Start here: how to learn with this site

Watching a good explanation feels like understanding, but most of it fades within days. What makes it stick is retrieval: pulling the ideas back out of your own head. Every chapter is built around that.

The routine for each chapter

1. Make a prediction. Each topic begins with a question. Choose an answer before opening the explanation; a rough attempt gives you something to test.
2. Investigate the idea. Change a model, sketch a diagram or work through the suggested comparison. Notice what changes and what stays the same.
3. Read the explanation. Compare it with your prediction, then follow the examples and try the topic's application questions. Hints and solutions are available when you need them.

4. Do the problems in order:

   • ★ warm-up: use one idea once;
   • ★★ standard: textbook-level, a couple of steps;
   • ★★★ stretch: combine ideas or estimate something real.

   Open a solution only after a real attempt. Getting stuck and then seeing the way through is where most of the learning happens. 5. Check yourself. Answer the topic's closing question and the chapter's recall questions out loud, from memory, without looking anything up. Pause at a topic boundary when you want a break. 6. Come back later. Try the recall questions again a few days later, and once more a few weeks after that. Review your questions collects questions you skipped or opened for help.

When a narrated video is available, watch it before or after the written lesson. Pause whenever you want to think something through.

Why this works

In a well-known experiment, students learned a short passage either by studying it in four sessions or by studying it once and then spending three sessions recalling it. Five minutes later the rereaders did slightly better (83% against 71%). A week later the recallers remembered far more (61% against 40%). Roediger & Karpicke, "Test-Enhanced Learning", Psychological Science, 2006 (PubMed).

The curriculum is also a spiral: each big idea comes back at a higher level, first as intuition and later with the full maths. This follows Jerome Bruner's idea of the spiral curriculum (The Process of Education, 1960).

What you need

• For Level 1: school arithmetic and a little algebra. Everything else is taught as it's needed.
• Paper and a pencil, and a calculator (or your phone) for the problems.
• From Level 2: Python, for simulations (the computation series C1 starts from scratch).

Ready to begin?

Begin: Numbers, units and estimation →

Or browse the curriculum and choose your own starting point.