The aspect of logical thinking and application of it develop along with the age of the students - usually a student can start to make sense in his/her own naturally around the age of 9 or 10 as far as I have been observing. Before that age, a student can explain "why" the same errors keep happening (if any) and come up with "how" and apply it in his/her own words to avoid the further repetitions of the same errors. This helps to achieve the same effect as "cause-effect" problem solving, being led by the teacher. A teacher's role is never to give out the answer, yet give the student some hints to help him/her solve problems independently and/or find their own solution which works. One learns the best when he/she thinks independently and use the solution to make it work, not when being fed with answers and directions what to do. As long as it is clear that the teacher is doing this not to penalize the student but needs to do so so that the teacher knows if he/she understood what to do to make improvements , it works perfectly. It also plants the "seed" to logical thinking to blossom later in one's life.
Musical study in one's life is often associated with better IQ or higher intelligence. I firmly believe that it is not just because of music itself and/or coincidence, yet years of such observing/ analyzing as well as problem solving among other skills required to play and make consistent improvements help one develop the effective way of thinking and mental/ physical application of the best solution on daily basis during their practice. Music truly helps one how to learn and maintain one's capability in his/her best shape possible - that makes a lot of difference.