See descriptions here:
http://www.numbrosia.com (Numbrosia and Numbrosia 2)
http://amichail.posterous.com/numbrosia-3-screenshot-and-description
The Numbrosia 2 and 3 descriptions are probably incomprehensible to most people.
I realize that videos would help considerably and I plan to make them, but I would also like to have text descriptions that are more comprehensible.
Okay - DL'ed and am playing. Tutorial is very well done - that is, until I got to the first Math move explanation. "Try adding 1 to row 2 by tapping it twice with the second tap to the RIGHT of the first one"
Whoa!
I did it but I don't know what happened. A highlight of, "Here's what happened after you did that" would have helped. I have no clue what I did because the popup screen completely covers up that section.
I was able to "get it" after going through the tutorial though (and solve my first one). I dig it - very cool idea.
So... to your question:
The terms "rotation moves" and "math moves" are confusing. I get "math moves" better than the other but it still isn't great. I don't think, actually, that you need to name the moves. In your explanation, you simple explain that you can move entire columns and rows and you can add or subtract 1 to entire columns and rows. "To move columns and rows, simply swipe the column or row in the direction you want it to go."
Thats the simple part - the hard part is explaining addition/subtraction. I think it needs more text than you currently have yet without the term "math move"