Revisiting Ill-Definedness and the Consequences for ITSs Antonija MITROVIC and Amali WEERASINGHE Intelligent Computer Tutoring Group University of Canterbury, Private Bag 4800, Christchurch, New Zealand tanja.mitrovic@canterbury.ac.nz , amali.weerasinghe@pg.canterbury.ac.nz Abstract: ITSs for ill-defined domains have attracted a lot of attention recently, which is well-deserved, as such ITSs are hard to develop. The first step towards such ITSs is reaching a wide agreement about the terminology used in the area. In this paper, we discuss the two important dimensions of ill-definedness: the domain and the instructional task. By the domain we assume declarative domain knowledge, or the domain theory, while the instructional task is the task the student is learning, in terms of problem-solving skills. It is possible to have a well-defined domain and still have ill-defined instructional tasks in the same domain. We look deeper at the features of ill-defined tasks, which all contribute to their ill/well defined nature. The paper discusses model-tracing and constraint- based modeling, in terms of their suitability for ill-defined tasks and domains. We show that constraint-based modeling can be used in both well- and ill- defined domains, and illustrate our conclusion using several instructional tasks. Introduction Recently there has been a lot of attention on supporting learning in ill-defined domains (aka ill-structured domains), as evidenced by the three workshops held in 2006-8 [1-3]. This attention is welcome, as ITSs for such domains are rare, and usually much more demanding than the typical ITSs for well-defined domains. However, there has been little agreement about the terminology used and the underlying definitions between researchers working in this area, even among those who presented their work at the workshops. Most researchers equate ill-defined domains with ill-defined tasks [1-3]. In this paper, we argue that it is important to make the distinction between instructional domains and tasks. We start by discussing instructional domains and tasks as two important dimensions in the light of ITSs. Section 2 presents a deeper discussion of instructional tasks, focusing on various factors which influence the nature of the task. We then turn to student modeling approaches which are appropriate for various instructional situations, and then show how ITSs can deal with ill-definedness. 1. A deeper look at ill-definedness: the two dimensions An instructional domain is an area of study, such as mathematics or philosophy. In order to learn a particular instructional domain, the student needs to learn the relevant declarative knowledge (i.e. the domain theory), and in many domains also needs to