Mrs Schack has resisted pressure from colleagues to go for headship, believing she has the best of both worlds: applying leadership skills and having contact with children.
But, said the 50-year-old deputy head of Clayton Church of England primary in Bradford: "You have to be careful you don't get complacent."
Half of her working week at the 450-pupil school is spent teaching, the other on leading areas such as curriculum and staff development.
"When you've done a job like this for a while, you can play a key role providing the experience and confidence to cover when the head is away, and you can also share the burden of leadership with them.
"But that doesn't mean you don't want to try new things."
The National College for School Leadership believes there are thousands of assistant and deputy heads who feel the same way as Mrs Schack and has devised a new training package for them, which starts this month.
Research by Peter Smith, head of Swallowdale primary in Melton Mowbray, Leicestershire, for the college also reveals that two-thirds of assistant heads do not want headship. Caroline Batchelor, an assistant head at his 420-pupil school, says that she does not want to leave the classroom.
His study, based on logbooks kept by assistant heads, shows they were happy being teachers with management responsibilities. "Leadership is not just about headship," he said.
Both Mrs Batchelor and Mrs Schack are hoping to join the second cohort of the national college's pilot programme for established leaders in September.
It introduces participants to new research and thinking on leadership and gives them time to reflect on their own role in improvement and raising pupil performance.
Chris Cotton, a leadership consultant involved in the design of the NCSL pilot, said: "The notion the head can lead the school singly just doesn't exist any more."
Shortage of heads, 25