First things first: there is no evidence of that quote actually appearing in a text of that era. This post by a historian goes into a search of the historical record. I can also offer that the moniker "principal" wasn't that common in 1815, much less widespread enough to have enough users to form an organization that released a publication. Most schools of the era were one-person shows - the teacher was the curriculum director, the custodian, the dean, and the instructional and managerial leader (without those titles or frameworks as they're all modern day demarcations in the work of educating children.) Some schools did have multiple teachers and required an administrator, but they were more likely to known as "Head Teacher," "Headmaster," or "Head of School."

Paper could be found in schools on that era, but generally speaking it was contained to books. Slates and chalk were available but were more likely to be seen in a college lecture space than a school building. The primary form of assessment of the era was known as "recitations." A teacher would read from a book or lecture and a young person would repeat back what they heard. They may repeat it back in a 1:1 conference, as a part of a small group, or in a choral response with their class. Students of the era were also expected to memorize content and recite it on demand or as a part of the college application process.

Individual sheets of paper for students to write on didn't become to norm until mid-century 1800's. The multiple choice test - a test entire done via paper - emerged in the 1910's.