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What About Math?
The most common question I get asked about unschooling is, “What about math?” There seems to be a belief that math has to be learned in a certain order at specific times, that math involves a lot of repetition and drill work, and that math can’t be learned without instruction. Watching my son for the last year and a half has convinced me that none of these concerns are true.
When Logan was three years old, I purchased a poster of the natural numbers zero through one hundred arranged in ten rows of ten. I hung the poster at Logan’s eye level in the kitchen. I never commented on the number chart, and it went unnoticed (from my perspective) for almost a year.
When Logan was four, he was counting Hot Wheels cars in a race. I knew he could count to seven accurately but wasn’t sure if he could count beyond that. He counted to seven, and then I saw him look at the number chart to help himself count higher. He counted to thirteen using the chart with no help from me. Over the next few days he counted many objects using the chart for help. In less than a week, he was able to count to twenty without the chart. I didn’t even know he knew the names for the numbers fifteen through twenty.
We had been adding numbers since Logan was three. For example, if he had five cars and I gave him one more, he then had six. He didn’t do addition by himself very often; mostly he asked me the answer, and I told him. About a month after he started using the number chart to count, he began using it to add. He would go to the chart, put his finger on the starting number, move his finger the number he was adding, and get his answer. This was usually part of his imaginative play. He would be building with Legos, and would run over to the chart, do an addition problem, nod his head, and run back to his Legos. I wasn’t part of this game and still don’t know what or why he was adding. Subtraction soon joined his game, and he was running to the number chart many times a day to solve problems.
After two months of intense use, Logan seemed to forget about the number chart, and it sat mostly ignored for nine months. During this time he referred to the chart once every week or so to solve some addition or subtraction problem. He seemed stuck at twenty as his maximum answer for any type of problem.
Around the time Logan turned five, his interest in the number chart renewed. He discovered counting by twos up to twenty. While doing this, he noticed that the squares the numbers were in alternated blue and yellow. He realized when counting by twos he was only touching the blue squares and was skipping the yellow squares. He told me that all the twos were blue, and that must mean something. He pondered this for many weeks and came up with the idea that the blue squares were ones where you added the same number to itself. We read a book that mentioned even numbers, and Logan realized that was what the blue numbers were. He asked me if the yellow numbers had a special name, and I told him they were called odd.
Logan had understood the concept of multiplication for a couple of years, but now that he could count by twos, he began solving multiplication problems. He started with twos, telling me things like, “Three twos is six, and five twos is ten.” He moved to the fives next, and then the threes and fours. Then, Logan seemed to become bored with multiplication problems where the answers were twenty or less and started really focusing on learning his numbers above twenty. Multiple times a day, he would point to numbers above twenty and ask me what they were. As he learned what thirty, forty, fifty and so on were called, he noticed a pattern. When you start at the next group of ten, you count up to nine until you get to the next ten. He realized if he learned to count by tens, he would know what each ten was called and then he could easily count to one hundred. After a few weeks of practicing, he was able to count to one hundred. He was excited, because now he could do higher multiplication problems.
About six months after turning five, Logan started using the number chart to divide. He likes to race his micro-cars on a car track. Part of this game is dividing his cars into teams. In the beginning he would divide the cars up by taking turns putting a car into each team until he was out of cars. At some point, he realized this was the long way of doing it and devised a way to use the number chart to help him. I’m not sure of his system, because he no longer touches the number chart to use it. But, he can divide numbers up to one hundred by two, five and ten. He even understands remainders, although he calls them left-overs.
The number chart is still used a few times a week for various reasons. Logan has recently become interested in big numbers and is requesting a number chart that goes to one thousand. The amazing thing to me is that all of the learning from the number chart was self-initiated. All I did was answer Logan’s questions. I never pushed his interests. His learning didn’t happen in any prescribed order, and in fact, he was doing multiplication before he could count higher than twenty. No drill work or repetition was involved in his learning. In a little over a year and a half, he has gone from being able to count to seven to doing division problems for fun.
So what about math? Math gets used naturally every day in life. Math is learned best when lived – no instruction required.