"Convince me that the belief that nothing outside the natural world exists is actually a scientific theory and not mere philosophy."

that's a bit off topic. we are able to experience some of nature with our senses. we experience more of nature with instruments that are sensetive beyond our evolved senses. sometimes these instruments or our senses surprise us and seem contrary to what we accept is natural. science is the investigation of such.

we teach science based on that. if anything non-natural is going on, by virtue of hte fact it's going on, it's natural.

if god exists, it's natural

if god doesn't exits, it's natural

the only time you ever need mention the supernatural in a science class is to answer questions on what poeple believed before science explained a phenomena.

the problem with regards to the thread is the fact that there will be children in class who's parents share beliefs with the unenlightened folk of antiquity who did not have the benefit of 21st century science teachers for guidence.

as for the nebulous nature of what you believe science can't tell us, it's the job of the science teacher to decide if a question is something best left until a student is at a more advanced level or to set them the challenge of thinking how a question that seems unanswerable should be reframed in a way that can be addressed using evidence alone.