Teaching strategies for reinforcing structural recursion with lists

Abstract

Recursion is an important concept in computer science and one that possesses beauty and simplicity, yet many educators describe challenges in teaching the topic. Kim Bruce champions the early use of structural recursion in an objectoriented introductory programming course as a more intuitive concept than traditional (functional) recursion. He uses many graphical examples for motivation (e.g., nested boxes, a ringed bullseye, fractals), providing concreteness to the recursive concept. Internally, most of those examples are disguised forms of a basic recursive list pattern. Recursive lists are important in and of themselves and a mainstay within the functional programming paradigm. However, further challenges exist in providing a tangible presentation for pure lists when disassociated from a graphical structure.We describe an active-learning exercise in which students play the roles of distinct objects that together comprise the structure of a single, recursive list. This activity establishes intuition that we later use when developing a complete implementation of a recursive list class. Our approach demonstrates a rich set of recursive patterns involving several distinct forms of a base case and varied use of parameters and return values.

A Survey on Teaching and Learning Recursive Programming

“…To overcome students' reluctance to use recursion within a course on procedural or object-oriented programming, it has been proposed to teach singly-linked lists before arrays and loops (Turbak et al, 1999, Bruce et al, 2005, Goldwasser and Letscher, 2007, which makes recursion appear as a rather natural way to move to and fro inside a unidirectional data structure. It is not surprising that this proposal, where recursion in data types comes before recursion in functions, often originates from the context of object-oriented programming languages (Felleisen and Friedman, 1997, Levine, 2000, Bloch, 2003, Sher, 2004, but is also prominent in statically typed functional languages -refer to the book by Felleisen et al (2001).…”

An unusual CS 1 with high standards and confirming results

“…One such element is recursion. Several papers have discussed the importance-and often, the difficulty-of teaching this "effectively", e.g., [4,2,7]. Since we do not introduce loops in the first part of the course, using recursion quickly becomes natural to our students.…”

A graphics package for the first day and beyond

“…They provide examples such as a ringed target or a fractal-based broccoli rendered using their objectdraw graphics package. While structural recursion can be demonstrated with non-graphical examples [5], the graphical examples carry great intuition.…”