The paper describes the design and implementation of an intelligent tutoring system for the Dijkstra-Gries programming methodology as defined by Gries (1981) in "The Science of Programming". The first part of the paper identifies the requirements of intelligent tutoring systems in general and those of the methodology in particular. It shows the suitability of the Smalltalk environment for developing expandable intelligent systems and the compatibility of Smalltalk's object-oriented paradigm with the Gries methodology's goal/plan approach to programming. We then describe how these requirements are met: an overview of the system's support of the methodology and the modules that enable the system to respond intelligently. As an example, a reusable tutorial part is presented, first from a student's perspective, then from an author's perspective. Finally the results of an evaluation of the system drawn from actual student experience are presented.>