Students need more exposure to the way everyday things work and are made.

“Making mathematics mandatory,” wrote Hacker, “prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower.”

In a paper titled “A Mathematician’s Lament,” Paul Lockhart rails against the modern approach to teaching math, typically three or four years of coursework in high school, starting with algebra and working up the chain: geometry, algebra 2, trigonometry, precalculus, calculus. Lockhart writes, “If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done—I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”

Donaldson and her research partner James McGarrigle found that even children as young as 4 arrive at correct answers when given “humanly meaningful context” (in their case, a naughty teddy-bear protagonist) to make sense of a problem. Children, like many of us, need ideas to be connected to real-world examples in order to grasp and implement them.

abstract reasoning is also developed through experience, which is a good argument for keeping all those extracurriculars.

The more students fail math, the more math we throw at them, and the more we test them. That has been the illogic of the past two decades.

No two people have the same intelligence, not even identical twins. And yet we persist in testing—and teaching—people in the same way. We don’t need Americans to be better at algebra, per se. We need future generations that can build and repair infrastructure, overhaul energy and agriculture, develop robotics and AI. We need kids who grow up with the imagination to invent the solutions to pandemics and climate change. When school fails them, it fails all of us.

Semantic algebra

The Atlantic • Against Algebra