Begun vs. began

My husband and I are the grammar police. And, we have this nasty little habit of taking great pleasure in correcting one another.

Today, he got me. I used began incorrectly. And, just so you will never suffer the same fate, here is the tip:
Began is the past tense. It occurs alone.
Begun is the past participle. It occurs after the verb 'have.'

Another tip and way to look at it:
Began is for the past, for example, yesterday.
Example: I began it yesterday.

Use have begun when talking about something you are doing. You have started it and you are still doing it.
Example: I have begun doing my homework.

Hat tip to Using English.