Going dancing?

[lil'changeling]

When using the suggestion 'What about going' with 'shopping' or 'bowling', I'm guessing that 'going dancing/going bowling' is out of the question. Correct me if I'm wrong. I imagine that teaching the kids 'going bowling' would cause them to giggle endlessly ... My little neighbors giggle at almost anything However, that will not stop me...
I hope to be a teacher soon, however there are some things that have to be ironed out...

[SoothingDave]

People go bowling or shopping or dancing all of the time.

[lil'changeling]

Did you not understand my question or did I not understand your answer?
I asked whether +ing such as bowlING can follow a +ing, as in 'What about goING bowlING. I do have a tendency not to be clear enough (sth else I'm working on).
If the fault was mine, please, do forgive me, and answer my question...

[Rover_KE]

What about going bowling/going dancing are natural and commonplace.

Rover

[emsr2d2]

What about going bowling?
What about going shopping?
What about going travelling?

They're all absolutely fine.

[SoothingDave]

I'd probably say "How about going bowling?" if I was proposing the activity.

[philo2009]

When using the suggestion 'What about going' with 'shopping' or 'bowling', I'm guessing that 'going dancing/going bowling' is out of the question. Correct me if I'm wrong.

You are, as it happens, since 'going shopping/bowling/fishing/dancing/skateboarding/...' are all fine, but your caution is understandable, given the fact that natives do avoid certain types of '-ing -ing' combination. Essentially, however, it is only where an alternative to the second -ing form exists (normally an infinitive), so that we do not say e.g.

*It was just starting raining.

since it is possible - without loss of meaning or naturalness - to rephrase this as

It was just starting to rain.

Where, however, no viable structural alternative exists, e.g.

I really wasn't enjoying being with them.

there is generally no problem.