\input zb-basic \input zb-matheduc \iteman{ZMATH 2016b.00267} \itemau{De Villiers, Michael} \itemti{Crossed quadrilaterals: a missed Lakatosian opportunity?} \itemso{Philos. Math. Educ. J. 29, 6 p., electronic only (2015).} \itemab 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. \itemrv{~} \itemcc{D20 E20 E40 G40 G90} \itemut{foundations of mathematics; defining; concepts; definitions; mathematics and philosophy; Lakatos; geometry; triangles; crossed quadrilaterals; angle sums; dynamic geometry; counter-examples; directed angles; Varignon's theorem; Pascal's theorem; crossed polygons} \itemli{http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome29/Michael%20DeVilliers%20%20I%20Have%20a%20Dream%20and%20Crossed%20Quadrilaterals.doc} \end