Is There Such a Thing as "Learning" Grammar?

Aw, remember the good old days, back at the age of 3, when your mom used to come over with the special book that taught you “Subject + Verb + Object”? Oh, and the lovely coming of age story at five years old when you finally understood the past participle? Aw. Oh wait, wait sorry that never happened…that memory must have been planted in me by my Chinese university professors.

The fact that you can't remember how you learned the grammar of your native tongue begs the question, when acquiring a second language do we really "learn" it's grammar? Is this even the right way to conceptualize it in the first place? What if grammar is simply a way for linguists to enjoy analyzing languages because its their nerdy passion?

Because grammar is a tool for discussing language, you first need some language to be able to discuss. In fact, you need a heckuavalot of language; you need a buttload of reference points in order for grammar to be at all meaningful.
— Khatzumoto,

Take a look at the sentence above. Even if you can’t explain why, you know it’s wrong. It’s an instant feeling based on years of contact with English.

This should be enough evidence to show you that grammar is not learned from a book. It is absorbed naturally. We pick it up through understanding what the people and books around us are saying. If you understand what you see and hear, you can mimic it, and your brain also naturally wants to repeat it. You DO NOT need to analyze the language further to be able to use it. 

By studying grammar rules from a textbook instead of naturally gaining understanding though reading and listening (just as you did with your native language) you are adding an extra step to speaking. 

Normally this is the process: Thought —> Speech

But by focusing on learning grammar points (instead of the natural way), the process changes to: 

Thought —> Is it right? —> Stammered Speech

Imagine that a cat is sitting on a vent in your house that has warm air coming out of it. Does that little fella need to know how the warm air is coming through? Do you need to understand bio-chemistry to eat a sandwich? 

Knowing about a language is not knowing a language. So, (especially at the beginning) don't waste too much time on grammar rules! A general understanding is good enough for our adult brains to recognize a pattern, but we don’t have to be able to recite the grammar rules for a test, so it is simply a distraction to focus too much on this layer of analysis.

All this being said, if you occasionally find grammar interesting and want to see what kind of progress you've made by acquiring the language naturally, I would recommend checking out Chinese Grammar Wiki, they have great plain English write-ups about all of the most important Chinese grammar points, and so it can be gratifying to see how far you've come with your acquisition, but remember, reading the grammar point alone does NOT make you able to use it. Happy studying!