Everything you need to know to get the most out of Build Understanding.
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The Philosophy
Build Understanding was created from a simple belief: you learn math best when you construct ideas from scratch, not memorize formulas. Every lesson is designed to walk you through the reasoning behind concepts, so that the formulas emerge naturally from your own thinking.
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Courses & Topics
Pick your course
Choose from the sidebar — courses range from Algebra 1 through Multivariable Calculus and AP Statistics. Each course follows a logical unit progression.
Read the notes
Each topic has carefully written notes that build the concept step by step. Read them actively — try to predict what comes next before scrolling down.
Try the Builds
Topics marked with a "Build" badge have interactive exercises where you construct the concept yourself through guided questions. These are the core of the app.
Prove It challenges
Some topics include Prove It sections — AI-guided conversations where you explain and defend your understanding. The AI pushes back if your reasoning has gaps.
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The Concept Map
Zoom to explore
Scroll to zoom in and out. When zoomed out, you see the full curriculum as colored course clusters. Zoom in to reveal individual units and their sections.
Click any unit
Clicking a unit card opens the sidebar detail view — it shows every section in that unit, plus all the prerequisite units from other courses you should complete first.
Follow the flow
Courses flow top to bottom. Arrows between units show the learning path. AP Statistics branches off from Precalculus as an independent track.
Navigate from the sidebar
The left sidebar lists the full curriculum progression. Click any course name to fly the camera directly to it on the map.
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AP Free Response
Real AP practice
The AP Resources section has past free-response questions organized by topic. Practice with real exam questions and get AI-assisted feedback on your work.
Guided FRQ mode
Instead of just seeing the answer, the guided mode walks you through the problem step by step — asking questions to help you figure it out yourself.
Built-in FRQ timer
Every FRQ page has a timer with three modes — Easy (1.5× AP time), AP Style (exact exam time), and Challenge (0.67× AP time). Minimize it to a sticky bar so it never gets in the way.
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Teach It
Explain it to learn it
Pick any topic and teach it back to an AI student. The AI asks clarifying questions and pushes back on shaky reasoning — the fastest way to find gaps in your understanding.
Socratic conversation
The AI doesn't just accept your first answer. It probes deeper with 'why?' and 'what if?' until you've worked through the full concept. If you can teach it, you know it.
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Practice Problems
Pick a topic and difficulty
Choose any topic from any course, then pick a difficulty — Foundations (1–2 steps, direct application), On Level (standard exam difficulty), or Challenge (multi-step, proof-style, tricky values).
AI-generated, never the same twice
Every problem is freshly generated by AI using your topic's notes as the source of truth. It matches the notation, terminology, and approach from the course — not a generic problem bank.
Full step-by-step solutions
After working through the problem, reveal the complete solution — every algebraic step, labeled with plain-English explanations, rendered in proper math notation.
Rate yourself
After each problem, rate yourself: Got It, Struggled, or Missed It. Your rating feeds the spaced repetition system so the right topics resurface at the right time.
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Daily Review
Spaced repetition — built in
Every topic you read gets added to your review queue. The app resurfaces it after 1 day, then 6 days, then progressively longer intervals — timed to just before you'd forget it.
5–10 problems a day
Each session gives you a short queue of AI-generated problems from topics you've already studied. Rate how you did and the algorithm adjusts — nail it and the interval doubles, struggle and it resets.
Streak counter
Complete your daily review and build a streak. The 🔥 badge appears at 3+ days. Consistent daily review is far more effective than cramming the night before.
Auto-populated as you study
You don't have to manually add topics. As soon as you read a topic's notes, it enters the queue automatically. Just study normally — the review system runs in the background.
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Tips for Success
Don't skip the reasoning
It's tempting to jump to the formula. Resist that urge. The reasoning is the understanding — the formula is just a shorthand for it.
Use the prerequisite map
If a topic feels hard, check its prerequisites on the Concept Map. You might be missing a foundation from an earlier course.
Come back and rebuild
Understanding deepens with revisiting. Come back to a Build exercise a week later — if you can reconstruct the idea again, you truly own it.
Do your daily review every day
10 minutes of spaced repetition beats 2 hours of cramming. Open the Daily Review tab each morning before school — it only takes a few minutes when kept up with.
Practice before the exam, not just after
Use the Practice Problem Generator the week before a test. Start with On Level problems, then push yourself with Challenge mode. Rate honestly — struggled means practice more.
Teach it to own it
After reading a topic, open Teach It and explain the concept from memory. If you stumble, you've found exactly what to re-read. This is the fastest feedback loop in the app.
Credits & Acknowledgments
Leo Eiger
Creator & Developer
Designed the curriculum, wrote the notes, and led the development of this app from scratch. This project is proof that you don't need to be handed understanding — you can build it yourself.
Cyndi Lui
Calculus Teacher
The most inspiring teacher I've had. Ms. Lui showed me that calculus isn't a set of rules to memorize — it's a way of seeing the world. Her passion for teaching is the reason this app exists.
Ms. Holly
Geometry & Math 3 Teacher · Mentor
Despite my poor performance in math my first semester of high school, Ms. Holly believed in me and helped me almost every day. By second semester I was doing outstanding in her class. She proved that the right mentor changes everything.
The first people to use Build Understanding and provide invaluable feedback that shaped the product. Their patience with bugs and honest critiques made the app better for everyone who follows.