I'm an educator (my supposed 13 year old kid is supposed to represent my students until I figure out how to get an educator account), and also a longtime Pokemon player, ever since it first came out when I was 11. HeartGold is not the best installment gameplay wise, but it's one of the more appropriate ones due to the lack of controversial content the Pokewalker, a pedometer that gives you in-game rewards for reaching certain stepcounts in th day.
In HGSS you play a ten year old kid. The local pokemon professor gives you a Pokemon and asks you to walk with it (instead of keeping it in a ball all the time like most people do) to see how that effects its development. You get a rival in the form of a kid who stole another pokemon from the professor, and you have to go up against Team Rocket, an evil criminal syndicate who want to use Pokemon for power and profit.
Gameplay is great, and as always educational. Pokemon is text-intensive and can help kids with reading, and I personally got through college math because Pokemon kept my estimation, multiplication, and algebraic knowledge fresh. You don't need to know algebra to play, but if you do it can be a lot easier to do well, as the game is controlled by a master equation consisting of your Pokemon's offensive stats, divded by the other pokemon's defensive stas, times the type multipliers. The violence of the game is comparable to boxing in our world, though very young kids might require a talk about this.
Concerns I have with the game are the fact that the rival isn't punished for stealing the Pokemon, the apparent aimlessness of Team Rocket, and of course the ridiculous levels of consumerism. Also, as it's very hard to cheat the Pokewalker, lazy kids might do adventurous things to get their watts, like throw the walker in the dryer or attempt to attach it to a treadmill (I, an adult, have already nearly broken the Pokewalker several times trying to cheat it when my feet were tired from teaching!). Luckily replacements can be cheaply ordered from Nintendo.
If your child has trouble with computers or reading you may want to get them Diamond/Pearl/Platinum instead. The computer system in which you store Pokemon is a little... confusing. Also very biased toward right-handed people.