Sorry to be a bit dense about this

I've had a look at the power head on a couple of websites and it says it's for under gravel filters or just to create a current. Do you have it attached to a sponge filter? Am I right in thinking it sucks in water through the sponge and then spits it out at the top?
[/quote]
I don't actually have an under gravel filter. I have never owned one, only because many people told me that they are a pain to clean/maintain. Don't quote me on this but I think that the power head somehow attaches to the under gravel filter to allow better water circulation. But again I really am not sure on that. From my understanding you do not attach it to a sponge filter. The sponge filter is a type of filter you can use instead of the under gravel filter, if you want.
Too be honest you are probably better off getting a cheap sponge, internal, or hang on filter, and not using the one that came with the kit. Most filters that come with the smaller tank (or cheaper) kits, usually aren't that great anyway. I mean try the under gravel filter and see, you might like it. It is just that everything I have ever heard about them says they are a pain to deal with. You can't really clean it completely without tearing down your entire tank, I have heard that frequently debris gets stuck under the filter and just sits at the bottom of the tank and rots away, causing water problems. Like I said, I have never owned one, never used one, so everything I know about them is hearsay. I mean try it if you want, you never know. But if it were me, I would start looking/pricing filters for smaller tanks, just to have a back up plan. Like I said I have the Aqua Clear 20 (I believe it is by Hagen) in my 5 gallon and I absolutely love it. It is a relatively inexpensive filter, it is small, quite, has an adjustable output, flexibility with media, it is a great little filter, I adore it and wouldn't use anything else on my small tank. But look around at your LFS or on-line. You can pick up filters for smaller tanks for fairly cheap, I have seen them for as little as $10 brand new on-line. Just bear in mind you do get what you pay for. But just look around for something that you like, just remember if you get a hang on type filter make sure it has a way to turn down and/or redirect the output current for the Betta, this may be something you want to check on with internal filters as well, don't know for sure I have all external/hang on filters.
Good Luck.