I have Living Spanish, French, and German on my bookshelf, and love the rigour of the grammatical approach, probably because I'm a child of the Sixties, and in those days a grammar school education entailed rigorous grounding in both English grammar and that of French and German. I dissent from the view that this is an "inefficient" way of learning a language, and find myself frustrated by a "colloquial" approach, where the grammar is sidelined, and you find yourself wondering why verbs change for example, and what lies in those huge gaps that you find appearing out of nowhere. It's bewildering after the initial parrot-like phrase memorisation, unlike the rigorous approach, which builds knowledge step by step from firm foundations.
I still have my old hardback copy of this book, and although I use a colloquial CD-based set when I want to "brush-up" for a visit to Spain, I invariably turn to Littlewood for the real deal. It is soooo well-laid out, so succint, so comprehensive, and so intelligently crafted.
Each chapter starts with a passage, from which lessons are then drawn. First, colloquial phrases are explained with examples, then the chapter's grammar is introduced, and illustrated again with key conversational phrases, so that the material is never "dry" or "academic", but living, as the title indicates. The layout of the pages is immaculate, and makes the book a pleasure to work with.
The grammatical approach has stood me in good stead, as I can carry out reasonable conversations in these three languages to this day, despite only having intermittent opportunities to use them. The language seems to come back quite easily, since it was so thoroughly understood in the first place.
It is a fallacy to assume that we adults must follow the same method as children born into a linguistic culture from birth, who never hear anything but that language, and yet still take many years to master it.
The grammatical approach is scientific, in that it enables us to short-cut this "baby learning by osmosis" process, by identifying PATTERNS, rules, so that in Spanish for example, we learn early on that there are three types of (regular) verbs ( -ar, -er, -ir ) , which ALWAYS have the same form. At a stroke, we are propelled miles ahead of the two-year old "learning by listening".
And the proof of the grammatical pudding is in the contrast between the generations who were taught grammatically, and today's UK (state) schoolchildren, who have practically zero ( and I mean ZERO ) language skills. I know a French lady living in Britain, who said that it's always the same - people of my generation regularly like to speak with her in some French, but never the younger ones, who are almost completely ignorant, as a result of "progressive" teaching methods.