Or maybe a game that allows you to use real-life physics and maths knowledge to your in-game advantage? Like, giving you enough data to compute the angle for a cannon to shoot at, while hinting you very delicately towards what knowledge you need to acquire to do that?

One of the biggest problems of maths and science education is that they're useless and boring as hell. Or, at least that's how it looks like from kids' perspective. I think that a first step towards teaching them those skills in an interactive way would be to create an interactive environment where maths (or physics, or chemistry, or biology, or astronomy) could be actually useful. Some way for knowledge to give you in-game advantage, or at least expand your gameplay. A game in which you could actually read where's north from the trees and stars. Etc.

There are several bridge building games, the oldest I can think of is called Pontifex. In the original Pontifex when you went to test your bridge it would dynamically color all of your beams according load and stresses and was my first introduction to Statics and Dynamics. It gave me a chance to explore why bridges are the way they are long before I learned calculus.

that's interesting. But I guess it's missing that fun factor...there has to something else to it to attract the attention of kids

You don't have to lead players along by the nose - open-world games are surprisingly attractive even to kids (maybe especially to kids, who haven't yet been conditioned that everything needs to be structured with explicit step-by-step goals).

When I was in high school I did a lot of volunteering at the local science-museum where we had terminals set up with the Incredible Machine. They were always occupied.

Kids have an innate love for exploring, moreso than adults. We beat it out of them later, but in the mean time open world, unstructured games are some of the best ways to teach things to people. Look at SimCity, Incredible Machine, etc etc.