
06539019
j
2016b.00267
De Villiers, Michael
Crossed quadrilaterals: a missed Lakatosian opportunity?
Philos. Math. Educ. J. 29, 6 p., electronic only (2015).
2015
Professor Paul Ernest, University of Exeter, Graduate School of Education, Exeter
EN
D20
E20
E40
G40
G90
foundations of mathematics
defining
concepts
definitions
mathematics and philosophy
Lakatos
geometry
triangles
crossed quadrilaterals
angle sums
dynamic geometry
counterexamples
directed angles
Varignon's theorem
Pascal's theorem
crossed polygons
http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome29/Michael%20DeVilliers%20%20I%20Have%20a%20Dream%20and%20Crossed%20Quadrilaterals.doc
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 readymade, 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, nonintuitive properties can be a positive step in incorporating some of the ideas of Lakatos into the classroom.