I really don't remember grammar being taught at school - I think it was just something that I picked up as a small child through reading an awful lot. My parents have always spoken properly too - no rubbish such as 'i ain't done nothing' that always sounded awful to me when other kids said it even when I was about 6.
Now I think about it, I actually think I learned a lot about grammar through studying French. Terms such as 'infinitive', 'past participle' and 'conditional tense' were only covered when learning foreign languages.
Looking back, certainly at secondary level as I really can't remember primary, English was all about Shakespeare, Austen and poetry, to the detriment of a fundamental education in the language. No wonder standards are so bad these days.
We MW young'uns have probably benefitted from our parents and an innate sense of standards!