… but then I think back: I so hated social studies in the lower grades and then history in the higher grades that it was palatable. I dreaded the classes. My projects were always turned in late. I barely passed some tests. The B or C on the report card drew everyone’s eye every time.

It turns out that I really did hate vegetables too!

It was years and years later before I discovered that I had some appreciation for either.

Maybe it’s heretical to say in some circles, especially from one of their own, but I think it’s perfectly okay to hate math! Embrace your hate! Scream and shout! Pull your hair and stomp your feet! And once you wear yourselves out and settle down to catch your breath, then that’s the time to let it go and to look a little deeper…

Maybe more so than any other subject—yes, I am slightly biased—mathematics claims an incredible breadth of subject matter that at first glance may seem completely unrelated and, thankfully, so much of it has almost nothing to do with numbers at all! And those different areas have people actively experimenting and researching, expanding the field everyday!

Arithmetic—adding and subtracting, multiplying and dividing, over and over and over again—is an infinitesimally small part of what is mathematics, but it is the first thing that we point toward and label “math” for our children.

“Sit down and drill times tables” = “math.”

If I told you “vegetables = don’t leave the table until you finish that bitter broccoli,” you might never discover the taste of sweet corn… That would be a shame. You might even pass that experience on to your own kids.

Labels matter… but that’s a different story!

Mathematics is more than ensuring you get the correct change at the grocery store. Mathematics, like philosophy, is about asking questions. Mathematics is about asking “Why…?” Why is that statement true in the first place? Mathematics, like philosophy, is about asking “What if?” What if I changed my assumptions? Would that still be true? Mathematics is about drilling down to the essence of a dilemma, discarding what is unimportant along the way. Mathematics is about seeing the inner patterns and rhythms in nature. Mathematics is about constructing entire universes, sometimes from a handful of simple rules, and setting out to explore them, discovering what follows from those rules. Mathematics is about making sense of what you experience around you, and it’s about hypothesizing about those things that you cannot see or feel.

And yes, mathematics is also about making sure: that you get the correct change at the grocery store; that you make the best choices; that you understand risks; that you are not cheated; that you understand politicians and their polls, and that you can detect erroneous assertions in their logical arguments; that your plane’s wings produce enough lift, that your ship is buoyant enough, and that your bridge will not collapse; that you can protect your information with strong encryption and that you can break your adversaries’ codes; that you can have more cable and satellite TV channels, clearer cellphone conversations; and so forth. It’s even about being a child with a crayon working through a maze, then speculating if there’s a way to solve them all.

My wife once complained that my daughter was zipping through a worksheet of addition problems—but she was doing them “wrong.” I watched my daughter and saw what she was doing: she was doing a few digits on each problem before completing any one. She had deduced the intent of the lesson—what the worksheet was meant to drill. She found the underlying pattern and exploited it, knocking out the page in no time flat!

I smiled. While her arithmetic was not getting any better, she was certainly doing math!

At the dinner table the other night, I asked:

(1) Suppose we take all of the counting numbers—1, 2, 3, …—and make two piles of numbers, the odds and the evens. Would one pile have more numbers than another? [Correct answer: No, they have the same amount of numbers.]

(2) Lets create a third pile, again, all of the counting numbers—1, 2, 3, … . Does that pile have more numbers than just the even pile? [Correct answer: They’re the same.]

(3) If they’re the same, let’s shuffle the odd pile back into the even pile. Now does it have more stuff than the all numbers pile? [Correct answer: “No, they’re still the same.”]

(4) Someone else asked: “Are there different kinds of infinity?” [Answer: Yes, there are—some are bigger than others.]

That’s math too.

Like homeschooling, it’s about finding the teachable moments. But it does mean having some understanding of what math is. Then you can learn that you like most vegetables, even if you dislike broccoli.

You're daughter's arithmetic reminded me of, I think it was Pascal's triangle, where as a kid I had an assignment to fill out the triangle to 16 rows and then color in all the odd numbers. Dense as I was, it took me to about row 8 before I figured out I didn't have to do all of the tedious additions, but only add the last digits to determine odd/even.

Loved the observations about Math, and I agree with every one of them. (except I think the world could do without non-linear differential equations, at least I could anyway).