For Students & Parents

Does Math Knowledge Build Like Lego Blocks? What If You’re Missing a Few Pieces?

By Daniel Brink, Ph.D. · June 5, 2026

There’s a common story among students who struggle with math: “I’m just not a math person.” They say it as if it’s a fixed fact about themselves, like being left-handed. But in 22 years of teaching mathematics, I’ve seen something different almost every time. The student isn’t bad at math. They’re missing a piece.

Math is the most sequential subject in school. Almost nothing in it stands alone. To solve a quadratic equation, you need to know how to factor — and to factor, you need to understand multiplication and distribution — and to understand distribution, you need to be comfortable with variables in the first place. Each idea is a Lego block that only snaps onto specific others. Skip one, and nothing above it fits the way it should.

This is different from almost every other subject. If you miss a unit on the French Revolution in history class, you can still understand World War I. The knowledge is mostly parallel. But in math, the knowledge is stacked. A gap from sixth grade can silently sabotage a student in tenth grade, and no one — not the student, not the teacher — can easily see why.

The most effective lessons I’ve ever taught.

When I prepare to teach a new section of mathematics, the first thing I do is map out its Lego blocks — the specific building blocks that students need to already have before the new material will make sense. Then I spend time on just those pieces. Sometimes half a lesson, sometimes a full day or two. Only once I’m confident students have those blocks do we dive into the real topic.

The difference is dramatic. Students don’t stumble. They’re not tripping over basic errors mid-problem because the foundation is already solid. I sometimes use a different image with students: tie your shoelaces before you walk, otherwise you’ll step on them and fall. When a student makes a basic error in the middle of harder work, I’ll point it out gently — “see, you stepped on a shoelace.” They always know exactly what I mean.

The tricky part: the gap hides itself.

When a student gets a question wrong, the obvious explanation is that they don’t understand that question. But often the real problem is buried several layers down. A student who can’t solve a word problem involving percentages might not have a percentage problem at all — they might have a fraction problem. Or a multiplication problem. The visible struggle is at the top of the stack. The missing block is somewhere in the middle.

This is why “just study harder” often doesn’t work. If you’re re-reading the chapter on percentages when your actual gap is fractions, more studying of percentages won’t fix anything. You’re reinforcing the top of the stack without repairing the foundation.

What this means for the SAT.

The SAT Math section tests skills that span years of mathematics. Some questions look like they’re about quadratics, but the real test is whether you can factor confidently. Some look like geometry problems, but the hidden demand is whether you understand ratios. A student who drills SAT practice questions and still can’t improve often has one or two foundational gaps that are quietly blocking their progress.

Finding those gaps is the most valuable thing you can do. Not guessing at them — actually identifying them. Once you know which blocks are missing, you stop wasting time on the parts that are already solid, and you fix the exact pieces that are holding everything else back.

That’s exactly what this site does.

Take a free diagnostic test. When you’re done, the results page shows you which specific skills tripped you up — not just your score, but the pattern underneath it. That’s the missing block. Fix it, and everything built on top of it becomes easier.