I love my mom for all the normal reasons -- the endless self-sacrifices she's made for her children, her boundless devotion to us, the great wisdom she's imparted. (Blah blah blah.) I also love her because we share a lot of the same passions, like education. Here's a story about that.
My mom is an elementary school teacher the way Michelangelo was a sculptor. She opens her classes by talking about the differences between ideas and apples: if you have an apple and I have an apple, and you give me your apple, now I have two apples, and you don't have any apples. But it's not the same with ideas. If you have an idea and I have an idea, and you give me your idea, now I have two ideas, but you still have your idea. And if I then tell you my idea, both of us will have two ideas. Ideas have a special quality about them: the more they're shared, the more they grow. (Hmm, maybe they are kinda like apples.)
This observation about apples and ideas is an amazing way to start a semester. It establishes an open classroom culture, one based around cooperation rather than competition. It encourages students to share their thoughts and help each other. Collaboration in academia is one of the things I love most about school, and hearing its beauty communicated in such a clear way to young children filled me with joy.
She continued by talking about the way she teaches subtraction. There's a lot of different ways of thinking about subtraction, she explained. For example, consider the math problem "23 - 8". (This is a problem a lot of her students have trouble with.) One way to conceptualize subtraction is as a disappearance of things. If I was thinking about subtraction like this, I would try to picture 23 balloons in my head, pop 8 of them, and count how many were left. Of course, this isn't very easy to do.
But there are other ways of thinking about subtraction. Subtraction is also a relative difference between two things. So if I was 23 feet tall and you were 8 feet tall (because you're a shortypants), "23 - 8" represents the relative difference between our two heights. And notice: This relative difference doesn't change if both our heights change by the same amount. So if we both get on a platform that's 2 feet tall, then I'd be 25 feet tall, and you'd be 10 feet tall, and the relative difference between our two heights would stay the same. "25 - 10" has the same answer as "23 -8", only it's a lot easier.
Here's a third way of thinking about subtraction: making change. If you're at the store, and you have $23, and you want to buy an $8 item, you don't hand the cashier $23. You hand the cashier a $10 bill, and the cashier hands you $2 in change. "23 - 10 + 2" also has the same answer as "23 - 8", and it's also a lot easier.
It was exciting to hear my mom talk about all these different ways of thinking about subtraction. It made me realize something I thought was really simple and boring wasn't as simple and boring as I thought it was. It revealed a richness and depth in the concept of subtraction I never noticed before. It was also humbling, because it showed how my mom understood a supposedly basic concept -- a concept I would consider "beneath me" -- far better than I did. But this isn't even the best part of the story, because after she finished describing all these different ways of thinking about subtraction, she told me she hoped some of her students would think of even better, more creative ways of thinking about subtraction, ones she hadn't even thought of yet. And she hoped by telling her students about the special quality of ideas in the beginning, her students would feel comfortable sharing these ideas with her, and she would learn things about subtraction.
Hearing her say this was a revelation. For all the humbler I thought I'd gotten in the course of this conversation, my mom was far humbler. Not only did she show me my own shallow understanding of a supposedly beginner-level concept, she also showed her willingness to learn from children aged 8-10. She was totally open to -- even excited by -- the notion that these young students would think of things she's never thought of before, and they could teach her things. She was looking forward to them enriching her own knowledge of subtraction.
Her story reminded me of all the reasons I'm so passionate about education: its capacity to ignite the imagination, to inspire people of all ages, to bring us closer in collaboration and community. I am unbelievably thankful for the great teachers in my life who did these things for me. My mom is one of the greatest.
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