What's amazing to me is that this is still being discussed, even though a solution to the problem was found decades ago:
https://en.wikipedia.org/wiki/Seymour_Papert
https://en.wikipedia.org/wiki/Mindstorms_(book)
I think that you might find Papert's ideas interesting; he based a lot of them on the foundations laid by Piaget:
https://en.wikipedia.org/wiki/Jean_Piaget
https://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive...
From what I remember all of the "educational computer games" I played in the early 1990s were more or less this.
There have been some better ones though, over the years. Say Lemmings or World of Goo.
The best is probably something like Logo or Scratch, with some help/guidance from an adult.
What kids play in school though these days (does that make me sound old?) are things like Prodigy (prodigygame.com), featuring decent graphics but mind-numbing content, with constant nags to upgrade to a premium account.
I have seen some that get like a special day at school. There was something they did with Scratch, for instance.
I've thought that part of the reason that all the studies are showing that computers don't seem to help with education are just showing that computers as they are currently used don't help with education. A key element of ... but on a computer! is that if you just take something from the physical world and put it on a computer, you end up with the disadvantages of both compounding. To successfully put something on a computer, you need to work out a way to harness the unique advantages a computer can give you to make up for the inevitable disadvantages it brings. Simply randomizing numbers for addition & multiplication isn't really it.
[1]: http://www.jerf.org/iri/post/2916