Modelling a Versatile Mathematical Curriculum for Low- Attainers
Katerina Georgouli · 2002
Abstract. In the field of Intelligent Tutoring Systems (ITS) the organization of the knowledge to be taught (curriculum) plays an important role. Different educational theories are used to organize the information, producing as many curriculum models as many ITSs exist. Most of these models are strict, leading to a teaching strategy unable to adapt itself to the student’s learning strengths. In this paper first, we describe the design of a versatile curriculum model for teaching mathematics to low-attaining students, who need individualized teaching. Next, we report on the development of an adaptive to the student’s strengths assessment system. In this report, we focus on the curriculum aspect and on the authoring environment, which has been developed to support curriculum editing. Finally, the evaluation of the assessment system, concerning the effectiveness of the curriculum modeling and the usability of its authoring environment, is presented. 1 Introduction One of the first steps of intelligent tutoring systems (ITS) design involves performing a cognitive task analysis of the curriculum to be taught and to decide about the curriculum model to be used. There are almost as many curriculum models as there are ITSs, and each one uses a different instructional theory [11] for the knowledge representation. In any curriculum model there are some aspects that are very important and constitute its quality. The quality of a curriculum can be described as: the conformity to the developer’s initial intentions. These intentions can be classified on three axes [5], which are teaching goals, the respect of a pedagogical model and the data structure recognized by the ITS. The data structure is the syntactic aspect of a curriculum, which concerns strictly the internal and external representation of the data. The pedagogical model is the semantic aspect of the curriculum. In this level constrains on data elements, and on their relations are defined. The teaching goals form the pragmatic aspect of a curriculum, concerning the material to be taught. The curriculum model we present in this paper has the following three axes of intentions: • Data structure: the curriculum model proposed in ASSA [6] (see next section). • Pedagogical model: the model proposed by Haylock [7], based on the objectives-and-assessment approach. • Teaching goals: elementary arithmetic problem solving