How to Learn
I've realised that trying teach a second/foreign language is just like trying to teach math: very few kids will actually understand the fundamental principles, so the best you can hope for is to teach a few basic patterns.
Recently was the fourth time I've had to start this new book and the very first unit has a lot of grammar specifics the kids are not too familiar with. Specifically, the book wants them to answer "Is it a ...?", "Are they ...?", "Is there a ...?", and "Are there any ...?"
Sadly, East Asian languages lack any distiction between singular and plural, which is quite fundamental in Indo-European languages. So the kids often use "is" when they should use "are" and they'll frequently use the singular nouns when they need to use the plural.
What I've done with all these classes is teach a very simple rule: The answers need to match the question. "Are they? They are." "Is it? It is." "Is there a ...? There is." "Are there any ...? There are." It's worked with most kids, though some need some more reinforcement.
But that's made me think of like in calculus with the formal definition of a derivative. Sure, I know it, I am a math major and I understand what the derivative is for. But, for everyone in the Calc 101 class, it's just a formula to be applied in set situations.
Or in Algebra, trying to solve a complex equation for x. Sure, I could think of a few ways to manipulate the equation and I know exactly why what I'm doing works. But, again, everyone else in high school only gets simple equations to work with and they must follow a set pattern of rules they've memorised.
In my own prior attempts to learn foreign languages at school, I've been quite rubbish at memorising all that vocabulary. As soon as I memorised one set of words to pass a test, I'd forget it all so I could do it again with the next set. However, I discovered that I learned the grammar rules rather easily. Even now as I try to learn Korean, I am frustrated/disappointed with my small vocabulary, but I have somehow started to internalise some grammar points. My experiences in school and observing my friends in England have taught me that the key to learning a language is to internalise as much vocabulary as possible and then to worry about forming sentences and grammar. For me, though, it just doesn't work that way...