Click the box that's circled, everything in that box changes what selections rotate and scale around.  So, for instance, if you're in edit mode and have some points selected, then hit 's' they'll expand and contract around the center of the object they belong to, the center of the selected points, the 3d cursor, etc.  Different selections are useful at different times, and not all of them are good for edit mode and not all are good for object mode.  I can explain more about them, but I often find it easiest to just put the cursor where I want to rotate and scale around and just use that.  To do that, select the option that says "3d cursor" as in the next image