Classification, Discussion, Recursion:
Helping the Development of
Computer-Science Concepts


Dalit Levy
"Migvan" - Research and Development in Computer-Science Education
Department of Education in Science and Technology
Technion - Israel Institute of Technology, Haifa 32000 Israel
tel: 00972-49835686
fax: 00972-49833605


This workshop presents a classroom activity, aimed at encouraging the extensive use of cognitive skills, in order to construct and refine the concept of recursion. The agenda involves different types of individual, small group and whole-class activities. This paper briefly describes the nature of the activity and raises some questions concerning its potential applications.


Learning Environments, Constructivism, Classification, Computer Science Education, Recursion.

1 Introduction

Recursion is a powerful concept. It is deep, rich, and interdisciplinary, but at the same time abstract, vague and difficult to explain or define [2,3]. This workshop demonstrates a class of learning activities, planned to expose learners to a wide spectrum of aspects and ideas related to recursion. Visualization, associations with everyday life, and the variety of different samples might encourage motivation, aid conceptualization and give a sound basis for subsequent formal studies. In the workshop, participants will experience the learning activity and discuss its theoretical background and the scope of its application.

2 A classification activity

The constructivist belief is that "knowledge is necessarily a product of our own cognitive acts" and that "we construct our understandings through our experiences" [1]. A general educational goal that could follow such a belief is to create a learning environment that encourages the development of intuition, reflection, conceptions, and ideas. More specifically, the learning activity presented in the workshop is planned to encourage the use of classification, generalization and reflective discussions in order to construct and refine the concept of recursion (and, similarly, other abstract concepts). The activity begins by presenting the learners with different examples of recursive phenomena, taken from various sources: pictures, music, literature, newspapers, mathematics and programming. The learners are then asked to classify these instances according to some criteria of their own choosing. There is no "right" classification, and the participants are invited to work in groups and to offer several different criteria. These criteria are often found to be important constructs in the whole construction of the recursion concept, as are the general names the learners choose for the categories of itemes created.

After the initial classification, each group shares its way of categorizing with the rest of the class. The teacher encourages a comparative and reflective discussion and finally, summarizes and offers generalizations and formal terminology for the constructs already mentioned. During this discussion, the learners are often exposed to new conceptions and to different ideas offered by other groups. This, in turn, encourages the reconsideration of their previous perspective.

The workshop will begin with experiencing the group-phase of the learning activity. The participants will be presented with the initial set of instances (on a large sheet of paper) and will work in groups in order to classify these instances, choose a new name for each category they create, and add some new items to each category. In the second part of the workshop we will discuss the outcomes of the participants’ classifications, the "conceptual map" of recursion that such an activity could establish, and the constructivist nature of the learning activity.

3 Applications

The classification activity has been used mainly as part of courses in computer-science teaching methods for pre- and in-service teachers at the Technion Israel Institute of Technology. Some open questions are: What topics and what learning stages can most benefit from this activity? What pedagogical variants are possible and desirable? In the last part of the workshop we will discuss these questions together with presenting some preliminary findings of ongoing research on learning computer science concepts through classification activities.


  1. Conferey, J. (1990). What Constructivism Implies for Teaching. In Journal for Research in Mathematics Education, Monograph 4, Chapter 8, pp. 107-122.
  2. Leron U. (1988). What makes recursion hard. Proceedings of the Sixth International Congress on Mathematics Education (ICME6), Budapest, Hungary.
  3. Troy M.E. & Early G. (1992) Unraveling recursion, part I and II. The Computing Teacher, March-april 1992.