FALSE. Old school gym class started with stretching before activity and working out. However, current research shows stretching before strength training and working out may not be the best thing for performance for two reasons. First, stretching "cold muscles" can cause trauma to connective tissue such as tendons and ligaments. Second, stretching before activities such as strength training or sports may cause the connective tissue which supports the joints to become loose and not provide the tension needed to support the specific joint(s) being used.
It is recommended to perform a light activity such as walking, rowing, light jog etc. to warm the muscles and connective tissue. When strength training, perform the first set with lighter weight for higher reps around the 15-25 rep range. This will draw blood into the muscles and joints as well increase the range of motion in the joints without becoming loose and risking injury. It will also warm the muscles and connective tissue being used for the workout.
Stretching after your workout is more beneficial because it will draw blood which carries oxygen and nutrients into the muscle to increase healing and flush out lactic acid. It will increase flexibility because the muscles will now be warm and more pliable. Think of a rubber band. A cold rubber band does not stretch well and may snap if stretched too far. A warm rubber band will stretch more effectively.