I have been asked by a few people about my view the importance of piano fingering when playing a song. There are two thoughts on this, and mine is probably somewhere in the middle. One extreme is of the strict and ridged approach where no varience is allowed, only the prescribed fingering is allowed, and to ensure the student gets it, the teacher may even cover the keyboard so the student cannot see the keys and must rely on the fingering to get through the piece. On the other hand there is the ideology that fingering is of little or no importance, and that as a student becomes more proficient and the music demands more agility, they will figure out a fingering style of their own. Let the kids have fun on their own terms as they explore the keyboard, formal fingering instruction can come later.
Both of these approaches have merit, and I find myself somewhere in the middle. On the one hand, using consistent fingering builds muscle memory which is critical if one desires to master their instrument. But if we are too strict, it can hamper creativity, and create a dependency on the written notes that can get in the way of improvisation. Here's how I try to strike the balance for my students.
Learn the correct fingering for the scales.
Don't fudge on the scales. Each scale has a standard fingering that was carefully and wisely chosen for the shape of the hand, the contour of the keys, and how the two work together. By learning and practicing the scales, and arpeggios too for that matter, every finger gets a workout. The muscle memory gained will help the student when they are sight-reading since there will be scale patterns that will pop-up in the music and they will be able to instinctively use the most logical fingering. Muscle memory will aid in improvisation as well because the musician will be able to focus their attention on what they are feeling, what their inner ear wants the fingers to play, rather on HOW the fingers will be able accomplish the task. One who has mastered the scales will have more freedom to explore the piano domain on their own terms than a student who has not put forth the time and effort to gain this intuition skill.
View written fingering as a suggestion.
When a piano piece has written fingering, someone has gone through the trouble of devising what they think to be the best fingering for that passage. Don't discount their suggestion! However, every hand is different. There are big hands and tiny hands that play on the piano, and this will effect what is most practical for the student. I remember as a child with tiny hands, my teacher would help me come up with the best fingering for ME, and then I would be sent home with the charge to learn that fingering and be consistent with it. Sometimes we would eliminate notes from certain chords because I was incapable of playing all of the notes with my tiny hands. Consider too WHO wrote the fingering. Some piano publishers hire amateurs to add finger numbers to their music to make it look more official. Other times, a true master has crafted the numbers. Was the fingering designed for children or adults? Is your student a child or an adult? Every hand is different, every song is different, but suggested fingering is, as a general rule, a good suggestion. Consider using it!
No suggested fingering? Try to use all of the fingers in a practical way.
For beginners, we really want to avoid only using two or three fingers to play an entire piece. However, there is a time and place for plunking out notes too. If it is their first time at a keyboard, there are so many things for them to learn and master. There's the idea that there are sets of two and three black notes. There's mapping out where "C" is, and how that relates to where "G" is. And if they are transposing a song from C to F major, there's the realization that a certain B-flat changes everything. I think there is little harm in plunking out the notes initially, so long as they do not plunk out the notes enough to gain bad habits through poor muscle memory. Striking a balance between free exploration in the area and being methodical is something that will vary piece by piece, student by student, and family by family.
My advice is to watch the child and try to guess at which wheels are turning in their heads as they are plunking on the keys. Are they just figuring out how the piano works? Are they concentrating on where "A" is? These things need to happen too, and too much information too soon can cause overload. Let them plunk it out. Sacrifice a few songs to bad muscle memory in order to allow them to know where everything is on the keyboard. On the other hand, if they are just being lazy, it's okay to step in and say, "Try it with this fingering. It will help you gain fluency as you practice more."
Encourage free-style playing.
Students should learn their scales, and they should be aware of finger numbers and how it works. Time should be devoted to learning this art. BUT there also is a time and place for allowing them to explore the keys on their own terms. I discourage the practice of not allowing students to look at the keys while they play, at least in the beginning. Masters such as Beethoven and Mozart learned composition right from the start, their training in keyboard harmony paralleled their formal piano training that more closely resembled piano instruction today. There are so many aspects of music to learn- feeling the rhythm and beat, note reading, theory, dynamics, and so much more. Fingering is important, but it's only one piece of the bigger picture. I know many people who had rigid sight-reading based piano training, and they regret not having the freedom to branch off on their own. They sight-read very well, but cannot play by ear. This skill comes from keyboard PLAY, unfettered, untouched by the listening parent. Such play should be encouraged, and piano teachers can help their students with this practice during lesson time too. I want my children to have the courage to improvise, and the knowledge in keyboard harmony to do it well. Having a mastery of the scales will help them, but so will encouraging free-play.
Closing thoughts and further reading
I hope this post has given you a few ideas on where to start and how to strike that important balance for your own children and students. I know there are are musicians on both sides of the spectrum who may disagree with me, and if you are one of these people, I encourage you to share your thoughts in the comments. I know there are things to consider that I haven't addressed. This is just my perspective in a nutshell. Here are a few links on the subject that may be useful.