Date of Award

5-2015

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Science (MS)

Department

Teaching

Advisor

Natasha M. Speer

Second Committee Member

Robert Franzosa

Third Committee Member

Eric Pandiscio

Abstract

Worldwide demand for college graduate in the fields of science, technology, engineering and mathematics (STEM) has never been higher than it is today. Despite this demand, the number of U.S. graduates in these fields has decreased over the last twenty years. Attrition among those that enter college as STEM majors is high. Nearly 50% of students who major in STEM disciplines either fail to finish their degree, or change their major. Though the reasons for this attrition are likely complex and varied, research has indicated that students’ experience in introductory calculus has a negative impact on this attrition.

One of the primary learning goals of introductory college calculus is to understand the first derivative of a function, what it represents, and how it is determined. The topic of derivative is difficult, and many students have difficulty developing and applying this knowledge, especially in the context of a real-world situation. The objective of the current study is to gain insight into what makes applying this knowledge difficult for students. In the current study, these issues are examined through the lens of applied optimization problems, a common applied problem that students face in many introductory calculus courses. Even though these are common applied problems in introductory calculus, there has been little research about student difficulties with these problems. This research made use of data collected from both written student work and clinical interviews. Findings indicate that students face a variety of difficulties as they attempt to solve these problems. Many of these difficulties relate to pre-requisite mathematics knowledge of function, geometry, and algebra. Findings also indicate that students often do not use the techniques of calculus, even when they have demonstrated competency in applying that knowledge in analogous problems in non-applied contexts. Understanding why students are unable to apply their knowledge of derivatives in an applied setting could lead to advances in teaching methods designed to allow students to better comprehend derivatives in college calculus. These advances could serve to improve student learning outcomes, and the student experience. Efforts to address these issues may lead to improved retention among students majoring in the STEM fields.

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