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ERIC Number: EJ1449036
Record Type: Journal
Publication Date: 2024-Nov
Pages: 28
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0013-1954
EISSN: EISSN-1573-0816
Students' Techniques for Approaching Defining Properties of Functions
Rosaura Uscanga; Kathleen Melhuish; John Paul Cook
Educational Studies in Mathematics, v117 n3 p457-484 2024
Functions are an essential concept in mathematics. The studies that have examined functions in advanced contexts have primarily focused on students' reasoning about specific types of functions (such as binary operations and isomorphisms) but not on the core characteristics of well-definedness and everywhere-definedness. Here, we report on a study in which we conducted task-based clinical interviews to gain insight into students' techniques for addressing "is the given relation a function?" tasks. We found that the techniques students employed necessarily extended far beyond those reported in the literature (such as the vertical line test) and relied on the previously undocumented notions of sameness, convention, and ambiguity (for well-defined) and notions of containment, existence, and set operations (for everywhere-defined). These techniques coordinated the domain, codomain, and rule, which previous research has highlighted the importance of but stopped short of directly investigating. Two contributions of this work include identifying successful techniques (as the landscape of functions literature predominantly focuses on challenges and difficulties) and identifying techniques for everywhere-definedness (which had not previously received any direct attention in the literature).
Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://bibliotheek.ehb.be:2123/
Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A