Parameters in connection lines?

Is there any way to use parameters inside of a connection line? For example, if I had a function like this:

function awesomesupercoolfunction(parameter)
	print("Wow, " ..parameter .." is great.")
end

And I wanted it to fire on a MouseEnter event,

creativenameforabutton.MouseEnter:connect(awesomesupercoolfunction)

or something like that, how would I go about doing this?

I tried

creativenameforabutton.MouseEnter:connect(awesomesupercoolfunction(parameter))

just in case it was that simple, but it wasn't. Is there any way to do this? I can accomplish what I want to do without it, it would just make the process much more simple. Any help would be appreciated!