It's not the teaching, it's the learning

...I was noting this in applying assorted practice methods for learning spelling, to wit: if you're copying without the letters being rehearsed, you're not as likely to remember the letters.
In this morning's math class, the same lesson was delivered in the math context: if you memorize and apply the "vertical line" rule, you'll get a right answer or two, but if you figure out *why* it is true and how it translates to the algebra (for each x there's exactly one y) .
And, once again, the ability to *stay* in abstract land comfortably is the deciding factor in whether or not such explanations will work. If you're in 099, you better should ought be able to.