No student's future should be decided by the teacher they happened to get.
Eduvectus is free math and science instruction built by a working classroom teacher — on conceptual understanding, not tricks.
Who's teaching you
William Chan teaches chemistry and mathematics at Clements High School in Sugar Land, Texas. He moved to the United States from Hong Kong at 16 and earned both his undergraduate and graduate degrees at the University of Texas at Austin, where he studied why students struggle to master chemistry and math — and how conceptual teaching fixes it. He has presented on conceptual teaching in chemistry at National Science Teachers Association conferences and trains chemistry educators at Rice University.
The teachers I got
I was not a smart student.
I say that plainly because it matters. In middle school and early high school I had several teachers who made mathematics feel like a wall — something you either had the talent to climb or didn't. I didn't think I had it.
Then I had two great teachers, back to back, in precalculus and calculus. Nothing about my ability changed. The teaching changed, and everything downstream of it changed with it.
That's the entire argument behind this site. If a brilliant student survives a bad teacher, good teaching looks optional. I'm the other case. For an ordinary student, the teacher is the variable — and which teacher you get is very close to an accident.
The students I've taught
I teach high school math and science now, and I stand on the other side of that experience. Students arrive in my room already convinced they're bad at math, memorizing procedures they were never shown the reason for. It holds until it doesn't, and then it collapses all at once.
One student was failing AP Precalculus and certain she wasn't a math person. It was not a quick turnaround — she was fixated on memorizing, and it took daily work to replace that with actual understanding. She's taking calculus now, and she doesn't hate it.
Another had already decided calculus wasn't for her. I insisted she was capable of AP Calculus AB and stayed with her through junior year. She earned an A in the course and a 5 on the exam. She didn't become an engineer — she's headed into medicine instead. That's the right outcome. She didn't need mathematics to become her identity. She needed the door left open, and her own judgment about her future left intact.
I found out about a third student sideways. His father came to me years later asking me to tutor his younger daughter, and mentioned in passing that the son — the one who had hated math — had gone on to major in it in college.
None of them asked for those futures. They had to be shown they existed.
What's actually wrong with how math is taught
It isn't a shortage of people who know mathematics. Some of the least effective instruction I've seen came from people holding mathematics degrees — which tells you the knowledge was never the missing piece.
It's that instruction gets organized around the subject instead of the student. Technically correct, and useless to the person in front of it. Nobody is trained to fix this, and nothing rewards fixing it: curricula reward memorization, so students rationally choose memorization. Free resources exist, but they're paced for students who are already succeeding, swinging between too easy and too hard with nothing in between. And much of test prep is known for its marketing rather than its teaching, at a price most families can't pay anyway.
When an adult tells me they hated math in school, I don't hear a statement about their ability. Far more often than we admit, it's what bad instruction leaves behind — and it was avoidable.
Curiosity is the engine. Questions are how it runs.
Nothing gets learned that wasn't first asked about. A student who asks nothing learns nothing.
But here's what took me years to understand: you can't ask about what you don't know enough to imagine. Someone who knows nothing about computers can't picture what AI might build for them. Curiosity isn't free-floating — it stands on knowledge.
That's why Curious and Rigorous aren't two separate goals here. They're a loop. Every concept you genuinely understand enlarges what you're able to wonder about next, and every real question drives you back into the material. Teaching the content well isteaching curiosity. There's no shortcut around it, which is the same reason there's no shortcut through it.
Then why start with the SAT?
A fair question, given everything above. The SAT is the most score-obsessed exam in American education, and I've just spent several paragraphs telling you scores aren't the point.
Here's why it's the right place to start. The hard SAT Math questions are not memory tests. They reward the student who can ask what if— who considers a scenario the question didn't hand them, who reaches for a second approach when the first one stalls. That's curiosity, operating under time pressure.
The score comes from a mentality, not a pattern library. Drilling patterns produces a ceiling that arrives fast and doesn't move. So the SAT isn't a compromise with what I believe about teaching — it's the clearest place to demonstrate it, on a test everyone already agrees matters.
How that shows up in the lessons
Concept before procedure
Every topic starts with why the method works. No shortcuts before foundations — because a procedure you can't explain is a procedure that will fail you under pressure.
Multiple paths to the same answer
Every question is taught more than one way. Students don't all arrive at understanding through the same door.
Paced for the student who's lost
Not for the one who's already ahead. That's the most common way good material fails the people who need it most.
What we won't do
- We won't sell tricks. A shortcut that raises a score and leaves you no better at mathematics is a transaction, not an education.
- We won't build for the top of the class.
- We won't put the lessons behind a paywall. Every video and practice set is free, permanently. Downloadable PDF materials are pay-what-you-want — including nothing. What costs money is my time: live instruction, essay review, and one-on-one support. Learning is not the part we charge for.
- We won't market our way to a reputation we haven't earned in the teaching.
About the name
Vectus comes from the Latin vehere— to carry, to convey. It's the root behind the English word vector.
Both meanings are ours. Learning is what carries a student forward. A vector is what gives that motion a direction — and often the direction that matters most is the one a student never believed was open to them.