This entry from the Oxford Dictionary of English Grammar may help:
gerund
The -ing form of the verb when used in a partly noun-like way, as in No Smoking (in contrast to the same form used as a PARTICIPLE, e.g. Everyone was smoking). (Sometimes called verbal noun.)
Both the term gerund, from Latin grammar, and the term verbal noun are out of favour among some modern grammarians, because the nounlike and verblike uses of the -ing form exist on a cline. For example, in My smoking twnety cigarettes a day annoys them, smoking is nounlike in having a determiner (my) and in being the head of a phrase (my smoking twenty cigarettes a day), which is the subject of the sentence; but it is verblike in taking an object and adverbial (twenty cigarettes a day), and it retains verbal meaning.
In other words, there's a continuum where it's pretty obvious what's a gerund at one end and what's a participle at the other, but with a whole lot of uses with mixed features in the middle which are more like or less like each end. Whether you want to point this out to their young innocent trusting minds is another matter.
Bingley
