After high school, Dave attended Purdue University, located in West Lafayette, Indiana.

Dave scored a career high 57 points on February 19, 1966, against Michigan, the second most in school history, only behind Rick Mount's 61.

Mainly an assistant to the freshman team, he joined fellow former Purdue standout, George Faerber, under coach Dave Toney.

Schellhase was the head coach at Moorhead State University from 1975 to 1982, where he led the Dragons to two NSIC titles and to six NAIA Tourneys and an overall post-season record of 8–5.

He was the third former Boilermaker to coach at Indiana State after John Wooden's successful tenure from 1946 to 1948 and Bill Hodges' stint from 1979 to 1982.

After his tenure at ISU at the NCAA Division I level, he returned to Moorhead State in 1987 where he led the Dragons to seven NAIA Tourneys and a post-season record of 1–6.

One of his star players, Brett Beeson, led the nation in scoring in 1995–96, before embarking on a lengthy career in foreign leagues.