The push-up is a moving plank. Doing a push up from your knees is not the same motion. Remember always to feel your core and glutes engage, just as performing a static plank hold thus eliminating any low back sag.
Follow these tips to either perfect your current push up or use these tips to progress your currently weak push-up.
Form and body positioning.
Start with your hands placed directly below your shoulders with your fingers pointed slightly outward. This will help position your elbows inward, at an approximate 20 to 40 degree angle. Do not let your elbows flare outward creating unnecessary joint stress.
Make sure you are now in position with proper form and slowly lower yourself to the floor. While keeping a strict plank position touch your chest to the floor and then push yourself back up to a fully locked out plank position. If you are unable to fully touch the floor then go as low as you can while maintaining proper form and return to the starting position.
Do not do push-ups from your knees! This will not help you progress to a strict push-up.
Instead elevate a bench, rings, or other device to help you progress.
Place your hands on a bench or box and repeat the steps above while practicing perfect pushup form. Slowly decrease the elevated device until you are performing pushups from the ground level.
Another alternative to knee pushups is to perform them in a reverse fashion. Start from the ground, then once contracting into a plank position (no low back sag!) begin pressing up from the ground to a regular pushup starting position. This can be performed from the starting push-up position as well by lowering to the ground from the starting position and not performing the push back up.
Your push-up form is directly related to many of the other movements you perform in the gym. It is important to focus and be strict with yourself while performing this and any other lift or movement.