There have been a few posts on the GIS Education Community blog that we think you'll find interesting. 

In the most recent post George Dailey, ESRI Education Manager, talks about mapping recycling sites with ArcGIS Explorer, and uses a list of recycling locations obtained from the City of Dallas Sanitation Services along with additional data downloaded from the University of Texas - Dallas. George uses ArcGIS Explorer's file import capabilities, the ability to read shapefiles directly, and geocoding and routing tasks to complete his project.

A second post by George highlights field trip planning using ArcGIS Explorer and uses its multi-stop routing capabilities to find the best way to get to the field trip destinations. George uses the Send To capabilities to use the geocoded museum and school location results as inputs to the Find Route task so solve the problem.

In another post covering GIS in education in Taiwan, ESRI Education Manager Joseph Kerski explores the country and imports his GPS track of his wanderings into Explorer, showing the vertical relief of the area and incorporating photos in popup windows.