Another question I see come up all the time in the context of homeschooling and especially unschooling is “How do you teach math?” There are lots of different ways. I know people that use curricula, I know kids that attend math circles where they work out math problems with other kids, I know kids that learn math as they run into a need for it in the real world. When the real world example pops up, people tend to ask, “Yes, but how will they learn complex math like algebra and trigonometry?"
To which I respond, “The kids here learn those things mostly by talking.”
And that’s how we do it. Talking. Usually in tiny snippets at a time. My partner and I started working with the kids on math as we hung around in coffee shops. We'd ask the kids—now 8 y.o. No. One, 6 y.o. No. Two, and 4 y.o. No. Three—questions about adding or subtracting. They'd generally work them out on their fingers. This worked great all the way through multiplication, but when we hit division the first time—then five year-old—No. One finally started using paper. We’ve done the same sort of thing for binary numbers, boolean logic, fractions, and now the eight year-old kid’s started in on algebra.
A few afternoons back my partner wrote down the latest algebra problem for One in an ice cream shop . (It seems algebra may be more of an ice cream than a coffee activity.)
Two looked at the problem, thought for a minute, and said, “Two. The answer’s two.”
Sure enough it was, and yet…
“Can you write down your steps?” My partner asked.
True to how she’s learned math, One talked about what she did, she didn’t write it down. “Well, I needed a number so that when I had three groups of that number and then took one away, the answer would be 5.
Again the kid was right. I hopped in, “Sounds good to me. Why right it down?”
“Yeah, let’s write down the steps anyway.” My partner said, following up with, “So, you can add and subtract anything from both sides of an equation right?”
“Yup,” replied the kid.
“Well, maybe add one to both sides then.”
One wrote dutifully. “Got it,” she said
“OK, then can you divide both sides by the same thing?”
“Yeah.”
“Divide by three.”
“OK, and now I have two!” the kid exclaimed. “Still, I had two to start with.”
My partner wrote down another problem.
Two looked at it again, thought, and then said her answer, “It’s one.” But, this time she was wrong. The problem took a few more steps, and wound up with a fraction as an answer instead of a whole number. Now that the kid had a problem that required working through the steps, she set about doing it with our help. At the very end, she and I talked about how once you had a fraction like ⅞, you could just say the fraction rather than going any further.
And, that was that. We’ll all mess with algebra another time, in another coffee, (or ice cream), shop, but this is probably how all the kids here will learn algebra. Talking. Just a little bit. Over and over and over. And it won’t be a big deal.
I’m sure there are even more ways to teach math I’m not aware of yet. What’s your favorite?
To which I respond, “The kids here learn those things mostly by talking.”
And that’s how we do it. Talking. Usually in tiny snippets at a time. My partner and I started working with the kids on math as we hung around in coffee shops. We'd ask the kids—now 8 y.o. No. One, 6 y.o. No. Two, and 4 y.o. No. Three—questions about adding or subtracting. They'd generally work them out on their fingers. This worked great all the way through multiplication, but when we hit division the first time—then five year-old—No. One finally started using paper. We’ve done the same sort of thing for binary numbers, boolean logic, fractions, and now the eight year-old kid’s started in on algebra.A few afternoons back my partner wrote down the latest algebra problem for One in an ice cream shop . (It seems algebra may be more of an ice cream than a coffee activity.)
Fun unschooling fact: subjects don’t proceed in order, so 3s and 6s can wind up backwards in algebra problems :)
Sure enough it was, and yet…
“Can you write down your steps?” My partner asked.
True to how she’s learned math, One talked about what she did, she didn’t write it down. “Well, I needed a number so that when I had three groups of that number and then took one away, the answer would be 5.
Again the kid was right. I hopped in, “Sounds good to me. Why right it down?”
“Yeah, let’s write down the steps anyway.” My partner said, following up with, “So, you can add and subtract anything from both sides of an equation right?”
“Yup,” replied the kid.
“Well, maybe add one to both sides then.”
One wrote dutifully. “Got it,” she said
“OK, then can you divide both sides by the same thing?”
“Yeah.”
“Divide by three.”
“OK, and now I have two!” the kid exclaimed. “Still, I had two to start with.”
My partner wrote down another problem.
Two looked at it again, thought, and then said her answer, “It’s one.” But, this time she was wrong. The problem took a few more steps, and wound up with a fraction as an answer instead of a whole number. Now that the kid had a problem that required working through the steps, she set about doing it with our help. At the very end, she and I talked about how once you had a fraction like ⅞, you could just say the fraction rather than going any further.
And, that was that. We’ll all mess with algebra another time, in another coffee, (or ice cream), shop, but this is probably how all the kids here will learn algebra. Talking. Just a little bit. Over and over and over. And it won’t be a big deal.
I’m sure there are even more ways to teach math I’m not aware of yet. What’s your favorite?
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