Integrated View at the MTCS Course Organization: The Case of Recursion - Guide to Teaching Computer Science: An Activity-Based Approach - page 220

the structure of a recursive description and practice the creation of recur-
sive descriptions. It is also important to emphasize the structure of a recur-
sive description (that is, naming the recursive phenomena, a base case, and
a recursive call). At this point, the meaning of the leap of faith approach
can be explained.
• If time permits, it is also recommended to start discussing with the stu-
dents the planning of teaching recursion. Though there are several relevant
topics with which the students are not familiar with yet (e.g., research
on recursion learning), a preliminary discussion, which emphasizes the
important role of nonprogramming activities in learning recursion (as the
ones presented above) can start at this point. The role of such activities
should be associated with the complexity involved in learning the concept
of recursion.
• Stage C: Summary (read a paper, write a program), homework
• The students are given the following tasks:
1. Read one of the following papers. Then, choose at least one aspect of
learning and teaching recursion that the paper addresses and that was
not discussed in the class and explain its importance:
− Leron U (1988) What makes recursion hard? Proceedings of the
6th International Congress on Mathematical Education (ICME6),
Budapest
− Levy D, Lapidot T (2000)Recursively speaking: analyzing students'
discourse of recursive phenomena. Proceedings of the 31st SIGCSE
technical symposium on computer science education, Austin, Texas,
pp 315-319
2. Write a Java program for the Fibonacci series by following the “leap of
faith” method. Explain the stages you followed (that is, how you used
the “leap of faith” approach while building your program).

12.4 Models of the Recursive Process

In this section, we focus on models of the recursive process. We assume that at this
stage learners got some experience with respect to the formulation of recursive
descriptions (Sect. 12.3) and therefore, they can proceed to the learning of the re-
cursive process (i.e., the execution of an algorithm).
Due to the complexity gap between the relatively simple recursive algorithm 4
and the complex recursive execution process, the recursive process is considered
to be one of the most difficult issues for understanding with respect to recursion.
All learners build mental models and use them as part of their learning processes.
In the case of recursion, research reveals that many learners hold a faulty model of

4 This simplicity refers to the fact that a recursive algorithm is usually short with only few instruc-
tions. This fact stands in contrast to the complex process invoked by a recursive algorithm.