During her tenure, Taylor has coached 19 first team All-Ivy recipients, one Ivy Player of the Year, two ITA Eastern Rookies of the Year, one ITA Eastern Senior Player of the Year, one ITA Eastern Player to Watch recipient, and one ITA Eastern Arthur Ashe Sportsmanship and Leadership recipient. The Brown Women's Tennis Team was the 1989 and 1996 ECAC Champion, and was the runner-up 1988. Under Taylor's direction, Brown has won two Ivy League titles, in 1991 and 1997, and has received three Team Sportsmanship Awards.
Taylor herself, just may be the only Rhode Island athlete to win state championships in three different racket sports: tennis, squash and racquetball. As a tennis player, Taylor began swinging a racket at the age of five and later achieved top rankings in New England in adult competition. Today, Norma continues to compete in adult senior events, including the National Grass Championships, the National Intersectional Championships, and Addie and Friendship Cups. Taylor and her partner ranked #1 nationally in the women's 45 doubles for 2001. Taylor and her partner Mary Rompf ranked #1 in the US in Women's Open Doubles for 2001.
In regards to other racquet sports, she was the Rhode Island women's racquetball champion in 1978, the Rhode Island women's squash champion in 1986 and the runner-up in the Rhode Island squash championships in 1987 and 1988.
Since graduating from the University of Rhode Island in 1974, where she played the #1 position for the tennis team, Taylor has pursued various instructional positions. She has taught full-time at indoor clubs and various tennis camps across the nation, including John Gardiner's in Scottsdale, Arizona and Sun Valley, Idaho. During the summers of 1986 and 1987, Taylor was the head teaching professional at the Newport Casino, home of the Tennis Hall of Fame, and more recently the Head Tennis Professional at the Warwick Country Club for the summer of 1997.
Taylor is a certified member of the USPTA, and in the past has served as a member of the Eastern Regional Women's Tennis committee. She has also coached many of the Girls' 18's Intersectional teams for New England, achieving a #3 national finish in 1992 and #2 in 1996 out of 16 teams. Norma serves on the board of the Senior Tennis Foundation, an organization developed to promote senior tennis players in New England.
Taylor lives on the East Side of Providence, close to the Brown campus.