
06619323
j
2016e.00740
Foster, Colin
de Villiers, Michael
The definition of the scalar product: an analysis and critique of a classroom episode.
Int. J. Math. Educ. Sci. Technol. 47, No. 5, 750761 (2016).
2016
Taylor \& Francis, Abingdon, Oxfordshire
EN
G70
E40
definitions
scalar product
sense making
doi:10.1080/0020739X.2015.1117148
Summary: In this paper, we present, analyse and critique an episode from a secondary school lesson involving an introduction to the definition of the scalar product. Although the teacher attempted to be explicit about the difference between a definition and a theorem, emphasizing that a definition was just an arbitrary assumption, a student rejected the teacher's definition in favour of his own alternative. With reference to this particular case, we seek to explore some ways in which teachers can introduce mathematical definitions to students so as to support, rather than attempt to circumvent, their mathematical sense making. In this regard, we believe that it is important to develop learning opportunities for students which help them to gain some appreciation of important structural and historical reasons that underpin the definitional choices made.