Students' Conceptual Knowledge of Limits in Calculus: A Two-Part Constructivist Case Study

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Adams, M. (2013). Students' Conceptual Knowledge of Limits in Calculus: A Two-Part Constructivist Case Study. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using 41 traditional textbook type tasks and non-traditional tasks, various ways students think about functions, limits at a point, limits at infinity and limits that do not exist were explored. Tasks included continuous and non-continuous functions; piecewise, rational and trigonometric functions, including those with oscillatory end behaviors. In Phase I, two students with different conceptions of limits and ability levels were selected for the initial analysis. The findings gave rise to a more in-depth follow-up investigation referred to as Phase II , which explored what students know about limits with respect to the definition of limit and infinity as well as knowledge of domains. Four student cases were selected out of nine based on similar emerging themes of understandings. The results are interpreted in terms of the constructivist framework and suggest that students assimilate information about limits into a variety of unique conceptual knowledge structures that ultimately develop into operational schemas. Given the nature of the content knowledge, these schemas are either appropriate or altered. Implications related to improving instructional practices, differentiating instruction for diverse learners and teaching limits in meaningful ways across the curriculum, are discussed.

Details
Author

Adams, Margaret

Title

Students' Conceptual Knowledge of Limits in Calculus: A Two-Part Constructivist Case Study

Physical Description

1 online resource (682 pages) : PDF

Date

2013

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using 41 traditional textbook type tasks and non-traditional tasks, various ways students think about functions, limits at a point, limits at infinity and limits that do not exist were explored. Tasks included continuous and non-continuous functions; piecewise, rational and trigonometric functions, including those with oscillatory end behaviors. In Phase I, two students with different conceptions of limits and ability levels were selected for the initial analysis. The findings gave rise to a more in-depth follow-up investigation referred to as Phase II , which explored what students know about limits with respect to the definition of limit and infinity as well as knowledge of domains. Four student cases were selected out of nine based on similar emerging themes of understandings. The results are interpreted in terms of the constructivist framework and suggest that students assimilate information about limits into a variety of unique conceptual knowledge structures that ultimately develop into operational schemas. Given the nature of the content knowledge, these schemas are either appropriate or altered. Implications related to improving instructional practices, differentiating instruction for diverse learners and teaching limits in meaningful ways across the curriculum, are discussed.

Genre

doctoral dissertations

Subjects--Topics

Mathematics--Study and teaching
Educational psychology
Adult education

Degree

Ph.D.

Keywords

Definition of Limit
Domain
Infinity
Relational Understanding
Undergraduate Students
Understanding Limits in Calculus

Subject Area

Curriculum & Instruction

Advisor(s)

Cifarelli, Victor

Committee Members

Morgan, Meg
Pugalee, David
Saenz-Ludlow, Adalira
Saurino, Dan
Wichnoski, Bruno

Degree Note

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2013.

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Rights Holder Information

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Identifier

Adams_uncc_0694D_10414

Permalink

http://hdl.handle.net/20.500.13093/etd:1082