The process of pairing a name with representations or peculiar properties permeates many mathematics classroom situations. In school, many practices go under the label 'definition', even though they can be very different from what mathematicians conceive as a formal definition, and in fact there are substantial differences between these different kinds of practices. This can create difficulties for pupils, since they may encounter non-coherent definitions of the same thing. Features of these schemes are exemplified through the analysis of some algebra high school textbooks, looking at the proposed 'definitions' of monomials and polynomials. We show how all these definition schemes are used in textbooks. Starting from the observed differences, we highlight some educational research problems.

Monomials and polynomials: The long March towards a definition

Andrea Maffia
2020

Abstract

The process of pairing a name with representations or peculiar properties permeates many mathematics classroom situations. In school, many practices go under the label 'definition', even though they can be very different from what mathematicians conceive as a formal definition, and in fact there are substantial differences between these different kinds of practices. This can create difficulties for pupils, since they may encounter non-coherent definitions of the same thing. Features of these schemes are exemplified through the analysis of some algebra high school textbooks, looking at the proposed 'definitions' of monomials and polynomials. We show how all these definition schemes are used in textbooks. Starting from the observed differences, we highlight some educational research problems.
2020
Giorgio Bolondi; Federica Ferretti; Andrea Maffia
File in questo prodotto:
File Dimensione Formato  
28_Bolondi_et_al_2018_Polinomi.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Creative commons
Dimensione 1.75 MB
Formato Adobe PDF
1.75 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/894493
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 4
social impact