My advise to you is not to 'try to play fast'.
My advise also suggests that you not instructing your students to 'try to play fast'.
Speed comes with absolute certainty with what you are playing. When we know repertoire, it becomes difficult to play slowly, because we are in fact holding ourselves back to do so. If you understand this fact, you will never 'try' to play fast. Instead, you will instead practise slowly, with the knowledge that when you understand it, you will begin to play it faster.
Poor technique and muscle tension comes from pushing your fingers, wrists, forearms, shoulders and back-muscles, beyond what it can adequately manage. This is usually because, a missing neural connection to the desired motor-skill action, is mistaken for a deficit in muscle mass. A student ploughs through, at high speeds, missing notes and detail in an attempt to ... get it fast.
I know with absolute certainty, that I can play four semi-quavers at 150 bmp. that does not mean that every piece is approached trying to push my body to this limit. Instead, when learning material, I play slow, knowing that when I fully understand it, I will gradually, and naturally play it faster with time. Speed takes care of it self, if you let it.
I have to prove this point to many arrogant young pianists who believe that 'fast' is better. Okay, its fast, but: Was it even? Did you crescendo? Were all the notes crisply staccato?
I spend a large amount of my lessons on scales. From the beginning, students perform scales counting the time between notes. In moments, they will always increase the speed. Suddenly, my slow speed seems too slow; reason is they now understand. At this point, I increase the tempo marginally, but still insist they count, what starts to happen is they learn to measure the evenness of time. The problem, and it is a big one. The more bold, arrogant, and sometimes contemptuous of student, will disregard this vital lessons, and insist they play at speed.
May I point out, these students are the ones who make little to no progress for years; usually asking "Why does mine not sound like that?", that being a good rendition.
In most cases, with the students who take time to listen and understand, I play chords, while they play diatonic scales, before long, they have stopped thinking about what scale they are playing, and they are making music. When I get louder, they listen and match my dynamic, when I get quieter they listen and match my dynamic. I say staccato, they play crisp even staccato. Sometimes, they play the chords to my scales.
When they need this for music, they already have this skill in their toolkit.
Part of the problem with playing fast is, it does not happen because we simply will it so. If you want your students to play fast, and you are their first teacher, you start by building and preparing this and them, from the very first lesson with the tools allowing them to reach that point.
The fickle part about music is, we (as teacher, or student) are always planning for where we want to be, or want our student to progress to, in one or two years from now.
Play slow today, for a faster tomorrow.
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PS: I can also endorse, amandack's teachers method. I was told this is called 'swinging' or 'reverse-swinging'.