Student Personal Concept Definition of Limits and Its Impact on Further Learning of Mathematics

摘要

Calculus is an introductory course for most students in Science, Technology, Mathematics and Education (STEM). Limits are an essential part of the learning of calculus. It has been previously documented that students tend to struggle when first learning the topic of limits. This paper is an investigation in to the personal concept definition of limits and how consistent a students personal concept definition to the formal definition of the limit after they have completed courses in introductory calculus. The study took place during a 15-week semester, with 28 students, who were taking either Calculus III or Ordinary Differential equations. These 14 male and 14 female participants attended the same Midwestern Public University. They were given a short, in-class, survey where they could demonstrate their concept definition and the operability of their concept definition as it pertains to limits and limit-based problems. Three categories were created to signify the students level of operability in solving limit-based problems based on their responses to the survey. The categories were Low, Mid, and High Scoring, which demonstrated an inoperable, partially operable, or fully operable concept definition, respectively. The majority of students fell in to Low and Mid Scoring categories, indicating their lack of operability in personal concept definition as it pertains to limits. This study suggests that students in mathematics should be encouraged to develop their conceptual understanding and move past procedural knowledge as a way of mastering a mathematical topic, such as limits.