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qsz comments on Open Thread, Apr. 27 - May 3, 2015 - Less Wrong Discussion
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Additionally, I'm a little worried about the control group part. I expect it's relatively easy to recruit people to play a game and have them be motivated to play it, but if I tell people that "oh, but you may be randomly assigned to the control condition where you're given more traditional math instruction instead", I expect that that will drop participation. And even the people who do show up regardless may not be particularly motivated to actually work on the problems if they do get assigned to the control condition, especially given that I'm hoping to also educate people who'd usually avoid maths. How insane would it be to just not have a control group?
If you didn't have any control group, you wouldn't be able to interpret any improvement between pretest and posttest, if you observed such a pattern: repetition or practice effects could explain any improvement. If you observed no improvement, you wouldn't need a control group because there's no effect to be explained.
Sometimes exploratory methods start out with no-control group pilots just to see if a method is potentially promising (if no hints of effects, don't invest a lot of resources in trying to set up a proper study).
Sometimes studies like this are set up with multiple control groups to address specific concerns that may apply to individual control conditions. Here it seems like two would be the minimum: one in which participants play a different game that is expected to confer no benefit for learning; and another with some kind of more traditional instruction.
In cases like this, recruitment is usually very vague - giving participants a realistic impression of the kinds of tasks they will be asked to do, and definitely no indications about who is assigned to a "control" group.