Is it possible to scale a mesh in one direction, rather than to scale the whole selection around it’s center?

Hit . (period) to change the pivot point for scaling and rotating to the cursor. Then position your cursor for where you want the mesh to scale from. One way is to just left click. The other is to select one or more verts and hit Shift+S>“Cursor to selection”. Then constrain the scale to an axis by hitting X, Y, or Z after you’ve started scaling.