Basic music theory.
Almost no one I encountered bothered to actually explain anything. They simply regurgitated things and I guess expected me to somehow intuitively understand something or other.
Almost no one I encountered bothered to actually explain anything. They simply regurgitated things and I guess expected me to somehow intuitively understand something or other.
My single largest goal when I'm teaching, is to find an appropriate analogy to a concept that my student already grasps, and bridge it to the new concept. Some fields make this super easy -- MechE and electronics, for instance, if you understand one, you're well on your way to understanding the other -- and some make it super hard.
Music theory is descriptive, not prescriptive. Is it any surprise that something we had to invent a whole new symbolic notation for is difficult to connect to concepts we can describe in natural language?
If you want to go really deep into the philosophy of music, to understand it from "first principles" so to speak, I highly recommend Leonard Bernstein's lecture series "The Unanswered Question" - https://en.wikipedia.org/wiki/The_Unanswered_Question_(lectu... (available on YouTube).
To paraphrase Bernstein's comment from his book "The Joy of Music": we need to stop comparing Beethoven to grassy fields and mountain streams. A "major seventh" or a "plagal cadance" are themselves the description of those qualities. By all means use music as metaphor, but when you're trying to describe it you're going to be using terms specific to its domain.
>The best math textbook (Theory of Algebra) I ever read had little sections about the person who revealed a particular subject, why they were studying it, and how the subject is used.
I've found the best type of books provide motivation for concepts, how they have evolved, etc.
Take Computer Science for example, many of its concepts were area of research for decades but from a student's perspective it seems these concepts were always here instead of being constantly refined until the states they're now in.
- Learn the definition - Learn the motivations and history - Peruse a few examples - Try to map the above to a brief synopsis that explains the concept in intuitive terms that relate to your own life. Rely on pictures.
Finally, I find it helpful sometimes to try and "deduce" identities from "first principles". e.g. assume I didn't know that n^0 = 1. How might I reach that conclusion? If I have an understanding of what exponentiation means I should be able to come up with a few different propositions (these could even be relatively informal) that make such a conclusion make sense.
My childhood was rife with mathematics teachers that focused more on rote memorization of identities instead of careful explanation of definitions and development of "intuition". There's pretty much no better way to ensure you'll produce students that dislike and suck at math for the rest of their lives than proceeding by mind-numbing rote memorization.
>There's pretty much no better way to ensure you'll produce students that dislike and suck at math for the rest of their lives than proceeding by mind-numbing rote memorization.
I couldn't agree more.
https://www.punkademic.com/course/music-theory-comprehensive...
Music theory is not inherently complex, but the notation adds incidental complexity -- it's sort of like the QWERTY keyboard; once you're stuck on a suboptimal way of doing things it's hard to move off.