Date of Award:

8-2020

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee

James S. Cangelosi

Committee

David E. Brown

Committee

Nathan Geer

Abstract

The use of precise language is one of the defining characteristics of mathematics that is often missing in mathematics classrooms. This lack of precision results in poorly constructed concepts that limit comprehension of essential mathematical definitions and notation. One important concept that frequently lacks the precision required by mathematics is the concept of function. Functions are foundational in the study undergraduate mathematics and are essential to other areas of modern mathematics. Because of its pivotal role, the concept of function is given particular attention in the three articles that comprise this study.

A unit on functions that focuses on using precise language was developed and presented to a class of 50 first-semester calculus students during the first two weeks of the semester. This unit includes a learning goal, a set of specific objectives, a collection of learning activities, and an end-of-unit assessment. The results of the implementation of this unit and the administration of the assessment indicated that when students were able to construct the concept of function themselves and formulate a formal definition, they had a deeper and more meaningful understanding of the concept.

In order to demonstrate its validity, the assessment was analyzed as to its relevance, reliability, and its test items’ effectiveness in discriminating between different levels of achievement. The results of this analysis indicated that the assessment was relevant to both the mathematical content and learning levels indicated by the unit’s objectives and had a high level of reliability. Additionally, the test items contained in the assessment had a reasonable level of effectiveness in discriminating between different levels of student achievement.

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