Curriculum Corner: 'Exercise for the Brain'
If arithmetic is the foundation of the house of math, algebra is the moody basement where the cool kids hang out playing Dungeons and Dragons. Strange symbols, esoteric rules, knowledge your parents pretend to understand but don’t …
By David Choquette, Blue Mountain School Copper teacher (9-11 year olds)
It was good to be back together after a bonus winter break [due to the wintery weather]. The Copper Class enjoyed watching the field change from tundra to swamp and back again each day. Students used hands, feet, and all sorts of tools to engineer their own rivers and lakes.
Inside the trailer, we were working hard on our biography projects morning, noon, and afternoon. We probably wrote more sentences this week than any Copper Class has ever done in a week before. Students took notes on their historical people. Then, they spent time determining the right order to present their facts and began writing their biographical speeches. Next week we’ll get those speeches revised, edited, typed up, and ready to share with the world.
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Before the snow days I asked students to write down a time they felt excluded or left out. I took those situations, anonymized them, and gave them back to small groups. Each group made up a skit to show good and bad ideas for handling their situation. When we performed for each other, we noticed that we started with different situations but ended up with three remarkably similar skits. It’s good to remember we all feel left out sometimes, and we all have the ability to make others feel included.
Math this week was algebra. If arithmetic is the foundation of the house of math, algebra is the moody basement where the cool kids hang out playing Dungeons and Dragons. Strange symbols, esoteric rules, knowledge your parents pretend to understand but don’t … For real though, equations are just puzzles whose rules rely on adding, subtracting, multiplying and dividing, and it turns out they’re a pretty fun game if you look at them the right way.
One student said it felt like preschool when we brought out balance scales this week and compared objects to find ones that were equal in mass. Why? That’s a concrete representation of an equation. Students realized they couldn’t actually find the mass of an unknown object unless they compared it to a known object — which is the first thing you need to know to solve equations.
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The second thing they discovered was they could add or subtract and keep the scale balanced as long as they added or subtracted the same thing from both sides. Time to jump from preschool to high school. In the Copper Class, we’re studying one-variable and two-variable algebra adapting the Hands-on Equations curriculum.
It sounds like one of those newfangled trends that come and go in education, but it’s actually been around since 1986. The manipulative kits help us think concretely about each term in an equation, and give us the chance to try out various strategies rather than just following a formula.
Thinking critically, working together, and learning how to explain and check our answers are more important than applying our skills to practical situations at this stage. When we dip into the murky realm of negative numbers, students often ask me what’s the point. We won’t see many practical uses this year, but thinking algebraically is like exercise for the brain. It makes us fitter and more confident in all the problem solving we do in math and in life.
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And it’s fun, really! Returning students have been begging for algebra since August. They’ll have the chance to move beyond the levels they reached last year and explore how equations interact with graphs. Students who are new will move through the levels at their own pace, gaining confidence from the fact that we really are doing work some students wait till seventh or eighth grade to see.
I urge families to ask their students to demonstrate their algebraic techniques at home using pennies or dice or whatever you have around. You’ll be amazed at what your student can do in just a short time. And don’t forget to keep practicing those multiplication facts. We’ll need our foundation every day!
Blue Mountain School is a progressive, contemplative school in Floyd where intentional curriculum planning is part of the everyday. Know a child who belongs here? Blue Mountain School is enrolling for next year — contact@bluemountainschool.net.
