The problem I see with forcing x amount of hours study before next having a lesson is that most teachers just wont want to do it. If you are a professional teacher you want your students to come consistently at a specific time. If you don't then your timetable will be haywire and you will lose money. It is a business as well as an educational service, you can't just focus on one or the other, you do want to give good education but at the same time you rely on consistent income and a timetable you can rely on.
Imagine if it took one or two months to accomplish the amount of work desired before meeting with a teacher again, for a beginner this is a big problem. The more time it takes to accomplish a task the more lost and distracted they will generally become. In fact I could imagine if it took a month to get through the work a beginner will have forgotten the majority of the hours they put in, they indeed simply could not even have many effective hours of work put in at all! A teacher can be used as a catalyst for their education despite the little time they have put in.
Consider this 25 hour regime for some set work for a particular student, of course these numbers can change depending on the individual but this gives some idea of what's happening.
The term efficiency used below = correct study with useful results, no wasted time floundering about, knowing what to practice and how etc.
EXAMPLE 1: Weekly lessons over shorter periods of study on a particular set of unchanging work:
- 5 hours of personal study in a week with 50% efficiency (2.5 hours efficient study),
lesson with teacher corrects inefficiency,
- 5 hours study week 60% efficiency (3 hrs efficient) ,
lesson with teacher corrects inefficiency,
- 5 hours of personal study in a week with 70% efficiency (3.5 hrs efficient study)
lesson with teacher corrects inefficiency,
- 5 hours of personal study in a week with 80% efficiency (4 hrs efficient study)
lesson with teacher corrects inefficiency,
- 5 hours of personal study in a week with 90% efficiency (4.5 hrs efficient study)
lesson with teacher corrects inefficiency,
TOTAL: 25 hours study in 5 weeks with 17.5 hours efficient
Compare this to:
EXAMPLE 2: Lesson after 25 hours study regardless of time it takes to accomplish a set of work.
25 hours of personal study in a 5 weeks +2 weeks (add two weeks because without a teacher to answer every week there is a much higher chance to get lazy and not do as much work during the week) at 50% efficiency
TOTAL: 25 hours study in 7 weeks with 50% efficiency (12.5 hrs efficient study)
Their input is around 17.85 hours 5 weeks at 50% efficiency that is about 9 hours efficient study.
So forcing a beginner or insecure student to work on their own for extended time without guidance often sets them up for a lot of wasted time. We cannot assume that all the time they put in will be retained or even is effective, a large part of the teachers job is to recapitulate and reinforce good ideas and reason through incorrect ones, allowing extended periods of time practicing wrongly can really waste their time and stamina and desire to learn. This is not to say doing something wrong is bad, I feel we learn more by doing something not completely correct and then seeing a better way, you appreciate the better way more readily, but doing something incorrect for a very long time is wasting your time.