The anatomy of the hand, in particular the cross tendon between the 3rd and 4th fingers, means that we need to give special attention to developing independence of fingers. This skill focuses on coordinating the lift and fall of fingers in specific and challenging patterns and can be developed by a whole range of technical exercises including scales, etudes and facility exercises (Schradieck, Sitt). It is most effective however to use the myriad of specific independence exercises by pedagogues such as Sevcik, Dounis, Varga, Gerle and Korguof.
The timing of the lift and drop is particularly important as pairs of fingers need to land together or one finger needs to land just as another lifts.
Often the exercises call for a finger to hover in the air, that is the momentum of the upswing will not give the energy for the fall back to the string. It is important to lift the finger high enough so when it taps down again it articulates the note clearly. It is also important to have the finger available to move at all times, that is not cramped while waiting in the air. See Height of Finger Lift
Many exercises hold the 1st finger down. The independence of the 1st finger tends to be neglected and if it becomes locked it will cause issues when crossing strings quickly or when moving from a low to high position at speed.
Invent your own independence exercises to supplement the existing ones. See Ch.12 Resources Bibliography for Qui van Woerdekom for excellent independence exercises including backward stretching of the 1st finger.
When practising these exercises it is important not to strain the hand. Practice silently at first to concentrate on the lift and fall of fingers.
Do not just start in 1st position on the G and D strings. Starting your practice in 4th or 5th position on the A and E string and working down is often easier, especially as the spaces between fingers are smaller and the strings are thinner. You can release the double contact of the index finger until you get down to 3rd position.
Practise in mixed rhythms as well once the exercises are fluid. Choose excerpts from upcoming repertoire and practise them concentrating on the independence of fingers.
Finger Action - Height of Finger Lift
Resources - Bibliography