// 01
Find the missing idea
Suppose you know how to keep an equation balanced, but get stuck whenever it contains fractions. Starting algebra again would make you repeat things you already understand. Continuing without fixing the fractions would make each new lesson harder to follow.
organises a subject as connected ideas. Each idea has prerequisites: earlier knowledge you need to use it. A course becomes a route through those connections. The map gives a large ambition a structure: what the goal depends on, where you already have a foothold, and which idea needs work next. These connections are the basis of the system: placement finds a starting point, practice informs the next step, and review checks earlier learning.
The machine-learning curriculum charts 2,143 ideas, called planets, grouped into 56 systems and 10 constellations. Of those, 290 form the required route. These counts describe the curriculum map, including surrounding territory; they are not a count of published lessons.
What the connection is for
In this example, the useful route goes back to fraction arithmetic, then returns to the equation that exposed the gap. Knowing which ideas depend on which others gives us somewhere specific to look. The answer you give decides whether that suspicion holds up.
// 02
Begin where you are
You may have met some of these ideas before, perhaps under different names or in a book you meant to finish. The opening diagnostic uses your answers to estimate where to begin. Each answer helps select the next question, up to a limit of 60 questions.
The map distinguishes what you have demonstrated directly from what it can only infer through related ideas. Unchecked areas remain uncertain. This gives you an initial route; later practice can revise it.
// 03
What does a correct answer actually tell us?
A correct answer shows that you succeeded on that problem, at that moment. To understand what will hold beyond the lesson, we need to ask different questions about the same idea.
- Mastery
- Can you apply the idea now, on your own?
- Retention
- Can you still retrieve and use it after time has passed?
- Discrimination
- Can you recognise when this method applies, and when another one is needed?
- Transfer
- Can you use the idea when the setting or representation changes?
The same idea, a different demand
Finding a percentage immediately after a worked example checks one kind of performance. Choosing how to calculate a discount a week later asks more: you must remember the method and recognise that it fits the situation.
pause & think
You solve a problem just after reading its solution. What have you not yet shown?
show reasoning
You have not yet shown that you can retrieve the method after a delay or choose it in a different setting. The immediate attempt is useful practice. A later, unfamiliar problem provides different evidence.
The example made sense.
Now close the page.
// 04
What happens inside a lesson?
A lesson introduces an idea, shows how the reasoning works, then asks you to use it. Each explanation sits close to the problem it prepares you for, so you can connect the rule to an actual decision.
- Understand the move. Read the explanation and follow a worked example, including why each step is valid.
- Try it yourself. Solve a problem that asks you to carry out the reasoning.
- Compare the reasoning. Once the attempt ends and is graded, read the worked solution and locate any difference in your approach.
- Use the idea again. Further practice changes the problem so that the method has to survive beyond the example.
Retrieval means bringing an idea back from memory. Your answer is your own. There are no hints during the attempt. The full worked solution is available once the attempt ends, including when you answer “I don't know.” In a question with several steps, a correct intermediate answer lets you continue; it does not reveal the remaining solution.
Getting stuck should lead somewhere. Compare your approach with the solution, find the first step you could not justify, and try the method on another problem. We want the effort to go into understanding that step. Prolonged bewilderment is not a learning objective.
// 05
What should a model do in a lesson?
An AI can explain a step, supply a counterexample, or help design a better exercise. Those are useful ways to teach. But if it chooses the next step during your assessed attempt, we lose the chance to see whether you could choose it yourself.
Our rule is to teach before, check after. Give the explanation before the attempt and the worked solution once it ends. Keep the answer between them yours. A more capable model can improve the teaching without quietly completing the assessment for you.
First decide what you want from the tool
- A result
- You need a working calculation or program. Use tools, then check the result as carefully as its consequences require.
- An ability
- You want to perform the reasoning yourself. Study the example, then attempt a fresh problem without its help.
