About two years ago, I posted short article about brain training (link). The commercials for Lumosity keep coming, but I still have not seen anything solid from them from research. Scientific American, addressed the story (link).
From my experience as a flight instructor, I know that I used to have students practice testing for the daily. To reduce the errors, I advised my students to study the questions that they got incorrect. This would be a better way to do it. Why study questions to which you already know the answer? It’s far more efficient to focus on the mistakes. Obviously, I am a believer in the testing bias idea.
With regards to doing better at the tests in Luminosity, it seems that the same idea applies. The more you study, the better you will get at that task. However, one must ask: does this task training have applications outside the current task? Stick to the math problems, proofs, and crossword puzzles.
If you really want to find something scientific, let’s start with Brain Rules by John Medina. Great Book. Here is a link to the author’s website.