[6] His education in cello and piano continued[6] at the Gnessin Institute and Moscow Conservatory, where he was instructed by Boris Khaikin, Gennady Rozhdestvensky, and Valery Polyansky.

[5][4] In the 1980s, he taught at the Gnessen Institute and then left the Soviet Union in 1990 for a teaching position at the University of Canterbury in New Zealand.

[6] In 1995, Ivashkin and his wife, the cellist Natalia Pavlutskaya, founded the Adam International Cello Festival and Competition.

He was also artistic director of annual festivals in London, including The VTB Capital Prize for Young Cellists.

As an author and editor, Ivashkin published more than twenty books,[3][5] and more than 200 articles in Russia, Germany, Italy, the US, the UK and Japan.

Ivashkin collaborated with composers such as Krzysztof Penderecki, Edison Denisov, Sofia Gubaidulina, Giya Kancheli, Rodion Shchedrin, Nikolai Korndorf, Dmitri Smirnov, Elena Firsova, Alexander Raskatov, and Alfred Schnittke,[3] as well as John Cage, George Crumb, Mauricio Kagel, Peter Sculthorpe, Brett Dean, Arvo Pärt, Vladimir Tarnopolsky, Augusta Read Thomas, James MacMillan, Lyell Cresswell, Roger Redgate, Gabriel Prokofiev and Gillian Whitehead.