Integrated View at the MTCS Course Organization: The Case of Recursion - Guide to Teaching Computer Science: An Activity-Based Approach - page 218

At least three factors contribute to these difficulties: (1) the gap between the re-
cursive (simple) algorithm and the recursive (complex) execution process: In order
to understand recursion, one must distinguish between the program (or method) list-
ing and its recursive process (algorithm execution) and further, these two instances
require different kinds of understanding, based on different cognitive models and
abilities, (2) learners' faulty mental models of the recursive execution process, and
(3) pedagogy of teaching recursion. Learners' difficulties of learning recursion are
elaborated in Sect. 12.5.
According to Leron ( 1988 ), in the first stages of teaching recursion, it is prefer-
able to concentrate on the relations between the algorithm and its product or output
(the result of the algorithm execution), rather than on the relations between the
algorithm and the process it invokes. This pedagogical suggestion is based on the
recognition that learners should understand first how recursive phenomena can be
described recursively and only then, to cope with the complex recursive execution
process. Harvey ( 1997 ) and Harvey and Wright ( 1999 ) call this teaching approach
a leap of faith .
In general, a leap of faith refers to one's belief in the existence of a phenomenon
that cannot be touched or proved and for which no evidence exists. In our case,
the leap of faith method is associated with the assumption that an algorithm one
writes works properly. It implies that the leap of faith method guides pupils to write
recursive descriptions even if they do not fully understand (yet) why and how this
“magic” works. It is recommended to start implementing this approach with respect
to recursive shapes (e.g., fractals or trees) or other recursive phenomena; then, once
pupils are able to write recursive descriptions for these instances, they can use this
approach for writing recursive functions as well (again, prior to their fully under-
standing of the function execution process).
Teaching the leap of faith method to learners is not a trivial matter and requires
some practice. Activity 92 aims at preparing the prospective computer science
teachers mastering this approach (Lapidot et al. 2000 ).
Activity 92: Mastering the Leap of Faith Approach
• Stage A: Toward the leap of faith approach, team work
• The students in the MTCS course are given the worksheet presented in
Table 12.2 to work on.
Table 12.2 Leap of faith worksheet
Worksheet: toward the leap of faith approach
In this worksheet, you are asked to work on four short tasks and then to design similar
tasks.
Worksheet, part A: Tasks