I know only two people who can readily recite the quadratic formula. My wife is one. She’s always been a whiz at school, but, as a choir teacher, she has absolutely no use for the equation (other than as an occasional party trick). The other person is my brother, who works with electron-beam technology as a mechanical engineer. He’s in the minority of people who actually use advanced math daily.
For most of us, the formula was one of many alphabet soup combinations crammed into our heads in high school long enough to pass a math test, then promptly forgotten. I’m queasy all over again just thinking about it. As a functioning adult in society, I have no use for imaginary numbers or the Pythagorean theorem. I’ve never needed to determine the height of a flagpole by measuring its shadow and the angle of the sun.
Only 22 percent of the nation’s workers use any math more advanced than fractions, and they typically occupy technical or skilled positions. That means more than three-fourths of the population spends painful years in school futzing with numbers when they could be learning something more useful.
I’m talking about applied logic. This branch of philosophy grows from the same mental tree as algebra and geometry but lacks the distracting foliage of numbers and formulas. Call it the art of thinking clearly. We need this urgently in this era of disinformation, in which politicians and media personalities play on our emotions and fears.
Logic teaches us how to trace a claim back to its underlying premises and to test each link in a chain of thought for unsupported assumptions or fallacies. People trained in logic are better able to spot the deceptions and misdirection that politicians so often employ. They also have a better appreciation for different points of view because they understand the thought processes that produce multiple legitimate conclusions concerning the same set of facts. They are comfortable with spirited dialogue about what’s best for our society.
I once asked my pre-calculus teacher whether I would ever use the information she taught in real life. Her answer was surprisingly frank: I probably wouldn’t. The reason to take the class was to score well on the advanced placement test, which would give me a leg up on the math requirements in college. In other words, numbers for the sake of numbers.
Math advocates claim to be teaching complex problem solving, mental discipline and a better understanding of our world. Logic teaches the same things more directly. Geometry can’t teach me when an argument is manipulating my emotions, but logic can. Calculus doesn’t help me solve moral dilemmas, but philosophy does.
Admittedly, all students need to master the basic math of everyday life so they can manage money, compare prices, find the center of a wall to hang a picture and so on. And some students, like my brother, will fall in love with math. That’s a good thing, because they will use it to make bridges safe, to predict the weather, to land spacecraft on the moon and Mars — you get the idea.
It’s reasonable to suggest that public schools all provide a standardized core curriculum. But what makes up a fundamental education? America has not thought through this question in a national conversation since the 1983 release of “A Nation At Risk.” The product of a presidential commission on education, this report warned of declining achievement in the country’s schools and diagnosed “the urgent need for improvement.” Among its recommendations were a minimum of three years of math for all high school graduates.
Since that time, the digital revolution has placed massive computational power in the palm of every student’s hand. Should the need for a cube root arise in someone’ life, Siri is available 24/7 to provide the answer. That same revolution has given us a crisis of conspiracy theories and a polluted public discourse. What’s at risk now is our ability to reason together as citizens. Skills such as these might not be able to solve for X, but they could go a long way in the pursuit of happiness and the health of America. You can’t punch those things into a calculator.
The need to solve problems is eternal, but many of life’s weightiest problems don’t boil down to numbers. Prioritizing higher-level numeracy over other forms of logical reasoning is not turning us into a nation of engineers and physicists. It’s letting us become a nation that can’t think straight.
America’s Founders knew it would take educated citizens for this democratic republic to succeed. But nowhere did they mention the quadratic formula.
https://www.washingtonpost.com/opinions/2024/02/06/end-useless-math-requirements/ (Archive)
