After three years of school, my eight-year-old believed he hated math. I didn’t send him to school thinking that, so yes, I consider this a failure on School’s part. I myself am quite comfortable with math; I got all the way up to Calculus, which was required for my BS in Natural Resource Science. I can remember doing my Calc homework as a break. I liked how orderly math was, the problem-solving required, the way the Right and Wrong are clearly defined. My point is that my children aren’t picking up on math anxiety from me.

My oldest, who was homeschooled through first grade using Singapore Math, began second grade in his alternative public school well ahead of grade level and continues to be a top student in math. His early-years math experience (and curriculum) was much different from his brother’s. My younger son had three years of Everyday Math, which, in my opinion, is a terrible curriculum. He never stayed with anything long enough to learn it. The curriculum jumps around, supposedly so lagging students get lots of repetition (but not all at the same time) and advanced students don’t get bored. For three years his only homework was math sheets and reading at home, and even though the math sheet usually took only ten minutes, we had to add in the twenty minutes of fighting about it. And it seemed he wasn’t learning anything. When he finished second grade, he was still shaky on, for example, time and money. All that fighting, and it was all a waste of time.

When I decided to homeschool him, I decided to start with Life of Fred, gently. We began over the summer with the first book, Apples. We began with me reading the chapter aloud and going over the questions with him while he wrote the answers. We did it all together for the first two books, a chapter per day. Some days he fought it, but it got better. By the time we hit fall, we continued with one chapter per day, but I began having him read the chapter on his own, do the questions, and then we’d go over the answers together. Again, he fought this sometimes, but it gradually got better. Now he reads the chapter, does the questions, checks his answers, and moves the paperclip to the next chapter, all on his own. If he doesn’t understand a question or needs help, he tells me. Sometimes he still whines about it. But he does it. He’ll be starting the fifth book soon.

I’ve toyed with the idea of introducing something more rigorous at the half-year point, but I want to tread lightly. I don’t want him hating math. I hope he comes to see it as I do, a useful tool to get to where you need to be. I use math all the time–in recipes, in knitting, in sewing–and I try to talk about it when I do. One day not too long ago we were talking about I don’t even know what when I mentioned an Ancient Greek had used only math to figure out the circumference of the earth, and he came super close to the actual measurement. How? my kids wanted to know.

So I looked up the details. My eight-year-old and I looked at our globe pillow and at the map. He said he pictured the equator as a rope around the earth. Perfect, I said, and we moved to our circle rug. Pretend the edge of the rug is the rope. Pretend we’ve cut the earth in half. He picked two points on the edge of the circle, we tried to find the middle of the rug, we measured the angle, we did the math. Mostly I did the math–it’s not easy math. But he was so excited by it.

This is not like school math! He exclaimed. This is math that really does something!

We borrowed The Librarian Who Measured the Earth from the library and read it aloud. I bought him his own protractor and showed him how to use it. I printed out a page of angles (from this awesome site) for him to practice measuring. Next up is drawing circles with the compass so he knows exactly where the center is, and trying to find the circumference using Eratosthenes’ method, a bit more precisely than we did with the circle rug. I predict we will be outside measuring the angles of shadows before too long.

I can just imagine if I’d decided it was time for him to measure a sheet’s worth of angles just because. Fight, fight, fight. (What’s the point? What do I need this for?) But because he is excited about the way this Ancient Greek used angles to satisfy his own desire to know how big around the earth is, he wants to know how to measure angles. And in this way, I remind myself (deep breath), he will come to learn what he needs to know.

Sometimes, you just need some flashcards.

My oldest, who returns to school this week, began learning multiplication two years ago in the third grade. But they don’t require them to memorize them anymore, apparently. This summer, I decided he was memorizing those multiplication tables before starting fifth grade. Mind you, his grades in math are fine. But as he moved into division this past year, I could see it was harder than it had to be. Do you remember chanting the times tables as a class? It was boring as anything, but knowing those facts make everything that comes after easier. My son, however, was really resistant to memorizing them. Eventually, early this summer, he was able to verbalize why: “I want to figure out the answer on my own.”

A-ha! He thought that memorization was somehow akin to cheating. I picked a neutral time–we were alone in the car together, on the way to the supermarket–to try to explain my reasoning to him. I told him that if he didn’t understand the process of multiplication, if he didn’t realize that 8×3 was the same as 8+8+8, then I wouldn’t want him memorizing the facts. Facts without understanding is no good. But he does understand the process, and now it was time to know these facts so well that his brain isn’t wasting time with 8+8+8, it just spits out 24. Just like he doesn’t have to start from A just to know what letter comes after T–he memorized the alphabet in order a long time ago without even thinking about it. That’s not cheating, he agreed.

He thought this over for a bit, and then he said, “I think writing them out would be a good way to memorize them. Often when I write myself a note so I don’t forget something, I end up not needing the note because writing it down made me remember it.” I told him I thought that was an excellent start, and chose not to remind him that I’d suggested this months ago and he refused. He needed to understand why he was doing this, and I was glad he came up with this strategy on his own.

Once he understood, the rest was relatively easy, because he was on board. I’d read somewhere to group the like tables, so we started with the 2s (easy), and followed that with the 4s and 8s. He wrote out the table, and I quizzed him with flash cards. I got out our Cuisenaire rods and we grouped them different ways to see how 2s, 4s, and 8s are related. Then we moved on to 3s, then 6s, then 9s, and finally 12s. I reminded him to use what he knew–if 7×2 is 14, then 7×12 has to end in a 4. If he wasn’t coming up with 12×8, I’d ask him 10×8 and then 2×8 before repeating 12×8. We left the 7s for last, because they’re not really related to anything else, but we’d covered everything in them by then, at least. (5s, 10s, and 11s didn’t need much work at all.)

They’ll need to be reinforced, of course, to make sure they stick. Sometimes I just ask him multiplication questions out of the blue, which has led to my youngest randomly stringing numbers together into math problems for us to answer. I wouldn’t have said I’m a fan of rote memorization, but it turned out I felt strongly that he should know these, really know them. Again, if he didn’t understand what multiplication is, I wouldn’t want him memorizing facts with no understanding. But I can also remember having to memorize oral presentations when I was just a little older than he is, and it certainly trained my mind in a certain way. Maybe next summer we’ll memorize some poetry…