Abstract: A computer stores a scheduled subset of learning activities. Each learning activity has a duration estimate. The system receives status data indicating a progress of a current learning activity of the scheduled subset. If the status data does not indicate completion of the current learning activity, and the scheduled subset has a sum of duration estimates that exceeds a remaining available teaching time, then the system automatically selects a replacement subset of the learning activities. The replacement subset has a sum of duration estimates that does not exceed the remaining available teaching time. The replacement subset of learning activities is automatically selected by the system based, at least in part, on at least one of: academic standards associated with each of the learning activities; and an importance score associated with each of the learning activities. The system establishes the replacement subset to schedule in place of the scheduled subset.

Abstract: Techniques for teaching geometric proof problems are described. According to one approach, the geometric proof application displays a geometric proof problem and a set of connectable nodes in an initial arrangement. A user then rearranges the set of connectable nodes and connects them using one-way connections to generate a solution. The geometric proof problem is solved if the user-generated solution indicates the correct logical ordering of the set of connectable nodes as determined by the geometric proof application.