She was an instructor at the University of Toronto’s Mathematics department while she was getting her PhD and after she completed it, she was promoted to lecturer. However, before she took that job, she decided to spend a year at the University of Gottinger in Germany first. Once she returned to Canada to take the job she didn’t get promoted to assistant lecturer until 1941. She taught thirteen classes a week in mathematics and engineering, with up to seventy-five students per class. This left very little time for anything else, but she still managed to work on her own research projects in the evenings. In 1952 she was promoted to associate professor.  She officially retired from the math department in 1961, but she kept teaching at the university for five more years. She was known for helping students and even held socials in her home. She was also an active participant in the Canadian Association of University Women.

She was a key provider for her sisters after their husbands died. She got married in 1953. After he died in 1968 she started teaching again, this time at Upper Canada college. She continued to teach there until she died in 1974. In 1995 the Kriegar-Nelson prize was created to honour an outstanding woman in mathematics.