"For the sole true end of education is simply this: to teach men how to learn for themselves; and whatever instruction fails to do this is effort spent in vain."
I must admit that reading about mathematics in the Classical Education method made me feel heavy and a little sad. I decided that I needed to understand more of the background to this educational style if I was to make an informed decision about how it might fit along side home made math resources. As a result this blog post is rather lengthy. If you use the Classical Method I am very interested to hear why you chose it and how you find it and to be correct if I've misunderstood it's implications. Please comment here or email me firstname.lastname@example.org
History of the Classical Curriculum
The Classical Education method can be traced back to 5th century (Middle Ages) when the author of Latin prose, Martianus Capella, wrote his allegory De nuptiis Philologiae et Mercurii. A work dedicated to his son, and in which the liberal arts are depicted as wedding gifts of
seven maids who will be Philology's servants: they are the seven liberal arts: Grammar (an old woman with a knife for excising children's grammatical errors), Dialectic, Rhetoric (a tall woman with a dress decorated with figures of speech and armed in a fashion to harm adversaries), Geometry, Arithmetic, Astronomy and (musical) Harmony…. Two other arts, Architecture and Medicine, were present at the feast, but since they care for earthly things, they were to keep silent in the company of the celestial deities.
(Quote from here)
These 7 liberal arts were considered as necessary for a free person partake in civic life in Classical antiquity (Sarudy). Although the work has been highly criticised (for its bizarre nature. Even C. S. Lewis said "the universe, which has produced the bee-orchid and the giraffe, has produced nothing stranger than Martianus Capella" ) it went on to strongly influence the curriculum of the early medieval period, throughout Europe, until the rise of scholastic Aristotelianism.
During the Renaissance Petrus Ramus, a French humanist academic, revived these liberal arts. Ramus’ works are highly controversial and written in a time of complex political and religious reform. It appears he viewed the Aristotelian curriculum as inefficient and set about to systemize the education system, enabling students to quickly learn subjects of use. Modern critics claim he oversimplified the arts and that his writings "are the amateurish works of a desperate man who is not a thinker but merely an erudite pedagogue" (Ong, The Barbarian Within, 1962: 79-80) (I looked up “erudite pedagogue” it means: 'well read, strict or pedantic teacher'). His reforms, however, greatly influenced the education system. Instead of reading lengthy ancient texts, students could now read a summary in textbook form. This made education cheaper and more readily available to the lower classes.
In the 1930s Mortimer Adler and Robert Hutchins compliled the “Great Books” of Western Civilisation, as a center point for a revival in secular Classical Education. Ironically Adler was a philosopher in the Aristotelian tradition (of whom Ramus was so famously critical). Hutchins was an educational philosopher, notably the president and chancellor of Chicago University where he implemented two year, generalist bachelors degree, reflecting the philosophy of Ramus (this was discontinued after his retirement). He notably removed the school’s football program, fraternities and religious organizations as they distracted from academic study.
The Christian Classical Education movement is owed mainly to Dorothy Sayers, a murder mystery author, and her famous essay “The Lost Tools of Learning” in the 1940s. Her outline of “the medieval trivium subjects (grammar, logic, and rhetoric) as tools to enable the analysis and mastery of every other subject” (Wikipedia) can be linked back to Capella and Ramus.
What is Classical Method?
Education in the Classical method is dependent on training the mind. As mentioned above, it commonly follows a 3 part process, or trivium.
The early years of school [grammar stage, grade 1-4] are spent in absorbing facts, systematically laying the foundations for advanced study. In the middle grades [logic stage, grades 5 to 8], students learn to think through arguments. In the high school years [rhetoric stage], they learn to express themselves.
- Susan Wise Bauerm, The Well Trained Mind
The trivium focuses on literacy tools and applies this theory of learning to all other subjects aka The Quadrivium consisting of the remaining of the 7 liberal Arts: Arithmetic, Geometry, Music, and Astronomy. For more info see the link above and read Dorothy Sayers, The Lost Tools of Learning.
Math in the Classical Curriculum
"Math instruction at the grammar level ought to concentrate upon the installation of foundational factual material into the minds of our children. The best installation of math facts into young heads requires that teachers present those facts in a connected and sequential manner as well as utilize constant repetition and speed drills.” - A. Becky Rathbun, Classical Homeschooling
I find this emphasis on fact memorisation ironic given that “Ramus… ridiculed the meaningless rules and facts that young students were compelled to memorize (Nancelius Petri Rami Vita: 212; cf. Ong 1958: 321n)" (Stanford Encyclopedia of Philosophy) . It appears to me that while modern implementers of Classical Education concede to the usefulness of concrete manipulatives as a tool for students to grasp “the foundational facts”, such as addition, subtraction etc., the main emphasis seems to be on retention of fact, rather than an understanding of concepts. Once again ironic, considering “Ramus wanted the study of every art to be directed toward practice. There was no point in memorizing rules unless one also learned how to use them" (Stanford Encyclopedia of Philosophy).
My reading of Dorothy Sayers seems to agree with the above statement that the grammar stage is primarily with memorising facts, particularly the multiplication tables. However she does go on to say that in later stages it should “take its place as what it really is: not a separate "subject" but a sub- department of Logic”. Seeming to imply that it is indeed more than the simple memorization of facts but part of our way of understanding and deciphering the world.
Can home made math be used with in a Classical Education?
When I originally wrote this article, I actually said a straight out "no" to this question, however I think if we look at the philosophy of Classical Education on a whole we may find space for home made math activities, particularly in the Logic and Rhetoric Stages.
Although no two educators will implement an educational philosophy in the same way, a strictly Classical Education seems to see math as more about training the mind to appreciate and retain facts than in creating environments to allow the child to build their own knowledge and apply concepts. Ramus, however, may have been more open to the type of activities presented here and you may find them useful too. Dorothy Sayers said, “But above all, we must not neglect the material which is so abundant in the pupils' own daily life.” I think you will find home made math to reflect this philosophy. It seems that although the educational philosophers behind the Classical method recognized the need for education to be logical, practical and applicable somehow mathematics gets bypassed and relegated to merely drill and fact regurgitation. Please don’t misunderstand me, I do think repetition and memory has its place in mathematics, and there are plenty of resources currently available elsewhere to fulfill this area of education. If you are looking for something beyond repetition and drill, which speaks to the beauty and practical, hands on application of math, then home made math is for you. Check out some of the free activities to see what I mean.