You can see that it works, but only because you have defined it to work that way. There is no explanation of why it works based on more fundamental principles.

You can see that it works, but only because you have defined it to work that way. There is no explanation of why it works based on more fundamental principles. With a much more advanced math education you can derive addition from more fundamental axioms, but that is way beyond what a child should ever be required to learn.