Definitions and examples in elementary calculus: The case of monotonicity of functions

Cristina Bardelle, Pier Luigi Ferrari

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Abstract

This paper is devoted to the investigation of students' understanding and handling of examples in the framework of an example-based introductory mathematics undergraduate course. The plan of the course included a wide use of graphs in standard lectures, tutoring sessions as well as in examinations.This study dealswith the notion of increasing function, which has been introduced by means of both the standard definition and a range of examples and non-examples, most often conveyed through graphs. We have analysed students' interpretations of the notion of increasing function as they applied them in a set of written examination tests. The data gathered have been completed by a number of interviews of students whose answers were difficult to interpret. The outcomes underline the importance of linguistic and semiotic competence and suggest that the design of innovative teaching paths should take care of the linguistic and semiotic skills needed to handle the representations involved.

Lingua originaleInglese
pagine (da-a)233-246
Numero di pagine14
RivistaZDM - International Journal on Mathematics Education
Volume43
Numero di pubblicazione2
DOI
Stato di pubblicazionePubblicato - mag 2011

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