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differentiation limit procedural knowledge conceptual knowledge

A Study of Pre-Service Teachers’ Performance on Two Calculus Tasks on Differentiation and Limit

Tin Lam Toh , Pee Choon Toh , Kok Ming Teo , Ying Zhu

The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on .


The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding  . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.

Keywords: Differentiation; limit; procedural knowledge; conceptual knowledge.

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