The role of phenomenographic research in the design of instructional computer applications for number concepts

Four principles of design and one overarching subject matter related principle were the guidelines for a project aimed at developing instructional computer applications based on phenomenographic research in the area of young children’s basic number concepts. The overarching domain specific principle was to promote structuring conceptions of numbers over counting conceptions. The four design principles were that the computer would be used to present crucial problems, to introduce variation in some important dimension, to present analogies serving as bridges between the familiar and the unknown, and to confront the children with the consequences of their conceptions, in situations where a less functional conception would be revealed by the computer as yielding an incongruous representation of the world. A number of educational games were developed in an iterative process of moving back and forth between software design and research aimed at exploring children’s conceptions of numbers in connection with use of the developed software. This paper presents a reflective analysis of the design, the history of development and the documented use in classroom based research of some of our games, focusing on how principles turn out when applied in practice. INTRODUCTION: THE APPLICATION OF PHENOMENOGRAPHY A thorough understanding of the potential variation in the learners’ understanding of a certain topic of instruction is invaluable in the design of interactive teaching/ /learning media. This means that for purposes of instructional design there is a demand for qualitative research on student learning. This symposium is devoted to a gathering and mobilisation of the experiences of researchers and instructional developers using a phenomenographic methodology for the “student learning” component of their diverse undertakings. Our specific contribution in this paper is a reflective (and retrospective) analysis of how a phenomenographic description of children’s ways of understanding numbers and simple arithmetic were translated with the guidance of four pedagogic design principles, compatible with the general methodology of phenomenography, into a set of educational computer games aimed at promoting a s t r u c t u r i n g conception of numbers over a c o u n t i n g conception — an example of instructional design based on ideas of what the learners need to learn (Laurillard, 1993). There are a number of questions: What kind of contribution can we see from a phenomenographic mapping, or outcome space, towards a specification of what students are to do with the computer? What is the relation between the phenomenographic description and the pedagogic principles? How are principles put into practice, i.e. how does the computer medium constrain their implementation and how does the actually produced software in its turn constrain the teaching/ /learning process? In the project we are referring to there was — as a third kind of principle, guiding the design process itself — an iterative process of moving back and forth between software design and research aimed at exploring children’s conceptions of numbers in connection with use of the developed software. Thus we have had the opportunity to make a reflective analysis of the design, the history of development and the