Gears are at the heart of so many things around here. Scott is building a race car for the Drag Strip that is around the corner from our house. Both boys like to build motorcycles and bikes, and finger bikes, and scooters and anything else with wheels, really. I can see them going into fields like engineering or design or drafting. They are artists. Anything to do with building seems to be their thing. And because of that, I taught myself to love math.

Math has not always been an interest of mine, or a passion, as it has become. I decided I needed to develop a love for it, in order to help my boys develop to their full potential. The way their minds work, the things they are interested in, all involve math; although at six- and nine-years old, they hardly understand that. I do. And so, it felt imperative to get my head around the beauty of math, the complexity, the poetry of it; whatever was lovely and intriguing about it, so I could teach it from a place of love.

This may seem like a completely different line of thinking – but it all comes back together in a moment. At dinnertime the other night, we had to address the issue of being Contrary, or “perversely inclined to disagree or to do the opposite of what is expected or desired.” (from the online dictionary)

Boys need to challenge one another, and themselves, to find their boundaries. Scott has explained this to me, because I didn’t understand their need for constant wrestling. It is something boys need to do. Not like girls never bicker. I grew up in a house full of girls, and we definitely did our share of arguing, we just were not physical about it.

That’s all well and good for the boys building their own strength of character or what have you, but they had started disagreeing with everything we said too. We had to nip that in the bud. Scott talked to the boys about taking a breath before simply disagreeing out of the habit of wanting to be opposite, or contrary.

The very next morning, as Ben and I were delving into our Math lesson, we started with a page out of the Quadrivium. It was only our second day of doing this, the first day focused on the Number One in Mathematics and Philosophy – one being a simultaneous circle, center and the purest tone… (and so much more – truly – this is gorgeous writing). On the second day we looked at the Number Two, and the idea of Opposites: two sides to every coin, “the essential basis for comparison, the method by which our minds know things.”

There was a discussion of two, duality, opposites in music as in a ratio of two to one, or various octaves. Of course opposites or the idea of two is pivotal in geometry, and in language even; we use the idea of two being used together with the prefix bi-, “but when the divisive quality of two is invoked, words begin with the prefix di-, thus discord or diversion.” We looked at the word bicycle, and then words meaning to take apart, like dissect. It was fascinating to see such a simple thing as the number two being used across so many disciplines. As well as helping me see that this phase of disagreeableness is something useful and a stepping stone for the boys to learn to compare and contrast, learn and understand.

Again, something we had been looking at on our own, in a dinnertime conversation, came up in the context of study. I love when that happens.

photo from here