Traceable Recursion with Graphical Illustration for Novice Programmers

Recursion is a concept that can be used to describe the phenomena and natural occurrences in many different fields. As many applications utilize computer software to model recursion, recursion is a particularly important concept in the computing discipline. However, it is a difficult concept for many undergraduate students to master. A Recursion Graph (RGraph) is one visualization method for representing recursion. This paper extends our previous work on RGraphs to include a tool for automatically generating complete and partial RGraphs from an arbitrary recursive program. Use of this tool allows for more flexibility in demonstrations and more focused pedagogical interactions on the part of students, thereby improving student learning in recursion. In mathematics, recursion is a method of defining a mathematical function based on previously defined terms of the same function. It is an important concept in Computer Science as well as many other disciplines. McCracken (1987) stated that "Recursion is fundamental in Computer Science, whether understood as a mathematical concept, a programming technique, a way of expressing an algorithm, or a problem-solving approach." In computing, it appears frequently in the study of algorithms, data structures, and artificial intelligence. In other fields of study, recursion appears as population and predator/prey models in biology, formal structures in linguistics, filters in signal processing, and genomic sequencing in bioinformatics. Fractals are self-similar, recursive patterns found in nature and simulated through mathematics with applications in art, design, and engineering. Although recursion is an important concept, teaching recursion to introductory Computer Science students is a challenging task (AP Central.) This has