Graduation Semester and Year
Fall 2025
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
James A. M. Alvarez
Abstract
This exploratory study investigates second-semester calculus students’ understanding of series convergence using both nonscripting and scripting-based tasks. Researchers recognize that students encounter difficulties with learning series, including series convergence, and that there is a need for more meaningful tasks that aid students’ learning of series. Script writing, used mainly with prospective mathematics teachers, can be used to explore mathematical understandings. Thus, this study examines how script writing, in the form of a scripting task, elicits students’ understanding of series convergence in contrast to nonscripting-based tasks to determine the potential of script writing in assessing this student understanding. We examine students’ concept image and concept definition of series convergence that both task approaches elicit in comparison to the formal concept definition. We address the following research questions: (1) What aspects of student understanding of series convergence arise, including how students attend to the connection between series and sequences of partial sums, when working a scripting task versus a nonscripting-based task? (2) What is the nature of possible conflict factors with regard to students’ concept definition and concept image of series convergence that arise in student responses to nonscripting-focused tasks and a scripting task? Using departmental midterm exam scores to select participants, 17 second-semester calculus students participated in two interview sessions in the last five weeks of a 15-week semester. Each participant either completed a nonscripting task on series convergence within the first interview session followed by a scripting task within the second session, or vice versa. This study’s analysis used a priori codes derived from the research literature and thematic analysis techniques to identify additional codes and themes. Findings reveal participants’ conceptions on the relationship between series and sequences of partial sums and the nature of potential conflict factors in participants’ concept image and definition of series convergence. Prevalent conflict factors arose in participants’ application of limits and understanding of notation that distinguishes sequences of partial sums and the terms of a series. This study supports the use of script writing as a research tool and as a viable method of assessing student understanding of series convergence. Findings suggest that scripting tasks may provide a robust way to assess student understanding of concepts in second-semester calculus.
Keywords
Series convergence, Scripting task, Script writing, Calculus assessment, Concept image, Concept definition, Approximations of practice
Disciplines
Other Mathematics | Science and Mathematics Education
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Torres Manzanarez, Eduardo, "EXAMINING STUDENT UNDERSTANDING OF SERIES CONVERGENCE USING SCRIPT WRITING" (2025). Mathematics Dissertations. 271.
https://mavmatrix.uta.edu/math_dissertations/271