Also, for Bernhard how do you help an adult beginner see rapid progress with your teaching program? The claims you make for being able to play Grade 6 (ABRSM) pieces in 6 months are absolutely amazing. Do you only see this kind of progress with your younger students or do adult students who are absolute beginners (not piano drop-outs!)
First we have lessons everyday. This is the single most important factor leading to quick progress.
Second I always start from a piece. Everything else – technique, scales, theory, etc. is related to the piece. I see no reason why an adult student should not start his/her piano students by tackling Chopin’s prelude no. 7 you mentioned, straightaway from the start.
Absolute beginners actually tend to progress quicker than piano drop-outs, since they come with less baggage and are more willing to try things on faith. Piano dropouts may come with all sorts of superstitions that may take quite a while to get rid of.
My question is: What is the most effective way to practice scales, chords and arps? Right now I am practicing them in a sort of circle of fifths progression starting with just the white key scales, then adding the black key scales. Is this a good way to learn them? I also practice major, minor, augmented , dimished triads followed by major 7, 7th, dim7 and aug7 chords (and their corresponding inversions) with each tonic key of the scale(s) that I am currently practicing.
The most effective way to practise anything is the way that will get you to your aim in the least amount of time with the least amount of effort.
Therefore it is a personal thing. First you must decide what is your aim in working at scales, chords and arpeggios, that is, what will you consider as a job accomplished? This is itself may constitute several quite different aims:
1. To play scales fast, evenly and cleanly.
2. To be able to identify a scale and its relatives at a glance.
3. To use such knowledge to transpose, for instance.
4. To use such knowledge to improvise, for instance.
5. Other.
There are physical aspects (fingering and movement) to be considered. There are mental (including intellectual) aspects as well (the mathematical relationships between the degrees of a scale and between different scales).
Personally, I always start with the B major scale (the easiest form a physical point of view), and I use scale improvisation from the very beginning.
You can have a look at these threads where this is discussed in more detail:
https://pianoforum.net/smf/index.php/topic,2313.msg19807.html#msg19807(Speed of scales – the important factors in speed playing - alternative fingering for scales).
https://pianoforum.net/smf/index.php/topic,2533.msg21955.html#msg21955(structured plan to learn scales and arpeggios – includes description of repeated note-groups and other tricks)
https://pianoforum.net/smf/index.php/topic,2619.msg22756.html#msg22756(complete unorthodox fingering for all major and minor scales plus an explanation)
https://pianoforum.net/smf/index.php/topic,2701.msg23134.html#msg23134(Teaching scales – the cluster method and why one should start with B major).
https://pianoforum.net/smf/index.php/topic,2758.msg23889.html#msg23889(scales & compositions – the real importance of scales is to develop the concept of key, not exercise)
https://pianoforum.net/smf/index.php/topic,2920.msg25568.html#msg25568(how to play superfast scales)
https://pianoforum.net/smf/index.php/topic,2983.msg26079.html#msg26079(Best order to learn scales – what does it mean not to play scales outside pieces)
https://pianoforum.net/smf/index.php/topic,2998.msg26268.html#msg26268(Scales HT, why? – why and when to practise scales HS and HT – Pragmatical x logical way of teaching – analogy with aikido – list of piano techniques – DVORAK – realistic x sports martial arts – technique and how to acquire it by solving technical problems – Hanon and why it should be avoided - Lemmings)
https://pianoforum.net/smf/index.php/topic,3499.msg31548.html#msg31548(using scales as the basis for free improvisation)
Best wishes,
Bernhard.