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This article seems to speak more to learning (or improving) new motor skills, although it's not hard to imagine that the same principles could apply to learning other skills too.
I'm pretty tired of these articles that grossly extrapolate conclusions from a very limited study.
I think the researchers are seeing the effect of mindfulness in action. Changing the conditions forces the body/mind to not go on auto-pilot and focus on the minutiae of the task. Consequently they improve through this deliberate practice. The changing conditions is forcing people to really think and focus on the task at hand. I would think it is also important to repeat things with same conditions long enough for the muscle memory/ heuristics to kick in. If you change conditions rapidly there will surely be no learning involved.
The argument can be made that this isn't anything new. Ericsson, "widely recognized as one of the world's leading theoretical and experimental researchers on expertise"[1], has been researching Expertise and Deliberate Practice for decades[2].

For example, "The superior quality of the experts' mental representations allow them to adapt rapidly to changing circumstances and anticipate future events in advance." [2] Indicates that the experts have already been practicing with changing circumstances.

[1] https://en.wikipedia.org/wiki/Anders_Ericsson [2] https://psy.fsu.edu/faculty/ericsson/ericsson.hp.html [3] https://psy.fsu.edu/faculty/ericsson/ericsson.exp.perf.html

There's also that study where kids trying to throw a ball into a basket from a specific distance improved quicker if they practiced throwing from two different distances, different from the one that was tested, than those practicing only the tested distance.

Edit: I think this is it: http://www.ncbi.nlm.nih.gov/pubmed/662537

No, they have discovered a much faster way of learning to "move a cursor across a screen by squeezing an object".
Waste of time article. A very small group try a very specific test and the researchers extrapolate it to learn to play music and tennis. The journalist should be ashamed.
Isn't this pretty much what musicians do anyways? When I was learning how to play piano as a kid the exercise books basically would take one pattern, make you learn it over the keyboard, and then the next exercise would be a slight variation on the previous one. Enough that you had to spend time with it, but not completely different than the last exercise.

All musicians I know do the same: scales, pattern exercises, and songs of increasing difficulty.

Surely such knowledge and technical skill in learning and teaching was arrived at by empirical methods. However, it is not subject to peer review and the controlled experiments one can run in order to verify it are not obvious. Watching an expert do their craft, one can observe their virtuosity and yet have not a clue how to explain it in words. There's no manual for teaching that one can read in order to become a master teacher. There never will be: skill is a knowledge beneath words. Still, whatever knowledge can be put into words ought to be. The best social science is the most modest: that which seeks to clarify and observe what human beings already do.

There is a double edge to this: institutions cargo culting science and producing monstrosities like the Common Core. Prescriptive social science can be a disaster. Teaching, being the most important profession, is a weird place where the people in charge completely disrespect the expertise of the people doing the work but understand that whoever controls it controls a great deal of society's functioning. That's why systems like the Residential Schools in Canada were allowed to do so much harm and why administrators are allowed to trample all over the interests of both students and teachers.

I wring my hands a lot over the bureaucratization, corporatization, and centralization of universities and schools. The powers that be most definitely wield the apparatus of science to harmful, unscientific ends.

Researchers actually found something that was already known for some time. 20 years ago I remember reading an old book about learning techniques. One of the techniques in it, and one that I use for myself and my kids is to sound out the answer to questions in various tones. For instance:

8 times 6 equals FORTY EIGHT (yelled). 8 times 6 equals forty eight (whispered). 8 times 6 equals forty eight (monotone). etc...

It does work, but it frustrates me that these researchers think this is something new.