Triangle and parallelogram area formulas: a critique of teacher education textbooks in Norway - Briseid, Eyvind; Forssell, Henrik; Smestad, Bjørn (NOMAD Nordic Studies in Mathematics Education, 2025)
We survey Norwegian textbooks for preservice teachers, looking for attention to generality in their presentations of diagrammatic proofs for the area formulas for triangles and parallelograms. We find that most textbooks do little to bring issues concerning generality to the attention of the reader in the presented arguments, neither explicitly nor implicitly. We also find that the textbooks fail, as a rule, to present correct proofs of the area formulas for parallelograms and triangles, even given a liberal view of what constitutes a proof. The presented proofs are incorrect in that they are insufficiently general; they fail to cover crucial cases. This is unfortunate, as preservice teachers should be made aware of issues concerning generality in diagrammatic proofs.