He graduated from Doland High School in 1953. From 1954 to 1955, he attended Bethel College at Saint Paul, Minnesota. From 1956 to 1957, he attended Huron College before serving in the United States. Army from 1958 to 1960.
He was the first Lieutenant Governor in the history of South Dakota to move into the Governor"s office. As of 2014, he is also the most recent Democrat to hold the title of South Dakota governor. In 1961, he obtained a Bachelor of Arts degree from Huron College.
From 1961 to 1965, he served as a teacher at Doland High School.
In 1965, he completed a graduate work at the University of South Dakota before becoming a farmer. Wollman, a Democrat from Hitchcock, South Dakota, was elected to represent Spink, Hand and Hyde counties in the South Dakota State Senate in 1968 and re-elected in 1970.
He was first elected Lieutenant Governor in 1974, on a ticket with Governor Richard F. Kneip.
On June 6, 1978, Wollman was narrowly defeated by State Senator Roger McKellips in a bid for the Democratic nomination for Governor.
However, Wollman was already scheduled to succeed to the governorship on July 24, 1978, when Governor Kneip resigned to accept an appointment as United States Ambassador to Singapore. The new governor"s term lasted a little more than five months, ending on January 1, 1979 when he was succeeded by Republican Bill Janklow (who defeated McKellips in the general election). While he was in office, he worked to speed the repeal of the property tax and increase the budget for higher education.
Wollman"s family originated from Russia and is of German descent.