He was born in Marietta, Pennsylvania and raised in Roxbury, Massachusetts. Serving in the Army for Korean War duty, Dawson played with the Army Dance Band while stationed at Fort Dix from 1951–1953. During his tenure, Alan explored the post-bop era by performing with pianist Sabby Lewis. After being released from the Army, Alan toured Europe with Lionel Hampton. 　　Dawson is best remembered as an early teacher of Tony Williams, and Sawyer Brown drummer, Joseph Smyth. Other former students include: Terri Lyne Carrington, Julian Vaughn, Vinnie Colaiuta, Steve Smith, Kenwood Dennard, Gerry Hemingway, Jeff Sipe, Billy Kilson, and many others. He began teaching at Berklee College of Music in 1957. Dawson suffered a ruptured disc in 1975 which led to him halting his touring schedule, to leave Berklee and limit his teaching to his home in Lexington, Massachusetts.