I'm a sound player. That's a euphemism for I struggle with speed.
But I've been working on it... for a lifetime really, but recently more intensively. Here are some strategies that have worked for me and that might work for you and your students, too:
The Elements of Facility
There are muscular, neurological, and psychological elements to the speed game. Here is a pyramid of the elements of speed. I say pyramid because they are independent variables but also interdependent.
1) How close is the next destination? If a finger is very far from it's next note (or God forbid facing in the opposite direction), you will have to move even faster to get to the next note. This is why set up is so key on most instruments. Double check how close you are.
2) How relaxed is your body and your arms? Tension is a handbrake. To know this is true, tense your arm in the air while not on your instrument and try to move your fingers really fast. Not possible. Next, relax the arm and trying moving fingers again. See?
3) How fast are you actually moving? Finger action, both up and down needs to be quick, even in slow practice. For most players, lifting fingers is more sluggish, so we need to train extra fast for lifting fingers.
Now, want to amp it up? Play in patterns and check all three of the above elements.
Download a page of "practicing in rhythms" I made a couple years ago. It's beyond dotted, it's all sorts of wacky stuff. See?
Need more ways to practice speed?
I have a playlist on my YouTube Channel that has 13 more ways to practice for facility. It's for violin, but most of these can work for other instruments, too:
