Operationalizing the Continuum between Well-Defined and Ill-Defined Problems for Educational Technology

One of the most effective ways to learn is through problem solving. Recently, researchers have started to develop educational systems which are intended to support solving ill-defined problems. Most researchers agree that there is no sharp distinction but rather a continuum between well-definedness and ill-definedness. However, positioning a problem within this continuum is not always easy, which may lead to difficulties in choosing an appropriate educational technology approach. We propose a classification of the degree of ill-definedness of educational problems based on the existence of solution strategies, the implementation variability for each solution strategy, and the verifiability of solutions. The classification divides educational problems into five classes: 1) one single solution, 2) one solution strategy with different implementation variants, 3) a known number of typical solution strategies, 4) a great variety of solution strategies beyond the anticipation of a teacher where solution correctness can be verified automatically, and 5) problems whose solution correctness cannot be verified automatically. The benefits of this problem classification are twofold. First, it helps researchers choose or develop an appropriate modeling technique for educational systems. Second, it offers the learning technology community a communication means to talk about sorts of more or less ill-defined educational problems more precisely.