A Semiotic Interpretation of the Derivative Concept in a Textbook

Differential and integral calculus textbooks are widely used as the main resource for teaching. They appear in a variety of forms and adopt various approaches to present the content. In this paper, we turn our attention to one chapter of a calculus textbook and our focus is on the introduction of the derivative concept. With the purpose of examining the presentation of the derivative concept in the textbook, we give a view of Peirce's semiotics, in particular of his classification of sign-vehicles. The analysis allows us to point out that the sign-vehicle in relation to the derivative concept may be iconic, indexical, or symbolic. These do not constitute mutually exclusive kinds of signs, but they are interrelated in such a way that we can identify iconicity in indexicality and indexicality in symbolicity. We conclude that the textbook has the potential to enable students to conceptualize the derivative. However, in some aspects, the book may constrain students' conceptualization and it could be improved to meet the students' needs to make meaning of the derivative concept.