In Jennifer Roberts' article The Power of Patience: Teaching students the value of deceleration and immersive attention she talks about intentionally slowing down to contemplate deeply a work of art. To my mind, the study of mathematics also benefits from slow and careful thought in a distraction-free environment, in addition to spending time on interactive discussion and group work.
Has research been carried out on immersive attention or sustained concentration when learning mathematics? If so, what were the results and are there any useful suggestions for teachers and students, both inside and outside of the classroom? This could include lesson pacing, variation of activities and selection of assignments, for instance.
Also, does anyone have experiences to share of the process and results of setting students an exercise that involved contemplation of a mathematical object or theorem for a seemingly-excessive length of time a la Roberts' example in the above-mentioned article?