One of the most important states of mind that we can help instill in our students is confidence. When a child or adult begins piano or other music lessons, they are often filled with excitement and anticipation, but too frequently also, fear. Fear of making mistakes, fear of looking bad, fear of feeling inadequate, fear of being perceived as having no talent... The worst thing we can do as teachers is to confirm or worsen those fears. We should help to alleviate those fears, to mitigate them, and ultimately to develop and restore confidence.
As a piano teacher, one way I strive to instill confidence at the piano is by introducing songs that encourage big, free movements of the hands and arms while playing at the keyboard, early on. Too many methods start students out with narrow, cramped finger positions, where the student's fingers seem glued to the keys, and students learn to feel afraid to move out of position or else lose their place. This results not only in timid playing but also introduces tension and teaches bad habits such as finger wiggling and crawling.
The best methods, including my own (Presto! It's Piano Magic), introduce students to songs that encourage freedom of movement, graceful swinging motions led by the wrist, hand movements flowing from the shoulders and arms, and allow students to play up and down the piano keyboard, getting comfortable and confident right from the start. It's fun, and young students feel really big doing it! Students avoid developing bad habits that will have to be corrected later, and learn tension-free playing technique. And, so importantly, we begin to cultivate confidence, poise, and self-assurance in our students' practicing and playing. No fear! :)