And my point was the the average student is presented with this giant, for them, formula as a finished thing and have no way to grok it.

And that if you instead start with squares and rectangles and built up to it, it'll be less daunting.

But my point wasn't about this one formula specifically, but about the approach in general.

Not sure this makes sense pedagogically. I would challenge you to try this in a classroom of average middle schoolers and see how it goes. I don't think you grasp the difficulties here.

Not sure why you think it doesn't make sense pedagogically. Counting and numbers are taught before addition.

Then addition is "proved" in terms of those.

Then multiplication is "proved" using addition.

One building on the next.

The proof for 1+1=2 is something like 150+ pages. We don't give that to kindergarten kids do we.

Hence the use "prove" rather than prove.

But the length of the real proof is beside the point. We teach them about 1 and 2 before going to 1+1=2. And when we do go to 1+1=2, we show it to them using objects and counting. We don't simply tell "here's the function for addition, just put numbers into to to solve problems".