David Watkin, newly anointed Head of Strings at the Royal Conservatoire of Scotland, is leaning forward at his desk, describing in animated detail a class he intends to introduce to the RCS curriculum.

'Wild-Card Thursdays' will see string students turn up once a week for a two-hour session about which they know nothing at all. They might be required to dance or to improvise theatre sketches. They might find themselves singing, playing their instruments to a backdrop of Latin verse or simply lying on the floor and breathing properly. It's all a long way from the traditional music-college diet of scales and arpeggios.

Watkin is what you might call a lateral-minded musician. He conducts and he coaches young people, but most Scottish audiences will know him as a superb cellist: he was a soloist, chamber player and principal cello of the Scottish Chamber Orchestra until an autoimmune condition forced him to stop playing just over a year ago. For many instrumentalists, such a blow would be spirit-destroying. Watkins doesn't suggest that the past year has been easy, but when we meet he is full of a drive and optimism that can't be feigned. "I've always been a musician first and a cellist second," he says. "Maybe losing the cello wasn't so bad because it's only ever been one avenue of musicianship for me."

In conversation, Watkin is rather like his playing: energetic and fiercely intelligent but also playful and light-handed. His references dart between obscure musicological texts and the Pixar film Ratatouille. He uses the latter example - a cartoon about a Parisian rat who becomes a chef - to illustrate how real expression can cut through any pompous guff. "Not everyone can become a great artist, but a great artist can come from anywhere," he says, quoting the movie's notorious food critic Anton Ego. I suspect it probably sums up his own approach to music education, too.

The new RCS job couldn't have been better timed for Watkin in terms of occupying the gaping space that cello playing filled for 40-odd years. But it's clear that the new position isn't just a fall-back. Watkin talks passionately about his father's work as a peripatetic violin teacher in Port Talbot during the 1970s - "he was teaching every kid the violin in the biggest council estate in Europe, long before Sistema" - and applies the same principles of broad reach to the RCS, talking intently about the importance of the institution being a resource for the whole of Scotland.

As for those Wild-Card Thursdays? If it all sounds a bit fuzzy - well, it isn't. At the core of Watkin's mission is a deeply serious approach to music-making that pivots around the decidedly unfuzzy discipline of theory. A couple of years ago he wrote a potentially game-changing article for The Strad magazine in which he outlined what he thinks is wrong with the state of string teaching in music colleges and string playing in general.

"At conservatoires," he wrote, "music theory has been pushed to the margins in the minds of many young performers (and often their teachers), whose goal is to build formidable technique. After all, technical prowess is easier to measure than musicianship, and it's generally the prime currency at conservatoires, auditions and competitions." The thrust of his argument is that a thorough grasp of theory is essential for any inquisitive, thinking musician. "How can we find real meaning in a piece if we do not understand how it works? How can we be eloquent without grammar? How can groups discuss interpretation without a common language?"

The article caused something of the stir he intended. "As I pinged it off, I thought, 'I can kiss goodbye to any guest teaching at any conservatoire in the English-speaking world.' It is quite damning of the status quo... But look," he beams. "The RCS gave me a job!"

Watkin himself never went to music college: he studied musicology at Cambridge (where he was also a choral scholar) and learned cello privately until he began picking up work in various London orchestras. Before long he was drawn into the early music crowd, attracted by its "genuine sense of discovery and revolution. This was the late 1980s," he says, "when there were still the real pioneers around. Today the technical standard has probably gone up in early music, but that sense of discovery has been diluted because it's being taught. It's a shame when early music, which was such a revolutionary thing, gets reduced to a new orthodoxy. When you get teachers saying, 'all you've got to do to get work in early instrument groups is play a bulge here and no vibrato here..."

At the heart of Watkin's approach to pedagogy is a desire to empower students to think for themselves, which can't be a bad starting point for any head of department. He tells me about something he almost wrote in that Strad article but didn't because he knew it would distract from the matter at hand.

"At that time there was a huge furore about scandals in music schools and colleges. For me, behind all the stuff about theory is the fact that a relationship between teacher and pupil cannot be dictatorial. It has to be a two-way collaboration; both people have to be learning. My dream is that one day the student comes back to the teacher and says, 'that's a minor subdominant chord there - so it can't be an up-bow like you told me to do'. The faults of the system can be righted from either side." Listening to him talk, I get the sense the RCS could have hired no better person to instigate the process.

Before I go, Watkin opens a desk drawer and rummages around for a CD. It's his last recording, Bach's complete cello suites, made in the months just before he stopped playing and due for release next week. Late in 2013 he was diagnosed with scleroderma, a chronic condition that relates specifically to his fingers: when he presses down on the strings, his blood vessels break. Now he can demonstrate a few bars in a lesson but six hours of rehearsal is out of the question. "I managed to get that recording done in early December," he says, looking down at his hands. "My fingers would be black and blue by the end of the day, but I got it done."

I head home and put on the first disc, and find myself in tears by the end of the first suite's Allemande. Watkin's playing is breathtaking: poised, tender, searching, eloquent. The fast movements really dance, the slow movements really sing. The sound is gorgeous - gut strings on a 1670 Cremona instrument for the first five suites and a smaller, earthier, slightly earlier five-string cello for the sixth. There is grit and solemnity, pain and resolve, but no trace of the anger that his illness must have caused during the recording. Mostly, Watkins shapes his phrases with all the time and love in the world. It's a truly beautiful parting statement.

David Watkin's recording of Bach's Cello Suites is released on Monday on the Resonus Classics label