Does fluency on a psychomotor task result from practice and a focus on accuracy? I know this formula, and I don't know where did I read it (or maybe heard about):


  Conscious accuracy + continuous practice = spontaneous fluency


It's an educational technique for long-term learning processes which require the learner to develop motor-skills, like playing piano, touch-typing, martial arts, etc.

This formula in brief says that:


You don't have direct control over your brain, and it's a black box to you
Your only duty is to provide content for you brain
Every action you do during learning process should be consciously accurate
You should practice more and more (PMP)
You should not care about becoming fluent, as it's not under your direct control
After a while, you brain reaches fluency
The more you provide accuracy for your conscious mind, and the more you practice, the more fluency you'll get from it


I Googled this formula and to my surprise I found almost nothing related. So, I have this question:

Is this a subject of cognitive sciences? And if so, is it valid? Do we have a theory regarding these arguments for developing motor-skills?
I have never heard of this formula, but from a cognitive psychology point of view you might look the theory of expert performance (Ericsson et al., 1993). In this theory it is argued that an important factor in the aquisition of expert performance is what the authors call deliberate practice. What is meant by this is an activity, wherein someone actively tries to improve his skills in some domain. Deliberate practice is not neccessarily an enjoyable activity, as it requires effort, concentration and persistence. It is definitely conscious. 

There is quite a bit of evidence from different domains. Ericcson and Charness (1994) report findings from chess, mental multiplicaiton and music. There even is a handbook of expertise and expert performance that sums up the field, if you are interested to go deeper (Ericcson et al., 2006).

The formula that you mentioned very much reminds me of the concept of deliberate practice. I would argue that the two things basically refer to the same processes.

References:

Ericsson, K. A., Krampe, R. T., &amp; Tesch-Römer, C. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100(3), 363–406. doi:10.1037/0033-295X.100.3.363 PDF
Ericsson, K. A., &amp; Charness, N. (1994). Expert performance: Its structure and acquisition. American psychologist, 49(8), 725. PDF
Ericsson, K. A., Charness, N., Hoffman, R. R., &amp; Feltovich, P. J. (Eds.).(2006). The Cambridge handbook of expertise and expert performance. New York: Cambridge University Press.