Dennis Lee is mostly right, but let me add a few things.
1) You say the only real difference with your approach is lessons everyday. How much practise would you expect from a student after each half-hour lesson? You obviously want them to come to the next lesson having improved in some way, how much inter-lesson improvement are you looking out for?
In the beginning I expect no practice at all: The student will be practising at the lesson. Lesson and practice will mingle seamlessly. Of course, if the student gets home and goes through the material he worked on the lesson wonderful. If not, it does not really make a difference, since we will be doing it again the next day. In fact in the first three months the student will be learning how to practise more than anything else. I actually prefer that they do not practise during these first three months, since typically they will be practising the wrong way. So typically there will be interlesson improvement as such, but there will be improvement along the week/month. Once the practice habit has been established and the correct way of practice has been ingrained then the student can become more independent and we move to three lessons a week (usually after 3 – 6 months). Then two lessons a week and finally one 1hr lesson a week. The most dramatic progress occurs in the first six months (with daily lessons). Then progress slows down with some of the students when they move on to once a week lessons. The reason is simple: they are not practising (or not practising correctly). So every summer holidays all students must endure an intensive 2 week daily one hour lessons to remember how nice it was when they practised everyday he he. (This why I attribute the progress to the frequency of lessons rather than teaching methods)
2) Anticipating that your answer is an hour's practise between each lesson, let's impose time and financial restraints. I can't practise on Wednesday and can only afford 3 lessons a week, say Monday, Tuesday and Friday. Do you think this would be a good compromise? Should I expect a linear interpolation of results, ie that at this rate and with a teacher as good as you (I don't believe, btw, that frequency of lessons is really the only thing setting you apart from other teachers ) it might take me 4 years to reach a level of grade 8?
I do not charge per lesson. I charge per month. Therefore the frequency of lessons has no consequence to affordability. Either you can afford my monthly fee, or you cannot. If you can you will get daily lessons. Everyone (contrary to what Dennis Lee thought) goes through an initial period of daily lessons. For adults (I do not do that with children because their attention span does not allow it) I have a special intensive course of daily one hour lessons. This means that they do their practice at the lesson. So busy adults with no time for practice can take this option (is more expensive though, but cheaper if you consider the total number of hours).
As for frequency of practice. The minimum is three 20 minute sessions a week. However in these twenty minutes you must concentrate in one single “problem”. I have discussed the 20 minute principle elsewhere. So you will not be able to do scales, three pieces, sight-reading, etc. in one session. You must have one 20 minute session for each task. The more 20 minute sessions you can cram in a day the faster you will progress because the more things you will be tackling simultaneously.
The three sessions per week works like that. Every day you practise something you get 5 points. Everyday you don’t practise you loose 3 points. It is that simple. Practising something twice in a day will not give you 10 points. You still have 5 points because you need one night sleep in between learnings. So it is more effective to learn something else in the second session in the day. Now if you do your accounts, you will see that if you practise something seven days a week you get 35 points (7x5). If you practise 6 days a week you get 27 points [6x5-3x1 = 27]. 5 days a week and you get [5x5-3x2=19]. 4 times a week and you get [4x5-3x3=11]. 3 times a week and you get [3x5-4x3 = 3]. 2 times a week and you get [2x5-3x5 = 0 (you cannot go negative)].
Now listen carefully for on this hinges the destiny of every pianist.
In order to learn any piece and be able to perform it flawlessly you need to accumulate a certain number of points. No one can tell you what this number of points is. But it depends on the person and on the piece. The only way to know it is to master the piece. Then you will know it. However for the sake of argument let us say that it will be necessary for you to accumulate 150 points to master a Chopin etude. If you practise it twice a week it will never happen (0 points per week). If you practise it three times a week (3 points), it will take you 50 weeks - almost one year – to master it. But if you practice it every day (35 points), in less than five weeks it will have been mastered. So there is a brutal difference between what you can accomplish practising everyday and practising 3 days per week. Practising everyday you will learn 12 times faster! What about that?
This of course assumes that you are practising correctly and with maximum efficiency.
Finally, what do you mean by grade 8? Taking the exam? Or playing pieces classified at that level? Taking the exam takes longer because there is much ancillary knowledge that must be digested. But if all you want is to play pieces of grade 8 (ABRSM), most of my adult students are doing that after 4 – 6 months. If you can find someone to break down the piece for you and instruct you in the best learning sequence, it is not difficult to learn any piece. It is a bit like building a house. Experienced builders follow a plan and a sequence of events. People who have never built a house make lots of expensive mistakes. In piano playing we make the most expensive mistake there is: we waste time. And time – as everyone discovers at the moment of death – is the only valuable commodity.
3) What percentage, if any, of your daily lessons do you feel are wasted because students, for whatever reason, come having not had a chance to practise?
My lessons are never wasted if a student does not practise because:
i. I get paid for it.
ii. I use the lesson time to learn about teaching.
iii. I use the lesson time to learn about the pieces the student has not practised.
iv. I use the lesson time to practise with the student (they know that if they don’t practise, we will spend the whole lesson practising, so they tend to come prepared, he he).
It is the student’s time that gets wasted (and their money). This of course is pointed out to them.
And as always, this is just the tip of the iceberg.
Best wishes,
Bernhard.