Most online education is a performance. A teacher explains something clearly and confidently. The student watches. The explanation ends. And then the student meets a problem, and finds that watching someone solve a problem is very different from being able to solve one.
This is not a technology failure. It is a design failure — a failure to understand what learning actually is.
Learning is not the reception of information. It is the building of understanding — a process that asks the student to be active, to struggle, to make connections, to be wrong, to adjust, and to arrive somewhere new. No amount of watching, however clear the explanation, does this on its own.
So everything here is designed around what the student does, not what the teacher says.
Start with a question the old idea cannot answer.
Each lecture in the Library takes one idea and stays with it. It opens with a puzzle or a real situation that the student’s current understanding cannot handle — a spring balance with evenly spaced marks, two codes that are easy to write and hard to undo, four unemployed people who are unemployed for four different reasons.
From there the idea is built one step at a time, with a picture wherever seeing helps. The formal statement comes after the understanding, not before it. By the time the formula appears, it is a short name for something the student can already see.
Along the way, Stop and think boxes pause the student at the exact point where most people go wrong. Worked examples build in difficulty, show the thinking rather than just the steps, and end with a check. The classic mistakes are named as traps, before the student makes them in an exam.
Think, then check. Not the other way round.
Most practice works like this: the student attempts something, is told right or wrong, and moves on. This produces a specific failure — a student who learns to chase the right answer, but not to judge whether their reasoning was right.
The interactive moments in each lecture are built the other way. The student predicts what will happen before the answer is revealed. They find the error in a solution that looks correct. They sort examples by the principle underneath them. They step through an argument one line at a time, and see why each line follows from the one before. When the explanation arrives, it explains why — not just what.
Every interactive sits at the point in the lecture where the idea needs it, and every one has to earn its place. If a still diagram does the job, a still diagram is used.
Change the variable. See what happens.
Some things can only be understood by experiment. Not the formal experiment of a laboratory — the informal experiment of a person who wants to know what happens when one thing changes.
What happens to a point and its mirror image when you drag it along a graph? How much faster does a ball leave a spring when you compress the spring twice as far? What happens to unemployment, and to prices, when a government spends more in a recession — and when it does the same thing in an economy that is already at full stretch?
The explorers and simulations in the lectures let a student answer these questions by doing: change the variable, and watch the system respond. A student who has spent ten minutes experimenting understands the behaviour of the thing in a way no explanation can fully replicate. They have intuition about it. They have felt it.
Then do it without help.
Every lecture ends with problems for the student to try alone, building to one that asks for more than the lecture showed. Then the bigger idea: where this one concept leads, in its own subject and beyond it.
And no lecture stands alone. Each one shows the lectures it builds on and the lectures it leads to, so a student who is stuck can go back to the place where understanding broke — and a student who is curious can see where the idea goes next.
Some students arrive expecting the lectures to feel easier than what they have met before. In some ways, they will — because the explanations are honest about what a concept actually is, and because the intuition is built before the notation arrives. Things that were mysterious become clearer.
But the problems will not be easy. The thinking required will be real thinking. There will be moments where the next step is not obvious. There will be confusion.
This is not a design flaw. It is the design.
Understanding is built in the gap between not knowing and knowing. The struggle in that gap — the discomfort of “I can’t see it yet” — is where real learning happens. Teaching that removes the struggle to feel more comfortable removes the learning with it.
So the struggle stays. What changes is the support around it — the Stop-and-think boxes, the worked examples, the interactives — so that the struggle is productive rather than paralysing.
There is a difference between confusion that is going nowhere and confusion that is going somewhere. Everything here is designed to keep the student moving towards the second.
Every lecture, in all four subjects, at every level, is free to read. No account, no payment. Learning should not have a paywall at the door.
For a student who wants a person rather than a page, I teach small live groups online: the Explorations for Grades 6–8, and the Deep Dives for pre-university and beyond. A group opens when four students are ready.
Tell me the student’s year and what they think about the subject right now. I will tell you honestly which course is worth their time, or whether none of them is.