Stephen Krashen and Tracy Tarrell have given an interesting approach to learning new languages which they call Natural Approach. In this approach, they bring the naturalistic approach of language acquisition (i.e. how babies "acquire" language without "learning" grammar) to the classroom setting. Over decades of research, they have found this approach to be effective.
Stephen Krashen has further formulated a set of hypotheses to explain why and how this works: https://en.wikipedia.org/wiki/Input_hypothesis
Among many things, these hypotheses primarily differentiate between "learning" and "acquisition". While the former is done deliberately through the conscious, the latter is subconscious. Krashen defines a term called "Comprehensible Input" which is input understandable by listeners even if they do not understand all of the words or grammar structures. They claim that learners can learn in a natural environment where they receive Comprehensible Input.
For more details on the theory, kindly refer to the linked Wikipedia pages.
Now, my question is this: Can the Natural Approach of learning be applied to other fields like Music and Mathematics? Music and Mathematics are also like learning a new language, and so can we learn them better if we don't focus too much on their "grammar" but rather try to "acquire" them in some manner?