Through my students, I learn that there are many types of Mindful practice that could help them.
1) Breathing before an important performance slows down heart rates, doing it while walking towards the piano helps focusing on body and mind as opposed to others and noise in the room. Once the student sits, he or she can mindfully (still following breathing) put hands in position, check on body position, (sitting too far, too close, too much to the left or right...) and listen to the silence and inner pulse or sounds before producing the REAL sound, which will seem miraculous because there was intense listening to silence right before!
2) Being mindful of our own speed, means to simply hear/feel a pulse AS IT IS! Easier said than done, as youngsters tend to speed up and often count at a certain speed before playing, and then pick up another speed when they actually play! If OUTSIDE of sitting with their instrument, students express that speed through walking, moving to a slower pulse, and subdividing with mouth sounds, or hand/head gestures, then they'll absorb that speed more. Experiential learning, body absorbing concept rather than intellectual counting. Many transfer students come to me counting perfectly, with the 1 matching what notes fall there, and the "and" matching which notes fall there, and so on. But this does not necessarily mean the rhythm was correct!
3) Being mindful of how children are impressionable: Sometimes we grossly exaggerate what happened in our mind when we made a mistake. Focusing on WHAT REALLY happened helps students stay with REALITY. Recording themselves is the first step. But some will still be bias while listening to themselves on the phone IF they do not let a lapse of time pass before they do the listening. I often ask students, right after they play the whole piece: So, tell me what you did well, and what needs work? forcing them to reflect, rewind, re-evaluate, and gain critical thinking. Mindful of how a mistake can be translated into a "do or die" attitude, I often do improvisation with them to show that mistakes can be corrected to something else, and that in improvisation or creation, there can be NO mistake! That is the attitude I wish for parents of my students.