My student couldn't understand why it was okay to use -ing with some of the verbs and not with others. He said, German is logical, English is not. Please explain to me, why is this?
English isn't so illogical when you look at the semantics behind the (patterns of) complements. That is, the fact that all the verbs you mentioned are transitive (require at least one "object", one thing) in the given context to logically "complete" their meaning shouldn't be too surprising for this learner:
*I (don't) recommend.
(?)You should visit. (Incomplete in this context of visiting London, not somebody's [only] home, and even the "home" context really needs something like 'us sometime' to complete it nicely).
?It's a good idea to take. (To take
what, in this context. Not just 'it', as far as we can tell so far).
To which we might add, the "starting suggesting question phrase/functional exponent 'How about' " also generally needs completing:
*/?How about(...)?
The obvious question is, what EXACTLY should follow the above verbs and phrase? Ask your student to think of the semantic "class" needed.
recommend - SOMETHING/DOING STHG... (advanced: - (that) sb do sthg): a gerund is the same as a thing, no?
vist - in this context, SOMEWHERE/SOMEBODY (both are SOMETHING, but it's better to be more specific wherever possible)
take - SOMETHING-CARRIABLE OBJECT
How about - (DOING) SOMETHING (related to 'recommend', above)
I suspect the confusion occurs in the learner's mind because the modal 'should' can be followed by another verb, but remember, there is only one "main"/lexical verb in the resulting verb phrase. That is, he has perhaps seen/viewed it as:
'You SHOULD VISIT',
and is probably wondering why
'I (don't) RECOMMEND (to) GO' is not "therefore" possible.
If we mark the MAIN, LEXICAL verb element in the VP in CAPITALS and only allow ONE (that is, we count/add them up), things should become clearer:
You should VISIT (somewhere)
I (don't) RECOMMEND (sthg/doing sthg)
'How about' is kind of idiomatic, in that it doesn't require a verb.
I could start mentioning finite and non-finite elements of five-element verb phrases, but I would probably end confusing myself as well as you! But you can find some interesting sites if you search for e.g. "finite and non-finite elements of the verb phrase", and perhaps add "Leech" before that etc.
http://folk.uio.no/hhasselg/terms.html (go down to "verb phrase")
http://www.soton.ac.uk/~enm/vbans.htm
Generally, it would have been better if you'd just stuck with 'should' or (How about
) 'could', both for "positive suggestions" (and both followed by a nice simple main verb). I realize you wanted to introduce the notion of "put sb off of the idea of", but isn't it obvious that e.g. "going to London in winter" is a BAD idea to start with (and not necessary to express)?!
If you really wanted to include these sorts of "warnings" then some simple "Dont's" (in addition to the above "Do's" - 'Hmm, London's cold in winter, so don't/you should't GO then, eh!' - reasoning laid out BEFORE potentially UNSPOKEN/NO NEED FOR/OVERKILL "advising/warning" modal) would have helped preserve the uniformity of the grammar for the learner just that bit longer (i.e. for the one lesson at least), and you could therefore have avoided the potential for confusion (you'll know next time, that this guy is a "logical" learner, who likes to put things into clear categories at the time he first encounters them).
Talking of "preserving" the grammar, 'It's a good idea to take' could be "streamlined" into something like 'You should probably take/Maybe you should take/You might want* or need to take/You'll probably want* or need to take', thereby avoiding the 'to-v' (after the main clause and object already) for a while at least.
Taking the above steps may seem like artificial contrivance, artifice, but it does help avoid dumping a potentially confusing jumble onto the learner's plate all at once.
'How about' is maybe a little out of place, the "odd one out" of the set. I mean, it is probably more used between two people who are now BOTH ACTUALLY IN LONDON, rather than discussing what to do LATER when person B is in London (your context is one person asking an experienced London-goer for travel tips and advice, no?).
From all the above, it is maybe sounding like I think your lesson was a total mess, and that you should do it all over again...repeating a task is something a learner might want to do if THEY got it wrong, to improve, but obviously, it is much more risky for a teacher to appear to be saying 'I made a dog's dinner of that'! But you might like to consider it...perhaps with a subtle change of destination, or better still, type of advice (e.g. things to do on a date, what to do at the weekend, how to save money, how to stay healthy etc).
By the way, 'should' is not the only way to offer e.g. travel, as opposed to potentially "unwanted/unwarranted to the receiver" advice (I myself tend to imagine it being used more as a way of saying "have to/must" or "mustn't" to e.g. a friend who doesn't wear a seatbelt, or perhaps drinks a little over the limit sometimes but still drives: You really should wear a seatbelt; You really shouldn't drink (so much) before driving). I know you have some alternatives there yourself, but should 'should' be the core item (it seems to be yours)?
Here are some alternative means of advising people, off the top of my head (you'd need to organize such brainstorms a bit):
Do you know X? (>'It...' below, which "explains" what X is immediately, and helps avoid "20 questions"**)
Have you heard of/(ever) tried/been to etc X?
It/X is great/good/interesting/a nice place/ serves good food etc
There's (always)...
(Me/myself), I'd...(instead)
Why don't you...
etc.
*See the paragraph a little above, beginning with 'By the way...', on why 'might want/need to' or 'will probably want/need to' are perhaps "better" than 'should' ('should' is perhaps a little too plain or "direct", and could create a subtle feeling or impression of "inappropriacy" or "forcefulness" in the mind of the listener/"advisee"). I suppose a large part of my post here is to do with "tentativeness", being tentative in what we say, to avoid possible conflict, even though this conflict usually never becomes obvious (that is, explicitly stated or remarked upon). That being said, too much subtlety would be lost and/or not required, though, considering how many learners speak more with other learners than with native speakers.
**A Japanese friend: Do you know Akihabara?
Me: Um, no....
(silence)
Me again: Is it tasty/a food; Is he a sumo wrestler etc
(The 'Have you p.p' makes it clearer if X is a place [been], food [eaten/tried] etc)
