Ramons suggestion is good but I think you may want all screen activity in your terminal applications buffer.
# To get screen to add lines to xterm's scrollback buffer, uncomment the
# following termcapinfo line which tells xterm to use the normal screen buffer
# (which has scrollback), not the alternate screen buffer.
#
#termcapinfo xterm|xterms|xs|rxvt ti@:te@
4.6.4 Disabling switching to the alternate screen
Many terminals, including PuTTY, support an ‘alternate screen’. This is the same size as the ordinary terminal screen, but separate. Typically a screen-based program such as a text editor might switch the terminal to the alternate screen before starting up. Then at the end of the run, it switches back to the primary screen, and you see the screen contents just as they were before starting the editor.
Some people prefer this not to happen. If you want your editor to run in the same screen as the rest of your terminal activity, you can disable the alternate screen feature completely.