Before society accepted the largely artificial oppositions between the arts and science, or between education and the 'real' world, people had other models that organized the way they worked in the world.
One of the oldest models is that of craft: it endures in our use of "craftsmanship" to reflect something produced with elegance and quality. When we talk about craftspeople, we generally refer to people who produce handmade or custom goods - often sold at "craft" shows. Somewhere along the way, industrialization stole our ability to relate to our work as masters of our crafts. We can take it back.
In the model of the guilds, an apprentice was a worker still learning a craft; a journeyman could be trusted to carry out most of the work of the business; a master was so skilled that s/he could teach the craft by the way s/he did the craft. The work of the master was not to choose between doing and teaching, but to do by teaching and to teach by doing. You will have seen something of the legacy of this when you watch television shows about teaching hospitals. The most accomplished doctors ply their crafts while young apprentices (called interns or residents) learn by observing and sharing the work of the master.
The doctors are not always good masters: their failings make for more interesting scripts. Those failings also reflect the difficulty of 'mastering a craft' in a society that has forged thick walls between teaching and doing. What would change if you had an 'intern' who was to observe or even participate in your most serious, highest level work? Would you be distracted or would you discover a new/old model of learning; a model in which both master and apprentice get better by working together?