I looked up schoolmasters in "Patrick O'Brian's Navy: The Illustrated Companion to Jack Aburey's World" by Richard O'Neill. This book says that "Many ships had a schoolmaster, whose primary task was to teach navigation and mathematics to the midshipmen, although some also taught the younger seamen and boys to read and write."

In some ships, the Chaplain acted as the Schoolmaster; he received extra pay for this task. Generally, a ship lower than a third rate did not have a Chaplain.