Big Ideas from Logic for Mathematics and Computing Education

Abstract

AbstractDespite logic and reasoning being considered central to mathematics and computing education, it plays a largely peripheral role in high school or undergraduate curricula. The language of propositional logic and formal deductions are taught in high school mathematics as well as undergraduate discrete mathematics courses. Opportunities for learning mathematical logic are few. In this paper, we address the question whether mathematical logic can meaningfully contribute to mathematics and computing education at the school level.Along the lines of Big Ideas of mathematics [4] we propose a set of “Big Ideas” of mathematical logic relevant to education: for instance, the notion of truth relative to a structure, construction of models for a set of sentences, consistency of procedures used for computation, comparison of algorithms, and so on. We discuss how they can significantly enrich mathematics and computing science curriculum and pedagogy, clearing up students’ common misconceptions, referring to some experiences with high school mathematics teachers and students.KeywordsHigh school mathematics curriculumMathematics educationAlgorithmsLogic