The Textbook Isn't Teaching Your Kid. It's Testing Their Tolerance for Confusion.

My son had a homework problem from his precalculus textbook. A Boeing 767 flies due south at 500 mph. The jet stream blows northeast at 80 mph. Find the plane's actual speed and direction "relative to the ground."

That's a perfectly reasonable question. Wind pushes a plane off course. How far off course, and how much does it slow down? Any teenager who has flown in an airplane can understand that.

But here's what the textbook actually gave him:

He's not wrong. The problem isn't that the math is hard. The math is two lines of addition. The problem is that every single sentence in this question is written for someone who already knows the answer.

"Relative to the air" means the speed the pilot sets — what shows up on the cockpit instruments. But the textbook never says that. "Relative to the ground" means the actual path on a map — what GPS would show. The textbook never says that either. "In terms of i and j" means break it into east-west and north-south components. You'd never know it from reading the problem.

And the answer is even worse. The solution produces an angle of −82.7°, then casually states "The 767 is traveling S7.3°E" with no explanation of how one became the other. A student is supposed to just know that −82.7° from the east axis is the same as 7.3° east of due south — because −82.7° is 7.3° away from −90°.

This is the textbook equivalent of showing someone a finished building and calling it an architecture lesson.

I asked my son what he thought "relative to the ground" meant. He said, "I don't know, the ground is everywhere. There's ground at the north pole and the south pole. The airplane could be moving toward or away from any of it."

That's not a dumb question. That's a smart kid engaging with the actual meaning of the words in front of him instead of just memorizing a formula. And the textbook punished him for it by never explaining the concept it assumed he already understood.

Once we cut through the jargon, the whole problem took about three minutes. Here's what it's actually asking, side by side with how the textbook presented it:

The math didn't change. The concept didn't change. The only thing that changed was that someone bothered to explain what the words mean.

Textbooks aren't written for students. They're written for professors who adopt them for courses. The customer is the department, not the learner. A book that says "where does the plane actually go on a map" might be seen as unserious by the committee evaluating it. So authors default to dense, formal language — because that's what gets adopted.

This is compounded by the curse of knowledge. The author has been immersed in this notation for decades. To them, "relative to the ground" is the simplified version. They've literally forgotten what it's like to encounter these ideas for the first time.

And the publishing model reinforces it. Publishers want books that look like other successful textbooks. Every edition copies the same tone that sold before. Clarity is a risk. Formalism is safe.

Here's the part that makes me angry. When a student reads a textbook and doesn't understand, the default assumption — by the student, by the parents, by the system — is that the student isn't smart enough or didn't try hard enough. Almost nobody asks whether the textbook failed to teach.

The chain looks like this:

Multiply this across every subject, every semester, and every student who quietly concludes "I'm just not smart enough" — and it becomes more than a pedagogical problem. Academic pressure is a documented contributor to student anxiety, depression, and crisis. Not because the material is too hard, but because the system makes struggling feel like a personal defect rather than a design failure.

I'm not pulling my kid out of school. He needs the structure, the social environment, and the competitive tennis. But I am doing something the textbook won't: translating.

When he hits a wall, we sit down and do what I did with this problem. We strip away the jargon and find the actual question underneath. I don't need to know the math. I just need to ask: "What is this actually saying in plain English?"

That one question — asked consistently — does two things. First, it gets him unstuck on the immediate problem. Second, and more importantly, it teaches him that when he doesn't understand something, the explanation might be the problem, not him.

That mindset shift is worth more than any formula.

Resources like 3Blue1Brown, Professor Leonard, Khan Academy, and Desmos are all free and explain things the way textbooks should have from the beginning. My son stays in school for the credentials and community but learns the actual concepts from sources that respect his time and intelligence.