Bruce A. Van Orden reports that Hyrum Smith went to school much earlier than Joseph.
Bruce A. Van Orden, "Hyrum Smith," Encyclopedia of Mormonism, 4 vols. (Salt Lake City: Deseret Book, 1992), 4:1329
Hyrum was born to Joseph Smith, Sr., and Lucy Mack Smith on February 9, 1800, in Tunbridge, Vermont. During his childhood, the family moved to eight different locations near the Connecticut River while the father struggled as a farmer, storekeeper, and tenant farmer. At age eleven, Hyrum was sent to Moor's Charity School, associated with Dartmouth College. About two years later, a severe epidemic of typhoid fever broke out and Hyrum returned home ill to find several siblings ill as well. Joseph, Jr., was stricken with the dreaded disease, which developed into osteomyelitis in his left leg. Hyrum, who was already recognized for his tender and compassionate nature, became young Joseph's nurse, developing an enduring bond between the brothers.