Abstract
This study investigates the effectiveness of a teaching activity that aimed to convey the meaning of indeterminate forms to a group of undergraduate students who were enrolled in an elementary mathematics education programme. The study reports the implementation sequence of the activity and studentsâ experiences in the classroom. To assess the effectiveness of the adopted approach, an individual homework assignment, in which students were asked to generate examples for indeterminate forms as geometrical constructions, was applied. The findings revealed that the students had various misunderstandings about the meanings of indeterminate forms prior to the study. Moreover, the use of the term âindeterminateâ to designate these limit forms was found to be inappropriate because of its connotation. In light of the results, some suggestions are made to improve the teaching of indeterminate forms. Key words: Calculus teaching, indeterminate forms, limit concept, concept of infinity.
Highlights
Indeterminate forms are special cases of limits that occur when it is not possible to determine the limit value of an expression solely by recognizing the limiting behavior of its subexpressions
This study investigates the effectiveness of a teaching activity that aimed to convey the meaning of indeterminate forms to a group of undergraduate students who were enrolled in an elementary mathematics education programme
Before the classroom intervention to reveal the meaning that students attached to the indeterminate forms, 0
Summary
Indeterminate forms are special cases of limits that occur when it is not possible to determine the limit value of an expression solely by recognizing the limiting behavior of its subexpressions. The most important indeterminate forms are the types 0 and , because to. 0 calculate the limit of the others, one should transform them to these types in order to apply LâHopitalâs theorem. Instruction on types of indeterminate forms and how to use LâHopitalâs theorem to compute their limit value is covered in analysis courses at the university level. On several occasions during teaching, it has been seen that most of the students who were able to use LâHopitalâs theorem to calculate the limits of indeterminate forms were unable to correctly grasp the meaning of what they stand for. Most students cannot interpret as the ratio of two quantities that increase without bound, or 0 as the ratio of two quantities both approaching zero.
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