id: 06619323
dt: j
an: 2016e.00740
au: Foster, Colin; de Villiers, Michael
ti: The definition of the scalar product: an analysis and critique of a
classroom episode.
so: Int. J. Math. Educ. Sci. Technol. 47, No. 5, 750-761 (2016).
py: 2016
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: G70 E40
ut: definitions; scalar product; sense making
ci:
li: doi:10.1080/0020739X.2015.1117148
ab: 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
teacherâ€™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.
rv: