The Language of Mathematics

We are not a STEM school because we don’t treat science, technology, engineering, and mathematics equally—or even close to equally. It would be more accurate to say we are a math and science school, in that order. Our goal is not to graduate trained engineers, programmers , or technologists. Our job, as a K-12 school, is to graduate students who are prepared to pursue any field successfully. While robotics and advanced experiments look great on social media, we must be humble enough to recognize our place in your child’s education. Our job in math and science is one of restraint—we must focus on the basics, not pursue flashy new things. In addition to being great writers and readers, our students must graduate with proficiency in the fundamental math and science necessary to be successful in any science or engineering field.

It is a common theme of progressive education to replace the fundamental skills that should be taught in K-12 with higher-level skills that sound impressive but that students are not ready for. In sports, it is equivalent to a youth league looking at the NBA and deciding to teach dunking and three-point shooting instead of dribbling and layups.

This idea of skipping the basics and jumping straight to advanced skills started on the language side of education and then made the jump to the sciences with STEM. It originally started with reading in primary school. Forty years ago, schools decided that what students needed to know was how to read, and that they were wasting time on rote phonics. So progressive educators decided to drop phonics and to teach reading by simply giving students books and letting them start reading. Teachers were skipping the foundational skill of phonics and trying to jump right to the advanced skill of reading. This “whole language” or “balanced reading” program proved a disaster, and nearly every state in the U.S. has abandoned it (except Kentucky and one other state). They have gone back to phonics because it is proven to work—though they now call it the “science of reading.” I think progressive educators were only convinced to go back to phonics because it was given a new name.

The next trend popped up in middle and high schools in the late 1990s and early 2000s. Schools had traditionally always focused on reading and writing, but in the real world, we were told, people actually needed to know how to collaborate on team projects and presentations. The focus of K-12 became projects and teamwork, not simple reading and writing. Poster boards, PowerPoints, and tri-fold project boards replaced books and papers. These time-wasting group projects only started to fade when STEM caught the attention of educators.

Today, it is STEM that has taken up the progressive mantle. Instead of teaching mathematics, biology, chemistry, and physics, we are supposed to teach robotics, app programming, and artificial intelligence. We are to glide over the fundamental sciences and mathematics and jump ahead to the final product of technology and engineering.

At Highlands Latin School and Memoria Press, we don’t do this. We never dropped phonics. You will hopefully never need a tri-fold project board. And we teach our students the skills of observation and classification in the lower school and biology, chemistry, and physics in the upper school. But far more than these sciences, we teach mathematics, the language of all science. We focus on math because math is the subject that most limits students in their science education. If you can’t do algebra you can’t be a chemist, and if you can’t do calculus you can’t be a physicist. Math is the language used to describe the logic behind the physical world.

So, what is our approach to math? I once heard IEW’s Andrew Pudewa give a terrific speech about the value of memory and memorization. In his talk he said that you can’t expect something out of a mind that isn’t already in that mind. You wouldn’t expect Chinese from a mind that doesn’t know Chinese. You wouldn’t expect Latin from a mind that doesn’t know Latin. And you wouldn’t expect great writing from a mind that doesn’t know English vocabulary and grammar and syntax.

The same is true for math. Mathematics is a language with vocabulary, grammar, and expression. Arithmetic is the vocabulary: It contains the building blocks for all mathematics. Algebra is the grammar of mathematics, where students begin to put simple sentences together. Calculus, proofs, and other advanced mathematics are the expressions of math—these are the beautiful novels and poems of the language of mathematics where we start to precisely represent the world around us.

When we understand that mathematics is just another foreign language, we immediately know what to do with the vocabulary, in this case arithmetic. We memorize it—to mastery. Just as having to constantly look up vocabulary in Latin will eventually be the end of any Latin student, having to constantly calculate simple arithmetic will be the end of any math student. When you don’t know the vocabulary you can’t translate, and you certainly can’t write. In math, when you don’t know arithmetic you can’t do algebra, and you certainly can’t do calculus.

This is why our focus in kindergarten through sixth grade is mastery of math facts. We demonstrate and practice mastery through daily timed speed drills. Our students will work twenty to forty thousand arithmetic  problems each school year in their speed drills. We make it really hard for students not to master their math facts.

The reason we want them to be able to compute arithmetic instantly, without thought, is because each algebra problem will have five or ten arithmetic problems embedded in it. If students must stop and think about the arithmetic each time, they will be too slow or make too many errors to solve their algebra correctly. Anyone who has taught algebra will tell you that the first year of algebra is really just easy algebra with hard arithmetic, and that students almost always make their mistakes in the arithmetic.

Does this approach to math and science work compared to a technology- and engineering-oriented STEM focus? It is one thing to talk about our theory of education and another to get results. At Highlands Latin this year, our senior class had an average SAT reading/writing score of 721, one of the highest in Louisville. People somewhat expect that from our students because we are known as a language school. But our SAT math average is 717. This is also one of the highest in the city, and over the last ten years our math scores have consistently averaged the highest in the city.

More than fifty percent of our graduates go into science, math, and engineering fields in college. That is compared to the national average of eighteen percent. Our high percentage is partially because our students are all capable of pursuing any major, but I think part of it is because they have a balanced education and are not burned out on STEM when they leave Highlands. (It could also be because they are running away from Latin!) I’ll conclude with one of the best arguments for a mastery approach to mathematics, a quote popularized by Mark Twain: “There are three types of lies: lies, d—ed lies, and statistics.” If our students don’t know math, we must be prepared for them to be deceived by those who do.