When a week goes by, and a piano student only has four measures of a new piece learned, you can anticipate the trajectory. If the piece is 32 measures long, it will take eight weeks to finish. But by then, progress will have been so glacial from here to there, no one will be having fun anymore. Compare that to a student who's figured out how to learn a 32-bar piece every week. In eight weeks, that student will have learned eight pieces. As momentum builds, excitement grows. Another example is the overwhelmed student whose parents ask to do lessons every other week. We don't do every-other-week lessons for two reasons. One, it's not sustainable for business (imagine if your boss said you would only be paid every other week for some of your hours). Two, it never works out for the student. When students have every other week lessons, they still progress about the same (if not worse) from lesson to lesson. The trajectory is not exciting for the student or the teacher. Inevitably, every other week is the first step towards quitting. We've all had students in the distant past who insisted on every other week. It's was literally a zero percent success rate. There's a peace in knowing your trajectory, though. Because if your trajectory doesn't look good, you can course correct. And if your trajectory looks great, you can keep doing what you're doing. But it all starts with acknowledging your trajectory in the first place.