Eta was born in Sunderland, one of four daughters of Jewish immigrants from Lithuania. When she was a child, her father bought her a violin. After leaving the Bede school, Sunderland, at 17, she began teaching the violin privately and in schools. She looked for a violin tutor book to assist her, but in 1933 there were none she considered adequate. Undeterred, she painstakingly wrote out each lesson for her students, basing each on familiar tunes, and skilfully organising the material. These lessons became the foundation for the first volume of The Eta Cohen Violin Method, published when she was 25.

During the second world war, Eta taught at Cheltenham Ladies' College. She took lessons herself with the distinguished violin teachers Max Rostal and Carl Flesch who influenced her thinking. In 1945 she married Ephraim Smith, a businessman working in the cloth trade, whose parents were also Lithuanian Jews. She joined him in Leeds, where their daughters, Maureen and I, were born. Eta taught from home with determination and passion. Further books followed: three more volumes of The Eta Cohen Violin Method, extra repertoire books, duets and rounds. The method is now available in a sixth edition.

She taught with energy, patience and imagination, tailoring her method to each pupil, and treating parents and students as friends. She thought that a parent should be present at lessons and supervise practising, and that conditions should be made alluring. For instance, she would check that the lesson time did not coincide with a favourite TV programme.