Tinkering in math requires loading the situation into working memory
Tinkering in math requires loading the situation into working memory. In a video game or application such as Duolingo, all of the objects are presented to you and you can immediately interact with them. In math, the objects are described on a piece of paper, but that description is not the same thing as the object itself. To be able to play with those objects -- to engage in tinkering -- you must first "load up" the objects into your working memory.
One thing is that once you "load" a problem into working memory, you can tinker with it like a game. It's just the translation from written to cognitive medium -- the "downloading into your brain" process -- that takes verbal effort. Can we present the intimate "cognitive medium stuff" as a computer simulation?
One problem with "Duolingo for math" is that in math, if you want to think about a problem or a theorem or whatever, you often need to load a lot of things into your working memory. So even just being able to "play" requires this initial loading. Once you have loaded things into WM however, you can often play in a fun way, and mini-tasks like in duolingo can work well.