Let's say that there's a man who is about to kill 100 people via the most painful means possible. The only way to stop him is to kill him. If I was to be deontological and keep to my rule of "do not kill", then surely the end result would be worse, and I would be, to a degree, favouring myself over the lives of 100. In this case, I would break away from my deontological perspective and act in a teleological manner.
I think it's a mostly redundant mode of reasoning, only applicable to genuine inventions rather than natural phenomena. It's popular in children, but tends to be grown out of in almost all areas of thought, with the exception of the origins of Earth, the universe and so on, in which case teleological argument is regularly employed to imply the existence of a creator deity.
By children I'm assuming you mean say under 6 years of age. This surely makes teleological reasoning seem... intuitive, furthermore I doubt most six years olds are fully aware of logic behind their reasoning, they wouldn't be able to mount a defence to any objections for example.