The mathematical work with the derivative of a function: teachers’ practices with the idea of “generic”
Tipo de documento
Autores
Lista de autores
Panero, Monica, Arzarello, Ferdinando y Sabena, Cristina
Resumen
This paper investigates the introduction of the derivative notion and, specifically, the introduction of the derivative function, as a significant moment in the development of mathematical work on functions. In particular, we analyse the process of genericization that two Italian teachers conducted with their grade 13 students, in order to make them shift from the derivative at a specific point x0 to the derivative as a global function in the x variable. Specifically, we analyse the role of the teacher in the semiotic genesis of this process and investigate the role of semiotic resources therein. As a result, we highlight the importance of conducting carefully this shift from the pointwise x0 sign to the global x sign, in order to gain an actual shift in the perceived properties of the derivative function, which depends on the x sign as a variable. In conclusion, we connect our findings to the model of the Mathematical Working Space of functions, with particular regard to the “visualisation” process and the semiotic axis.
Fecha
2016
Tipo de fecha
Estado publicación
Términos clave
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Volumen
30
Número
54
Rango páginas (artículo)
265-286
ISSN
19804415
Referencias
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