Students Think about Domain and Range
Dorko, Allison; Weber, Eric
Research in Mathematics Education, v16 n3 p269-287 2014
We analysed multivariable calculus students' meanings for domain and range and their generalisation of that meaning as they reasoned about the domain and range of multivariable functions. We found that students' thinking about domain and range fell into three broad categories: input/output, independence/dependence, and/or as attached to specific variables. We used Ellis' actor-oriented generalisations framework to characterise how students generalised their meanings for domain and range from single-variable to multivariable functions. This framework focuses on the process of generalisation--what students see as similar between ideas in multiple contexts. We found that students generalised their meanings for domain and range by relating objects, extending their meanings, using general principles and rules, and using/modifying previous ideas. Our findings suggest that the domain and range of multivariable functions is a topic instructors should explicitly address.
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A