Doctor of Philosophy (PhD)
Teaching and Learning
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
E. Michael Nussbaum
Number of Pages
This task-based interview study examined the development of prerequisite skills and concepts and calculus skill and concepts of students who entered a first-semester calculus course with a low level of prerequisite skills. The participants in this study completed three task-based interviews with two tasks in each interview. The research question addressed by this study was, To what extent do task-based interviews reveal students’ prerequisite skills and conceptual understanding for applications of the derivative and how do these skills and understanding develop for students who have been classified as having low levels of prerequisite skills upon entering a calculus course? The theoretical framework used to track the development of students’ prerequisite and calculus skills and concepts was developed by Pirie and Kieren and contains eight layers of mathematical understanding. An assessment of prerequisite skills was used to identify students who are classified as having low level of prerequisite skills. The development of students’ prerequisite and calculus skills and concepts over the course of the three task-based interviews in this study provides a rationale for how instructors of calculus and prior courses can emphasize certain skills and concepts to help students have the necessary prerequisite skills to succeed in a calculus course. Data collected included an initial student survey, scores from the research-based assessment on prerequisite skills, and three task-based interviews from each of the participants in the study. Interviews were conducted at three different points in the semester: the second week of the semester, the seventh week of the semester after the participants learned procedural calculus rules, and the twelfth week of the semester after the participants learned applications of the derivative. Overall, each participant showed some improvement in prerequisite skills and concepts and most showed some improvement in calculus skills and concepts. While each student was initially classified as having low levels of prerequisite skills, improvement varied across the participants. One participant showed minimal improvement in prerequisite and calculus skills and concepts. One participant showed adequate improvement in prerequisite and calculus skills and concepts based on one of the tasks in the interviews, but minimal improvement based on the other task in the interviews. One participant showed an improvement in prerequisite skills and concepts, but no demonstrated improvement in calculus skills and concepts. Two participants showed substantial improvement in both prerequisite skills and concepts as well as calculus skills and concepts. Implications for researchers and teachers are discussed for the benefits of using rich tasks to reveal students’ thinking and the importance of making connections between tasks and connections between procedures and concepts.
Prerequisite skills; Concepts; Task-based interviews; Calculus students
Science and Mathematics Education
University of Nevada, Las Vegas
Wong, Nicholas, "The Development of Prerequisite Skills and Concepts from Task-Based Interviews in Calculus Students with Low-Levels of Prerequisite Skills" (2021). UNLV Theses, Dissertations, Professional Papers, and Capstones. 4272.
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