We survey the literature about the teaching and learning of recursive programming. After a short history of the advent of recursion in programming languages and its adoption by programmers, we present curricular approaches to recursion, including a review of textbooks and some programming methodology, as well as the functional and imperative paradigms and the distinction between control flow vs. data flow. We follow the researchers in stating the problem with base cases, noting the similarity with induction in mathematics, making concrete analogies for recursion, using games, visualizations, animations, multimedia environments, intelligent tutoring systems and visual programming. We cover the usage in schools of the Logo programming language and the associated theoretical didactics, including a brief overview of the constructivist and constructionist theories of learning; we also sketch the learners' mental models which have been identified so far, and non-classical remedial strategies, such as kinesthesis and syntonicity. We append an extensive and carefully collated bibliography, which we hope will facilitate new research.
When first introduced to the analysis of algorithms, students are taught how to assess the best and worst cases, whereas the mean and amortized costs are considered advanced topics, usually saved for graduates. When presenting the latter, aggregate analysis is explained first because it is the most intuitive kind of amortized analysis, often involving enumerative combinatorics. We show how the aggregate analysis of functional queues can be carried out accurately and graphically, without combinatorics nor analytical tools like asymptotics, hence making it amenable to undergraduates. Our presentation is independent of any programming language.