One of my favourite childhood games (Logical Journey of the Zoombinis) was all about maths, logic and problem solving, and I credit it for a lot of my early interest (and success) in those areas.
As a quick plug for something I loved - they recently kickstarted a remake http://www.zoombinis.com/ - I'd highly recommend it. (Not involved, besides backing the kickstarter).
Yes, exactly that.
My biggest problem with the education ecosystem is that adults try to bullshit kids instead of facilitating learning, and at the same time they forget children have perfect bullshit detectors - they haven't yet learned to question their intuition that something is pointless, or lie to themselves to get through drudgery.
Games are not made by just colorful graphics and telling a story. Kids can tell when you try to trick them into doing something they think is pointless, and it also erodes their trust quickly.
My 5 y. daughter is completely enthralled by a spelling and reading game on IPad. This leads me to disagree and claim instead that a crap game is not made good by educational goals but a good educational game is provably plausible - it just needs to be a good game.