I was helping my son solving some quadratic equations the other night. (They’re still fun, for the record.)
He first had to solve some using the “reverse-FOIL” – basically a logic puzzle, and then later had to solve some using the Quadratic Formula, which you might remember as a complex formula that uses the coefficients of any quadratic equation to give the answers.
He rightly pointed out that he could have solved every problem on the page with the Quadratic Formula, because it’s reliable, if cumbersome. My counterargument was the other methods served to improve logical and mathematical thinking, which are much more valuable tools in the long run. The two methods are necessary and have different strengths. It’s knowing when to use them that makes is important.
My desire to encourage musical thinking in my students leads me to prioritize music-reading skills, real-time analysis, and various other literacy skills. They help me think like a musician and will help my students do the same.
But it can be just as valuable, in the right situation, to skip over the musical thinking, the intellectual work, and use the formula that gets us to the right solution, quickly and reliably.
Both have value. They have different strengths.