America’s Math Curriculum Doesn’t Add Up

America’s Math Curriculum Doesn’t Add Up (Ep. 391) - Freakonomics Freakonomics

"In 1820, for instance, Harvard began requiring knowledge of algebra to gain admittance. As a result, secondary schools started teaching algebra. Fifty years later, Harvard added geometry to its requirements, and the secondary schools followed suit.

After the Soviet Union launched Sputnik in October 1957, math education became a matter of national security. The math curriculum was overhauled with two very different goals in mind. The first goal was to increase the number of engineers, mathematicians, and scientists. This led to the introduction of higher-level, more abstract math in the high school curriculum. The second goal was to develop a workforce that could do the complex calculations required to support the military and space efforts. Remember, this predates the age of modern computers.

BOALER: It’s funny, really. When I was in school and many years ago, the joke of maths teachers used to be, “You’ve got to be able to do all these calculations because you’re never going to be walking around with a calculator in your hand.” Well, turns out that everybody’s walking around with a calculator in their hand... Teaching is always very hard to change because people learn it from their own school days, and then they want to become the maths teacher they had. Well, maths teachers do anyway. And when people have tried to change, they’ve really received aggressive pushback, which has caused some of them to sort of withdraw and go back into teaching the way that they were...

Boaler knows firsthand what this pushback is like. During the early 2000s, she found herself caught up in what’s known as the “Math Wars,” a debate over the math curriculum between reformists and traditionalists. And if you think “wars” is an exaggeration:

BOALER: People went to extreme lengths to try and stop reforms. I think somebody went on a hunger strike, even, in L.A. Yeah, it was really a battleground...

SADOFF: We always think of teaching to the test as a bad thing, but we want people to teach to the test. We put those concepts on the test because that’s what we want students to learn...

COLEMAN: We survey first-year math teachers and first-year college professors not only in math but outside of math, and we analyze which math is most used in their courses. That’s a knowable question. At the same time, we ask high-school teachers what math is the most important for use in college and compare those two data sets...

The college teachers say, “Very few things matter and matter a lot.” The high school teachers say, “Everything matters.” Think of the stress of that. They must do everything, or they are betraying their kids, which forced them to race through the curriculum lest their kids are not ready.

What the college teachers say but is not heard is, if your students can do these core set of things, we can do the rest. But if those are shaky and they’re merely faintly aware of them and aware of a lot of other mathematics, we’re stuck...

The first is the most humble, but it’s powerful, is arithmetic. The command of the four operations: subtraction, multiplication, division, and addition — but crucially, fractions. The next area of math that’s hugely predictive of your future success is what I would call data analysis and problem-solving, including rates, ratio, proportion, designing quantities that interact with one another in that way, and watching their growth over time in development. The third area of math that’s extremely widely used is what I would call the heart of algebra, which is linear equations. That portion of algebra is then very widely used in other disciplines to open up many other problems."