New beginnings

The Shem Mi'Shmuel explains that the Kedusha of Shabbos lingers the whole week and its influence carries us through the week until the next Shabbos comes. Therefore on the Shabbos before a new month we daven that Shabbos should spill over into the new month.
On the Shabbos before Rosh Hashana which is a new month and new year we certainly should daven [for the new month] on the Shabbos prior to it, yet we don't. The reason we don't is because Rosh Hashana is a new beginning as it says "Zeh HaYom Techilas Maasecha". Just like when Hashem created the world there was no Shabbos before it so too Rosh Hashana is a new beginning as if nothing took place previously. This teaches us that we have a chance to start new without any consideration of being locked into to our previous patterns.
http://www.revach.net/moadim/elultishrei/Elul-Shem-MiShmuel-Why-Is-Shabbos-Before-Rosh-Hashana-Not-Shabbos-Mivarchim/997