[candu]

Well, if you want to be _extremely rigorous_, there's always https://en.wikipedia.org/wiki/Principia_Mathematica ;)

Less flippantly: pedagogically, there's a big difference between "here's your addition tables, memorize them" and "if I have 1 of _anything_ and another 1 of that same thing, I now have 2 of that thing." The latter offers way more opportunities for further thought: by that logic, if I have 2 things and I take 1 away, I now have 1 thing! If I have 2 rocks and 2 sheep, I can count the sheep by laying out 1 rock per sheep! And since I can add more things, maybe there are more numbers for those amounts of things too? And what about differently-sized things? Or parts of things? Or...

That's the difference between getting "1 + 1 = 2" across as a literal by-the-book fact, and getting it across as an invitation to build / connect ideas and ask further questions.

[jstanley]

I'm pretty sure that is already how addition is taught. I'm not a fan of formal education at all, but I'm not sure what you think schools are missing here?