Content area
Abstract
It is observed that students often have difficulties in understanding why L'Hôpital's Rule works. These difficulties may stem from a shallow understanding of indeterminate forms, functional behavior, and rate of change. This study was designed after the conclusion of a preceding study concerning students' understanding and recognition of indeterminate forms. As such, this study attempts to describe a spectrum of students' conceptions of L'Hôpital's Rule and to discover the depth of mathematical connections that are associated with those conceptions. It is proposed that students' understanding of L'Hôpital's Rule may be represented as a schema.
The research questions, and interview protocol, are informed by APOS Theory. Data were collected in the form of written tasks in an interview setting from ten current Calculus II students. The tasks and interview questions were designed to develop a picture of the type of understanding students may have of L'Hôpital's Rule and to what degree that understanding is connected to relevant topics in calculus. An initial genetic decomposition was created to represent the proposed schema.
The results indicated that the participating students did not have a well-developed understanding of L'Hôpital's Rule, despite facility with other concepts in the calculus such as limits and derivatives. These students had difficulty discussing the relationship between L'Hôpital's Rule and indeterminate forms, and demonstrated little understanding of the role of derivatives in the rule.
Analysis of students' responses and written work supported the use of a schema to represent students' understanding of L'Hôpital's Rule. The initial genetic decomposition was found to be adequate in describing students' coordination of concepts in forming their understanding of the rule. Developmental levels were also formed describing the progression of student understanding of L'Hôpital's Rule. Specific suggestions for improving classroom instruction and continued research on students' understanding of the rule are provided.
