Computational Labs in Calculus: Examining the Effects on Conceptual Understanding and Attitude Toward Mathematics

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dc.contributor.authorSpencer-Tyree, Brielle Tinsleyen
dc.contributor.committeechairBowen, Bradley D.en
dc.contributor.committeememberClark, Aaron C.en
dc.contributor.committeememberUlrich, Catherine L.en
dc.contributor.committeememberWilliams, Thomas O.en
dc.contributor.departmentEducation, Vocational-Technicalen
dc.date.accessioned2019-11-22T09:00:27Zen
dc.date.available2019-11-22T09:00:27Zen
dc.date.issued2019-11-21en
dc.description.abstractThis study examined the effects of computational labs in Business Calculus classes used at a single, private institution on student outcomes of conceptual understanding of calculus and attitudes towards mathematics. The first manuscript addresses the changes in conceptual understanding through multiple-method research design, a quantitative survey given pre and post study and qualitative student comments, found no significant gains in conceptual knowledge as measured by a concept inventory, however, student comments revealed valuable knowledge demonstrated through reflection on and articulation of how specific calculus concepts could be used in real world applications. The second manuscript presents results to the effects on attitudes toward mathematics, studied through multiple-method research design, using a quantitative survey given at two intervals, pre and post, and analysis of student comments, which showed that students that participated in the labs had a smaller decline in attitude, although not statistically significant, than students that did not complete the labs and the labs were most impactful on students that had previously taken calculus; student comments overwhelmingly demonstrate that students felt and appreciated that the labs allowed them to see how calculus could be applied outside the classroom. Overall students felt the labs were beneficial in the development of advantageous habits, taught some a skill they hope to further develop and study, and provided several recommendations for improvement in future implementation. Collectively, this research serves as a foundation for the effectiveness of computational tools employed in general education mathematics courses, which is not currently a widespread practice.en
dc.description.abstractgeneralStudents from a variety of majors often leave their introductory calculus courses without seeing the connections and utility it may have to their discipline and may find it uninspiring and boring. To address these issues, there is a need for educators to continue to develop and research potentially positive approaches to impacting students' experience with calculus. This study discusses a method of doing so, by studying students' understanding of and attitude toward calculus in a one-semester Business Calculus course using computational labs to introduce students to calculus concepts often in context of a business scenario. No significant gains in conceptual knowledge were found as measured by a concept inventory; however, student comments revealed valuable knowledge demonstrated through articulation of how specific calculus concepts could be used in real world applications. Students that participated in the labs also had a smaller decline in attitude than students that did not complete the labs. Student comments overwhelmingly demonstrate that students felt and appreciated that the labs allowed them to see how calculus could be applied outside the classroom. The labs were most impactful on students that had previously taken calculus. Overall students felt the labs were beneficial in the development of advantageous habits such as persistence, utilizing resources, and precision, introduced them to coding, a skill they hope to further develop and study, and students provided several recommendations for improvement in future implementation. This research provides a foundation for the effectiveness of computational tools used in general education mathematics courses.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:22917en
dc.identifier.urihttp://hdl.handle.net/10919/95835en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectSTEM Educationen
dc.subjectComputational Labsen
dc.subjectCalculusen
dc.subjectMathematics Educationen
dc.subjectCollege and University Calculusen
dc.subjectUndergraduate Mathematicsen
dc.subjectIntegrative-STEM Educationen
dc.titleComputational Labs in Calculus: Examining the Effects on Conceptual Understanding and Attitude Toward Mathematicsen
dc.typeDissertationen
thesis.degree.disciplineCurriculum and Instructionen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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