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Astronomy is the capstone of the Quadrivium because it is number in time and space, which is to say that the whole cosmos is a dance, which is a form of play.
In Laws VII (819) Plato tells us, when the Athenian is describing how children should be taught the fundamentals of mathematics, that it is best to imitate the Egyptians. “In that country,” he says, “arithmetical games have been invented for the use of mere children, which they learn as a pleasure and amusement.”
Most of our traditional childhood games are of this nature. There are the obvious games involving cards and dice where you have to count and keep score, and games like jacks, hopscotch, and jump-rope that require not only counting but physical movement.
Still less obvious are the nursery games that parents play with their children. Many of these involve rhythm and movement, such as “Pat-a-cake, pat-a-cake baker’s man.” Something mind-blowing that I learned recently is that there’s a part of the brain that specifically links your fingers to numbers. Think of the finger game that we sing with our babies “Where is Thumbkin?” When I sang that to my babies, if I thought of it as anything educational at all, I thought of Object Permanence. But when we have our little ones make their own hand motions to that song we’re giving them a physical skill that will translate to physically preparing their brains for a deep understanding of Number.
Here’s another one that lays the groundwork for mathematical thinking—Twenty Questions. When you ask the first question, “Animal, vegetable, or mineral?” you’re asking about categories, and then the second question, “Is it bigger than a breadbox [or microwave for most of us nowadays]?” asks a comparison question that is mathematical in nature.
The only curriculum I’ve ever seen that’s even remotely close to this understanding, is the out of print book by Horace Grant, Arithmetic for Young Children. In that book, he has the students use a collection of objects to play with Number, presented in an orderly fashion. Along with this, he asks questions that spark the imagination and help the child make the leap to mental math. Formal, written arithmetic is delayed until the book Second Stage of Arithmetic, and is introduced along with having the child think through numeration (why we name amounts the way we do) and notation (why we write numerals the way we do). It’s a brilliant presentation, which is begun around ten to twelve years of age, far later than most of are comfortable with, used as we are to rushing academics, but I think it’s developmentally appropriate.
Another resource I recommend highly is Denise Gaskins’ Let’s Play Math website and book series. They’ll give you lots of ideas of things you can do to prepare your child for the formal study of the Quadrivium.
I haven’t used this finger math curriculum with young children (I’m generally against formal lessons for children under six or seven years of age), but it seems to fit my qualification of playful. I suspect it might work for older students who may have missed all these games and may need remedial arithmetic.
