Instrumental vs Relational Ways of Understanding

The most striking aspect of this week's reading is the example of teaching students music. As someone who studied music and learned to play piano growing up, I went through the same methods that the passage described as "relational" (it's funny that my way of learning a musical instrument was not "instrumental"). Perhaps this also explained why I found the theory part of music tedious and was not very skillful at techniques such as sight-reading and harmony identification. In mathematics, there are similar questions we can ask regarding the two different ways of understanding. There are benefits and disadvantages of treating one as superior over the other. The passage questions whether they're separate subjects or just different ways of looking at the same thing - and I would lean toward the latter. My own experience from my time as a math student and then a tutor dictates that the relational way can definitely be helpful to students who need immediate results and accuracy with future problems that could be perceived to be in unfamiliar territory. The important task is for students to ask why this works? Because relational understanding is especially helpful in developing the critical thinking skills. I feel as teachers, we need to devise a strategy (i.e. visuals, graphics) on how to teach students that creates a mental map of different concepts they have learned and how they can work together, because nothing that is taught within one course is left on a single island. It is also important to consider whether students are receptive to the relational understanding of mathematics, because if they're only thinking about the "instrumental" way, then there's a misalignment between the messenger and the receiver.