I swallow my gum. I have ever since I can remember. In fact, I swallowed my friends' gum for them when I was in elementary school and in high school I use to eat entire bags of double bubble. Sadly, my "adultness" (not a word) has made me stop doing such silly things.
Well, my kids love gum too! And I never taught them to chew it and then spit it out. Gum is like candy. Jesse is, of course, too little for not swallowing and Emree.... well, why not swallow.
My philosophy has since been confirmed. One anonymous Grandpa taught little Em to just chew her gum. Today I found pieces of it chewed up and spit out gum all over my house and a little in her hair. I promptly asked her to swallow it next time. (We love Grandpa for lots and lots of other things he teaches!)
I know the real answer is that I probably shouldn't give my three year old gum, but don't judge me :)