Finding Math

and below that:, an older Ethan, and factorials at the dentist's office

Karen James wrote:

One of the things that worried me most about the idea of homeschooling Ethan was the thought of "teaching" him math. Although I knew I had Doug, I also felt like I responsible for our homeschooling. I hadn't really looked into unschooling at that point. I knew about it from a friend, but I didn't understand the principles of it.

Doug and I both knew in our hearts that homeschooling was a better option for Ethan, so I needed to move past my math worries. One way I did that was to ask myself how I taught Ethan to walk. It donned on me. Wait a minute...I didn't teach him to walk! He learned to walk. Well, how did *that* happen?

I facilitated an environment for a child who was learning to walk. I made sure there were no sharp corners at his head level. I got a couple of things he could hold on to, pull up on, push, and explore. I let him hold my fingers and walk between my legs. One of his most favourite things to do was push our dining room chair around and around the dining room table, with either Doug or me holding on to the back of the chair to keep in on it's path. We made sure there were not obstacles in the way of this path, because it seemed so important to Ethan to do this every day, multiple times a day. Doug and I use to giggle over the idea of anyone watching either Doug or me doing these laps around our room. Anyone could see us clearly through our large window that was right close to a walking path.

Okay, so we didn't teach him to walk. But how did we teach him to talk? We didn't. Huh. He learned that too?! He was surrounded by language. Doug and I read to him often, some books over and over upon Ethan's request. We played with words. We repeated words that Ethan liked to repeat. Ball. Ba. Ball. Ba! Yes, ball. Ba! Yup, ball. You get the idea. Again we facilitated his exploration of language. We played with him as he explored. We made his environment rich with what he was interested in. And he learned! Wow!

(It is interesting to note too, that Ethan was almost 2 years old before he said his very first word, and he didn't babble. But within weeks he was saying full sentences with humour. Now he has a lovely vocabulary. His word choices delight me.)

So, I took the leap and we began homeschooling, with me trusting that like walking, talking, reading, writing, and all the other things he had managed to learn through his play and exploration and with our active support, he would come to have a meaningful understanding of math too. When I came to a greater understanding of unschooling, I suspected we had not made a error in judgement. As I have watched Ethan's relationship with math grow and deepen, I knew we had not.

What I didn't realize when I was worrying about how to bring math to Ethan, was that Ethan had already found math. He found it on his fingers. He found it in the seeds of an apple I had cut open. He found it in the peas spread over the tray on his high chair. He found it in every repeated drop of his cup or spoon. He found it in the music we listened to. He found it in the timing between jumps on his jolly jumper. He found it in the balance he needed to take the next step. He found it in the distance between steps. It was everywhere already, and he was already finding the art in it. I just needed to stop my worrying and start having fun.

So I have.

Karen James, published (rerun) on Facebook February 28, 2014

Karen, nearly two years later:
Yesterday, at the dentist's office, after learning we homeschool...

Dental hygienist, to Ethan: "So...what's your favourite subject?"

Ethan: "Well, I really like math."

Dental hygienist: "Really?! That's great! What are you doing in math right now?"

Ethan: "Well I really like factorials and...(looking at me) what were we talking about the other day?"

Me: Pausing to think, while my brain reboots.

Dental hygienist, to Ethan again: "So, you like fractions."

Ethan: "Yeah. But I was saying I like *factorials*."

Me: Remembering what we were talking about the other day, "Oh! Exponents."

Ethan: Face lit up "Yeah! Exponents. That was fun."

Dental hygienist: "What are exponents again?"

Me: Looking out the window, thinking about how I love it when things go differently from how I expected.

Dental hygienist: Leaning toward me, "What are exponents?"

Me: "Oh! You're talking to me! A number to the power...like squared or cubed or to the power zero..."

The rest was mostly talk about movies and water slides, flossing, and how we like California so far. This part was noteworthy to me because of the fact that he said he really liked math, and I'm confident the hygienist's version of his experience with math was different from what Ethan was expressing a love of.

Factorials interest Ethan because they can lead to some really big numbers. That came up years ago in a book we were reading at night together. I forget which one. Maybe "If..." but I'm not sure. It was a book on pondering big questions. Ethan loves those kinds of books. Anyway, the question was something like would you rather have $100 a day for a whole month, or would you rather get paid 1 cent the first day, doubling your earnings every day for 30 days--basically the factorial of 30, which turns out to be a really big number, wowing Ethan into a love of factorials that has lasted for years, or so it seems.

Exponents was something that came up the other day. Somehow we got talking about squares and cubes, which led to higher exponents and us wondering how they might look in other dimensions. We talked about how one solves for them, as he and I did a quick scribble on a scrap piece of paper. We talked about how the reverse of a squared number is the square root. Then, when we got stumped thinking about what a number to the exponent 0 would be, we watched a short video on Khan Academy about it together, figured we understood it a bit better but not completely. Ethan said "That was fun!" and I agreed, because it really was, and we went on with other things. So when Ethan said that he really liked math I was delighted. I wasn't delighted because I think math is more valuable than anything else. It's just that math is one of those practices a person can learn to hate and fear by being repeatedly made to think about and do things one doesn't fully understand or have a perspective on that allows their learning to be relevant to their own experience. Early on, I picked up some math books. At first Ethan really enjoyed them, but they quickly got repetitive and boring and he lost interest. I pushed a bit, saw that I was making his experience unpleasant, guessed that I could do some real damage, and backed off.

I backed of the books and the schoolish approach to math, but not the math. Math is everywhere, and we start experiencing it early. If we can continue to experience it in a way that's relevant to us, it can be something fun and interesting life-long. So, when Ethan said he really liked math, I did a little celebration in my head because the math he likes is big and whole and integrated into his life. That's just so cool to me! I hope that's always true for him, but even if it changes, I'm glad it's been true for as long as it has.

Karen James, September 23, 2015, here.

and she added:

This is the book I was referring to above. It's a great book even if it doesn't have the example I was speaking of. If... (Questions For The Game of Life). (Great book for people who like to ponder these kinds of things. Not so great for those who don't, of course. So, don't push it!)


Unschooling and Math More by Karen James Discovery