When Clark and Jain get to the quadrivium in The Liberal Arts Tradition, they make a case for the manner in which the mathematical arts of the quadrivium shape the heart and soul of man just as the arts of the trivium do.
Christian classical schools must uphold a high standard for mathematical education precisely for its special role in human formation and developing the virtue of the mind.
They don’t condemn the practice, but they do point out that rote memorization of math facts isn’t the point of arithmetic. Its classical purpose was different, as demonstrated by Nicomachus in the first century AD.
For Nicomachus, deeply understanding the necessary connections and relationships among the numbers would have been an essential element of the liberal art of arithmetic.
If you know Charlotte Mason well, you are probably nodding, and thinking, “Oh, right, education is the science of relations.” Math is so often a stumbling-block for students, and we tend to prize computation and right answers above this intuitive sense of the relationships that exist in numbers. I really love that Clark and Jain introduce the idea of wonder into arithmetic—something I suspect few of us ever experienced. Besides the personal delight in math that this affords for each student who experiences it, wonder actually has a practical side as well.
Students who encounter mathematics in wonder are far more likely to commit to the rigors of the work.
Maybe not all of them, but you are definitely increasing the likelihood of a student progressing well in math if has learned to enjoy it. I’m reminded of Charlotte Mason’s justification for mathematics in the curriculum:
We take strong ground when we appeal to the beauty and truth of Mathematics; that, as Ruskin points out, two and two make four and cannot conceivably make five, is an inevitable law. It is a great thing to be brought into the presence of a law, of a whole system of laws, that exist without our concurrence,—that two straight lines cannot enclose a space is a fact which we can perceive, state, and act upon but cannot in any wise alter, should give to children the sense of limitation which is wholesome for all of us, and inspire that sursum corda [a call to lift your heart in worship and praise] which we should hear in all natural law. (Philosophy of Education, p. 230-31)
This is one of those things that a trained math teacher probably finds it easier to do than a homeschooling parent who may have had a bad experience with math. Miquon Math, which I used with most of my early elementary students, went a long way toward giving me some joy and wonder and sense of relationship in arithmetic. I have also discovered that simply slowing down the process of arithmetic so that a child has time to enjoy success and feel competent at one level before moving on creates a better relationship-building environment.
But wonder in arithmetic is only the beginning—it can take you further.
Wonder was not the only end of arithmetic. The ancients also believed that arithmetic led the soul from wonder to wisdom.
The discussion in The Liberal Arts Tradition gets a little heady at this point, and I really encourage reading the book and tackling the ideas for yourself. Read the footnotes, too. Even if math isn’t your forte (it isn’t mine), you might hear the sursum corda and catch a glimpse of wonder, or at least hear a whisper that might help you understand why others love math so much. That’s worth something.
You’ll want to read what Brandy thought about this section, too. I think she heard the sursum corda.
Copyright 2018 Karen Glass
Link to all the posts in the Liberal Arts Tradition discussion.