So I got to the title screen. When I click "Play", it tells me I do not have enough energy. I don't have any gold so I can't buy any from the shop. I click learn and I get a slideshow of how to do basic arithmetic, but still no energy. Thus, I have no way to play your game
Even if there is a way to get enough energy to play your game, I would remove this barrier. You don't want to turn people off before they're gotten a chance to decide whether game is worth their time.
Under the Learn section, presenting Multiplication and Division in terms of circled groups of stars illustrates these concepts well, and I think will make them easy to understand for someone just learning. However the Observation screens could've done more to communicate the pattern I'm trying to observe. Maybe underlining the pattern when the user clicks would be enough to fix this. (Ex: in 3x1=3, you could underline both 3s).
And although I know this is for research, I think the highscores would be more rewarding if they were presented on chalkboards with an A+ in the corner instead of the tan boxes.