Lets take learning off of strict academics for a second. Imagine playing a guitar, the guitar method of just reading some guitar books and listening to music, will definitely work for motivated students, and it is a necessary at some point to reach this independent learning level. The most common reason why most guitar students don't progress is because they don't do the necessary boring ass drills, scales, arpeggios, chord movements, slurs etc. This is ok with guitar, it fine to just lose the 75% of students who really want to learn the guitar, and have some motivation, but dont have the ingrained motivation to do 20 minutes of pentatonic scales a day for 6 weeks. However it is not ok with practical math, its not ok to just lose the 75% of students who don't have the ingrained motivation to memorize the times tables. rote memorization and practice is important in education for most students.