Okay. Grammar geekry coming up.
"Gerund" vs. "Participle" is confusing because there's no definitive usage of the terms; some use "gerund" as a synonym for all "-ing forms", so that they can use "participle" for all "-ed" froms. But most distinguish between "gerund" and "participle" along "nominal" (a noun) or "adjectival/verbal" uses.
The distinction isn't unchallenged. The Cambridge Grammar basically abandons the distinction, talking about a "gerund-participle".
Basically, it's like this:
There is a verb:
I write a story.
Easy to spot, isn't it?
Now add an -ing to the infinitive:
"writing"
Now you have a new form, but you can't tell what it is. This form could be used in various contexts:
1. I am writing a story.
Here writing is the main verb of the sentence, while "am" is the auxiliary verb. Most theories would call this a "participle".
2. I don't like bad writing.
Here, writing functions like a noun. See how it takes an adjective, "bad"? Only nouns take adjectives. This people call "gerunds".
2.a. Your constant writing is getting on my nerves.
Gerund again. See how, in addition to the adjective "constant", we have a possessive pronoun? It's definitely used as a noun isn't it.
Easy? Good.
Now we're arriving at dpaterso's:
3. Do you mind my asking you...
Ah. A gerund. There's a possessive prounoun in front of it, so it has to be a noun, right? Easy again. Phew.
Oh, wait. "my asking you..."
Nouns don't take direct objects. Only verbs take direct objects. Ah... so it's a verb? A participle? Um...
Tug of war. "my" pulls one way, "you" the other. Is it a gerund? Is it a participle?
See the ambiguity? Fine. Now consider this:
4. Writing is hard.
Gerund or participle? We have no grammatical hints at all. Some people would argue that because "writing" occurs in the subject slot it must be a noun and thus a gerund. I don't buy that:
5. Writing well is hard.
See? Basically the same situation as 4., only modified by an adverb. (I could have different modifications: "Writing about kittens is hard." etc.
The above would have to be a participle, then, as only verbs (or adjectives) get modified by adverbs.
Ah, darn it, but you could also have:
6. Creative writing is hard.
Adjective? Gerund? Aha!
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Basically, gerund vs. participle is a mess. And, practically speaking, the distinction is not all that important in English. Basically you have an -ing-form, that's derived from a verb. And it could be used as a verb or as an adjective or as a noun, or as anything inbetween.
I'm not going to comment on avoiding the -ing form or not, as that would only send me down another rant.