- A direction
- You are deciding what to learn. Ask for examples and connections, then follow the question that makes you want to look closer.
The distinction matters when we record progress. Reading an explanation does not earn mastery. Graded answers give the system evidence about what you can do; delayed checks give it evidence about what you can still do. We cannot infer either from the quality of an answer a model produced for you.
pause & think
A model offers to complete the next step while you are still working. Should the lesson accept that help?
show reasoning
If choosing that step is what the question tests, the help would change what your answer tells us. Finish the attempt, or say you do not know, then study the solution. A new problem gives you a chance to use what you learned from it.
// 06
Give the idea something to act on
A NAND gate takes binary inputs and produces an output. Connect its inputs together and it becomes a NOT gate: an input of 1 produces 0, and an input of 0 produces 1. On a circuit board, you can wire that connection and watch both cases happen.
Gateworks, our circuit workshop, lets you build and test these constructions. Change a wire, run the inputs, and inspect where the result differs from your prediction. The interface makes a relationship available to experiment with. Its value lies in what you can investigate.
Efficient is not the same as quick
A moving diagram earns its place when changing something helps you understand a relationship. Otherwise a still diagram may do the job better. The same applies to an exercise: choose the form that lets you practise the intended skill, with as little unrelated work as possible.
pause & think
You copied a working circuit. What would tell you more about whether you understand it?
show reasoning
Predict its output before running it, explain why a connection is needed, or build a circuit for a different target. Each asks you to do something that copying alone leaves untested.
// 07
Why return to something you already learned?
You understood it on Tuesday. Unfortunately, memory does not consider the matter closed. Spaced review brings an idea back after a delay, so you have to retrieve the method rather than repeat what you just saw.
uses your review history to estimate when another attempt is due. Successful recall on later days can increase the interval before the next review. A miss gives the system a reason to bring the idea back sooner.
The schedule is an estimate, not a reading taken directly from your memory. Each answer can correct it. That is the purpose of coming back: to check whether you can still use the idea later, with the original explanation out of sight.
pause & think
You answer the same problem several times in one sitting. Does that establish that you will remember it next week?
show reasoning
It shows performance within that sitting. To check next-week recall, time has to pass. does not increase memory stability through repeated success on the same calendar day.
// 08
What should happen after a mistake?
A wrong answer can have several causes. You may have made a slip, forgotten a step, applied the wrong rule, or relied on a prerequisite you do not yet understand. Diagnosis means using the answer to investigate which explanation fits.
Look for the first step that stops making sense
Return to the equation with fractions. If you rearrange it correctly but add the fractions incorrectly, the useful repair is fraction arithmetic. If you add them correctly but change only one side of the equation, the repair is the rule for keeping an equation balanced. The final wrong answer alone would hide that difference.
uses graded attempts and prerequisite relationships to guide further practice. The aim is to address the gap and return to the problem that exposed it. A diagnosis remains an estimate that later answers can correct.
// 09
Become ready for larger work
An education for a post-AGI world needs a way to tell whether greater capability in a model is becoming greater capability in the learner. Generating more explanations cannot answer that question. What happens when the learner meets another problem?
Perhaps you can now solve the equation that stopped you earlier. Perhaps you remember the method a week later, without opening your notes. These are changes in what you can demonstrate. They give us a reason to change your route. Reaching the bottom of a page gives us rather less to go on.
That is why the route and pace can vary. One learner may need an earlier idea repaired; another may be ready for a new application. The route should respond to that difference while keeping the same question in view: what can you now do with the idea?
We want that ability to serve questions of your own. With a causal model, you can state what you think produces an outcome, consider another explanation, and propose a test that could change your mind. That is why technical foundations matter to the education we are building: they give you something to reason with when you choose what to investigate or attempt.
Return to the equation with fractions. It once stopped you; now it is a step in a larger problem. That is what we want each part of the route to make possible. The mathematics behind a model becomes something you can work with, and the next question can be more ambitious because you have somewhere to begin.