Teach More, Not Less Computability Theory in CS202X A Case for Teaching Multiple Representations of the Church-Turing Thesis

This paper posits that the Algorithms and Complexity (AL) knowledge area in the Computer Science Curricular 2013 report contains several "flaws" concerning the teaching of computability theory that should be corrected in the upcoming CS202X curricular report. These flaws undermine the understanding and appreciation of computability theory that computer science graduates are expected to have. Specifically, it is argued that two of these flaws contribute to a theoretical knowledge gap in a significant percentage of CS graduates and a third contributes to a missed pedagogical opportunity to increase a graduate's understanding and appreciation of computability and the Church-Turing thesis. Evidence for the impact of these flaws is based on an existing survey of Bachelor of Science in Computer Science (BSCS) programs and a new study presented in this paper of required computation theory courses in five-hundred BSCS programs. Proposed resolutions to these flaws are presented as simple curricular changes for CS202X and the introduction of a two-tiered course unit, which utilizes a multiple external representation pedagogy to teach multiple models of computability and the Church-Turing thesis. This unit is derived from experience with using this approach in a Computation Theory course.