I have a point layer of students, and a polygon layer of district boundaries.
How can I select those students who are not in the district boundaries, a Select By "Not-in" Location, so to speak.
Use Select By Location, have it select all students within the boundaries, then reverse the selection. Ta da, you have a "Not-In" selection!
To reverse the selection, use the "Switch Selection" command. This can be accessed from at least two different places in ArcMap.
Within the attribute table:
Or, from the Table of Contents, right mouse click on a layer menu:
An alternative to this method would be to select all features, use Select By Location, pick the "remove from the currently selected features in" selection method, and have it remove all features that intersect the source (boundaries) layer.
One way to do this would be to create a new field in your students featureclass, then select the features that ARE within your district boundaries and calculate the field you just created to whatever value you deem necessary... as an example the field could be named "IN_DIST" and the points that are within the district get a value of "Y". Then you can use select by attribute to get records where "IN_DIST" does not equal "Y".