Although we may want to pursue the wonder of the world and open the beauty of creation with mathematics, we often find ourselves in the weeds. We teach our children to identify numbers, patterns, and symbols. We teach them to compute sums and products as though the calculator didn't exist. In short, we teach arithmetic. Why do we place such an emphasis on teaching our children to do what a calculator can do?
The answer to this my friends, can be found in the hidden meaning behind the numbers. As Nicomachus so clearly tells us, "Any attempt at philosophy must start with these mathematical subjects. They are the bridges that take us from the sense and opinions to the mind and understanding, from the concrete and familiar objects to immaterial and eternal abstractions, from matter to soul."
From matter to soul... By starting our study of the world with arithmetic, we are leading our children from the concrete to the abstract, from the matter in front of us to the soul behind it. That addition problem isn't about creating a calculator out of our own flesh and blood, but rather about leading a child towards the creator.
These mathematical subjects that launch philosophy are the study of quantity through arithmetic and harmony, and the study of size through geometry and astronomy. Of these four, arithmetic comes first, because the study of harmony, geometry, and astronomy rely on the language of numbers. In arithmetic, we are not simply teaching children to compute, but rather to think, comprehend, and communicate in a celestial language.
Algebra 1 and 2 math masters have been reading about these truths from Nicomachus this year while learning the advanced arithmetic and algebra techniques. What feels like a great balance to me is an essential need in mathematics learning which speaks to our souls and reminds us of what it is to be human. Let's glory in our creator together as we dive deeper and deeper into the study of number, infinity, and beauty.