A list of All Great West Conference Schools. Every college and university within the Great West Conference has been included. This conference competes in Division I of the National Collegiate Athletic Association. Division I tends to be made up America's largest colleges and universities. By definition, Division I schools are allowed to offer athletic scholarships. The NCAA (originally known as the Intercollegiate Athletic Association) was originally founded in 1906 to make collegiate sports safer due to the growing number of injuries and deaths occurring out on the field. Suffice to say, college sports are much safer today due to the NCAA's efforts.