In high school geometry courses, students are often given a prepackaged statement that they are asked to prove. In these situations, the process of writing proofs is being abridged, if not misrepresented. To provide her students with a more authentic experience in writing a proof, the author provided them with a summative project for which they…

During the last decades of the twentieth century, changes in school curricula have resulted in proof-free or proof-lite curricula. In this article, the author argues that proof is, and should be seen to be, a central component in the school curriculum--from at least the middle of the primary years and upwards. He identifies proof with problem…

In set theory, one comes across the notion of "vacuous truth." A statement is vacuously true if it is true but does not quite say anything. The structure of a vacuously true statement is typically of the form: everything with property A also has property B, with the caveat being that there is nothing in property A. For instance one could say: all…