id: 06539019
dt: j
an: 2016b.00267
au: De Villiers, Michael
ti: Crossed quadrilaterals: a missed Lakatosian opportunity?
so: Philos. Math. Educ. J. 29, 6 p., electronic only (2015).
py: 2015
pu: Professor Paul Ernest, University of Exeter, Graduate School of Education,
Exeter
la: EN
cc: D20 E20 E40 G40 G90
ut: foundations of mathematics; defining; concepts; definitions; mathematics
and philosophy; Lakatos; geometry; triangles; crossed quadrilaterals;
angle sums; dynamic geometry; counter-examples; directed angles;
Varignonâ€™s theorem; Pascalâ€™s theorem; crossed polygons
ci:
li: http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome29/Michael%20DeVilliers%20%20I%20Have%20a%20Dream%20and%20Crossed%20Quadrilaterals.doc
ab: From the text: Though there appears to be fairly widespread consensus among
the mathematics education community about the validity and value of a
Lakatosian perspective on mathematics, it is strange that very little
of this sentiment translates into specifically designed learning
experiences that show and engage students with the evolution and
modification of definitions and theorems over time. In most cases
textbooks and teachers typically introduce students to concepts with
ready-made, polished definitions, and no opportunity is created to show
either the process of defining or how definitions may change and become
more precise in light of new, challenging examples. However, rather
than confining crossed quadrilaterals to the proverbial mathematical
trashcan, utilizing their strange, non-intuitive properties can be a
positive step in incorporating some of the ideas of Lakatos into the
classroom.
rv: