You could also consider Construct 2. It's very quick and to get a basic game up and running using built in "behaviours", and programming is done through a visual "event" system. It's similar to Game Maker, but I think the interface is a bit nicer.

Scratch is a good option though.

I too recommend GameMaker. It has the drag&drop things that can do some work, and even can handle loops, variables, etc.. But then it also has GML, which is a scripting language with similarities to C/C++/Java/Javascript/Delphi/Basic. It doesn't require semi-colons except for a very few cases, and is fully capable of about any 2d game play, though there are limits, which are mostly performance based. Of course, for your class, I seriously doubt you would run into those limits, as most "serious" developers don't.

I could also mention that there are a couple of books, namely the Game Maker's Apprentice and the Game Maker's Companion, which include what you are looking for in the class. Not only does the software itself get taught, but general game creation concepts are also taught, including game design, and in the second book, a detailed part about stylistic art. The first book also has some things about balancing multiplayer games, just to give you an idea of the game design topics that are not software bound.

Another good thing about GameMaker(I sound like I work for YoyoGames, but I don't) is the relatively new export options. GM Studio, which you may not want to use in your class, can export to mobile platforms and HTML5/Javascript code. Considering how iOS and Android are the "hip" things these days, it may make your class somewhat more intersting to the kids knowing that if they come up with something nice(and some cash either saved are as a gift) they could make games for these devices.

You could also consider Construct 2. It's very quick and to get a basic game up and running using built in "behaviours", and programming is done through a visual "event" system. It's similar to Game Maker, but I think the interface is a bit nicer.

Scratch is a good option though.

Does Construct 2 let you drop down to the code level? It's ultimately an HTML5 code generator, no?

I think this is the key to any visual builder style programming, you need to be able to look behind the curtain, so to speak.

The first Constuct Program(Construct Classic) had it where you could go down to python code as parts of the event sheet, but the new one does not appear to do that. Supposedly, all of the coding was to be done in the event sheet, but there was code in the actions/behaviors, which takes care of the need for code.

GameMaker on the other hand, besides the event system with drag&drop "coding" you can also use GML, which is actual typed code, which seems like it could be better for the class. If you really want just concepts, then Construct2 may do it, but if you want any coding, it likely won't. Also, Scratch isn't typed code either, though the blocks somewhat resemble what could be some kind of scripting.