DecSys: An Intelligent Tutoring System for Decimal Numeration

This technical report describes the design and construction of a teaching model in an adaptive tutoring system designed to supplement normal instruction and aimed at improving students' conceptions of decimal numbers. Distinctive features of teaching task are: (i) the domain abounds with misconceptions;and (ii) the aim is conceptual change rather than the acquisition of new facts or arithmetic procedures. The teaching model exploits cognitive conflict and incorporates a model of student misconceptions and task performance, represented by a Bayesian network. The system allows students to work through a diagnostic test and four computer games, which are designed to develop conceptual understanding of decimals. Preliminary evaluation of the implemented system shows that the misconception diagnosis and performance prediction performed by the BN reasoning engine supports the item sequencing and help presentation strategies required for teaching based on cognitive conflict. Field trials indicate the system provokes good long term learning in students who would otherwise be likely to retain misconceptions. Appendices to this technical report include detailed descriptions of: (A) the known ways of decimal thinking upon which the tutoring system is based;(B) detailed descriptions of the computer games with example screens;(C) a full description of the types of items presented to students by the system, which correspond to the observation nodes in the Bayesian network;and (D) a list of the hypothesis nodes used in the network.