Traditional grip is the
technique used by early
drummers to play a
snare drum, back during the
American Civil War for
example. In those days, the
drum was connected to a single
strap going over the
shoulder, and the
drum was
tilted a few
degrees clockwise (from the drummer's point of view).
To utilize traditional grip, first grip the right hand drumstick with your palm about 2-3 inches from the back end of the stick. Keep all four fingers on the bottom of the stick, and your thumb on the inside. You should be able to use a mix of wrist and finger action to strike downward.
Now, for the left hand. First, hold up your hand with your palm facing yourself, like you're waving at yourself. Position the stick horizontally and put it between your thumb and hand, flat against the rest of your hand. Place your pinky and ring finger under the stick. Your ring finger should meet the stick right at the base of the fingernail. Curl your pointer finger around to meet the thumb, to make a circular shape between them. You should now be flipping a bird away from yourself. Bring the middle finger down to meet the stick.
Tricky, eh? The left hand is played with wrist motion complimented by some force of the fingers. You should now be able to bring both sticks together out from the center of your body.
This type of technique is utilized today by the marching snare drummers of many drum cores and drumlines, although the matched grip is also used for that purpose.