Abstract: Techniques are described for problem selection algorithms for providing a multi-layered cognitive tutor. A repository of problems is maintained, which associates the problems with the improvement of corresponding skills according to a cognitive model. User skill levels are maintained in a user profile. Problem sets are then presented to the user in phases, where each phase may utilize different selection criteria for selecting from the repository. By varying the selection criteria between phases, for example from problems testing familiar skills to problems testing new skills, or from problems teaching few skills to problems teaching many skills, problems can be selected to address the unique requirements of each tutoring phase, from beginning to middle to end.

Abstract: A method of facilitating the entry of a mathematical expression into a workspace provided by a software application is described. The method includes receiving a plurality of characters input into the workspace by a user and, preferably, determining whether the characters represent a mathematical expression having at least a predetermined level of complexity. If the characters represent a mathematical expression having at least a predetermined level of complexity, the method further includes converting the characters to a corresponding mathematical representation and creating an image of the mathematical representation and displaying the image to the user, preferably at a location adjacent to the workspace and optionally replacing the character's input into the workspace with the image of mathematical representation.

Abstract: Method and apparatus are provided for use in a frame-based semantic network wherein at least one specialization slot-control frame defining a specialized behavior is linked to a base slot-control frame defining a global behavior in a hierarchical data structure. Slot behavior is attached to an occurrence of the slot in any other frame such that the slot and its behaviors are inherited to related frames as a unit. All specialized behaviors are compiled into a compact internal format and stored in a reserved space in the slot-control frame. The method and apparatus have particular utility in knowledge-based or expert systems.