How We Teach Fundamental Math

The Tragedy of How We Teach Fundamental Math

How do schools teach logarithms? With a puzzle: \[ \log_{2}{8} = 3 \]

That’s not computing a logarithm — that’s just matching symbols in your head. You already know \(2^{3}=8\). Nothing is discovered. Nothing is understood. And no one asks the real question: what about \( \log_{2}\)? How would you actually compute that?

How do schools teach sine? With a triangle chant: SOHCAHTOA. Memorize ratios, solve right-angle problems. But sine is not a triangle trick — it’s the language of cycles, vibrating through music, physics, engineering, even your heartbeat. The classroom version is a flat shadow of the real thing.

These two — logs and sine — are among the most fundamental relationships inspired by nature. Logs and e are just two directions of the same exponential relationship. Sine is the essence of cyclical behavior. They are the backbones of real modeling in science, finance, and engineering. Yet in school, they are reduced to fragments: formulas, drills, practice sheets — with no end use in sight.

The result? Students march from one half-digested concept to the next, drained of curiosity. Schools seem to build complexity not to inspire questions, but to silence them. “Why are we doing this at all?” becomes the one question you’re trained not to ask.

I’ve lived this. I hold one bachelor’s and two master’s degrees. I studied logs, exponentials, and trigonometry many times. I even used logarithms in my finance job. But one day it hit me: I didn’t really understand what a log return meant. My understanding was fragile, paper-thin. And looking back, I know why. In school, the way logs and e were presented had no natural connection to the log I later used in finance. The bridge was never built.

Here is the deeper truth: the best way to understand math concepts is to weave them into real life applications. Otherwise you will only ever have x and y to talk about; otherwise log is always a shadow of e, not having its own identity. Real understanding also requires rounds and rounds of deep thinking. Following textbook definitions, solving canned examples, checking off exercises — these don’t build understanding. They train you to follow, while giving you the illusion that you are making progress.

I strongly urge K-12 teachers: have the courage to project your so-called understanding into real-world problems. If you can’t make the connection, then it’s not true understanding. Yes, you may pass exams and recite formulas, but that is no different from what AI does today: spitting out the next symbol based on what’s most likely, manipulating symbols without seeing their meaning.

This is the tragedy of how we teach fundamental math: we strip concepts of their identity, dry out curiosity, and turn powerful ideas into empty drills. And then we wonder why so many students walk away thinking math is useless.

If you want to see math alive in applications, here are a few of the bridges I’ve built:

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