Commonsense computing (episode 6): logic is harder than pie

Since logical statements naturally occur in programming and other computing work, educators may hope that all beginning computing students can employ basic logical thinking even if they are not familiar with the formalized mathematical notation. However, Herman and others found that even after being taught logic, students can still fail to correctly apply the logic of NAND and if-and-only-if. This paper reports on an experiment based on Herman's study of IFF and NAND using their "Apple pie recipe." We asked introductory students (before formal logic training) to indicate which of a set of pre-defined pies are "valid" based on the rules of the recipe. We found through online surveys, and confirmed through revised in-class surveys and interviews, that beginning students struggle to correctly interpret if-and-only-if, as reported by Herman. Additionally we confirmed that students are most likely to interpret if-and-only-if as if-then and provide new evidence that students can correctly interpret an English rewording of the form "either use both or use neither". However, in contrast to Herman's findings, we find that 90% of introductory students have a correct understanding of NAND.