He received his doctorate in 1918 with the dissertation Norsk skulesoga det store interregnum, 1739–1827 (Norwegian School History.
He participated in an investigative committee on the issue from 1920 to 1921, and he even conducted a college course at Bondi in Asker that same year.
When the Norwegian College of Teaching in Trondheim was established in 1922, Høverstad was selected as a lecturer in history by the majority of the expert committee.
However, the ministry chose to follow the committee's minority, and it appointed Arne Bergsgård instead of Høverstad.
He served as the publisher and editor of Norsk pedagogisk tidsskrift (the Norwegian Journal of Education) from 1917 onward.