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Why do the colours change at the end?

Because the two halves of the picture come from different places.

When the replay finishes, the key lets you switch between the two. Without a file made by the latest exporter (or a share link made from one) there are no Math Academy levels to show, so the whole graph stays an estimate and the key says so.

Math Academy’s own levels (the finished picture)

The exporter asks Math Academy, once per course you have studied, how long it expects you to remember each topic you have practised (its “half-life”: roughly how long until your chance of recalling it falls to 50%) and how many times it counts the topic as practised. That count includes credit passed down to prerequisites, so it is higher than your number of tasks. The finished picture uses these numbers as they were when you exported, so it matches what Math Academy itself shows.

The estimate (the replay, and files without Math Academy’s levels)

Math Academy’s numbers exist only for now, not for each past day, so the replay as you scrub or play draws its own estimate from your task history. It is a picture of the journey, not a measurement, and it can differ from Math Academy’s own numbers, particularly at the end of a replay.

1. Each task becomes a rating. The points a task awarded are compared with its base points. Nothing awarded counts as forgotten; part of the points counts as a hard recall; full points count as a good one, and a clear bonus on top counts as an easy one. Lessons are slightly more forgiving: 90% of the points is treated as full marks.

2. The ratings feed a memory model. Tasks on a topic are replayed in date order through FSRS, an open-source spaced-repetition model also used by flashcard apps. For each topic it tracks how long the memory is predicted to last, as a half-life: roughly how many days until your chance of recalling it falls to 50%. A good recall after a gap makes the memory last longer, a miss makes it shorter, and the days between tasks are taken into account. Quizzes, and the credit Math Academy passes down to prerequisites, are not part of this estimate.

3. That length becomes a colour. As you scrub or replay, every topic shows the level it had at that point in your history.

The memory levels

• Not startedNo completed task on the topic yet.
• FreshNewly learned: the memory is predicted to last under about 2 days.
• ShakyPredicted to last about 2 to 8 days.
• DecentPredicted to last about 8 days up to around 3 months.
• StrongPredicted to last from around 3 months up to 5 years.
• Locked inPredicted to last 5 years or more.

What it can’t see

Only completed tasks and your topics’ current memory levels are in your file. Anything you did outside tasks is invisible here, and Math Academy’s levels are a snapshot of the moment you exported, so export again to refresh them. A topic Math Academy did not report (for example one that only appears as a prerequisite) keeps the estimate.

The stats panel shows your XP divided by the time you spent, as a running figure up to the point you have scrubbed to, for the courses you have ticked. It is shown with a “~” because the time is an estimate.

Where the time comes from

Math Academy’s own XP per minute counts only the time spent answering questions, taken from each answer’s timer. Fetching that would take a request for every task you have ever done, which is too much to ask of Math Academy’s servers, so the exporter does not. Instead the time between a task’s start and finish is used, capped at 30 minutes (a task left open for hours was paused, not worked on).

That span includes reading and pauses, most of all in lessons, so it is scaled down by task type: lessons to 65%, reviews to 80%, quizzes as they are, multistep tasks up by 30% (they often run past the cap) and placement tests to 75%. These shares were measured against Math Academy’s own timings for one learner’s 2,916 tasks, where they bring the total to within about 1% of Math Academy’s figure (about 600 hours and 0.74 XP per minute).

How far to trust it

Treat it as roughly right, typically within about a third, not exact. How much of a lesson goes on reading changes over the months, and one learner’s measurements may not fit another’s: for the same learner the lesson share was 43% of the span early on and 90% later. Individual tasks can be off by a few minutes either way. Trends and comparisons between your own courses are more reliable than the exact number.

A course’s progress is the topics in its list that have at least one task in your history, out of every topic on that list. The list is the one saved in your export, so it can run ahead of what you did: Math Academy adds topics to courses over time, and one you finished a while ago may have grown since. Topics can also be credited without a task of their own, for example when you pass a more advanced topic and Math Academy counts the ones it builds on. Neither shows up as a task, so those topics stay uncounted.

The totals here come from the course lists in your export, not from the live course page. Math Academy revises its courses (topics are added, moved or removed), so the live page can list more or fewer topics than the course had when your export was made. A topic shared by several courses is counted once when you show more than one. Export again to pick up the latest course lists.

A list of completed tasks. Each needs a type, a completed date and its topic with that topic’s prerequisites. Without prerequisites you still get the topics, but no connecting lines. The file can also be an object with tasks and topics, a list of { id, halfLife, repetition } for the topics you have practised: that is what the exporter makes, and it makes the colours Math Academy’s own.

The graph itself, squeezed into the link after the #, which browsers never send to any server: topic names and how they connect, the order they were learned, each step’s colour, XP and minutes, and each topic’s final colour (Math Academy’s own levels, if your file had them). By default calendar dates are removed, so a shared replay shows “step 400 of 1,200” instead. If you choose to share the full journey the days are included too, and the share panel warns you first. Anyone with the link can open it, and it cannot be taken back once sent, so share it only with people you trust.

A link holds only data: names, numbers and colours, never code or scripts. Everything in it is shown as plain text, and the viewer checks every link before using it, so a damaged, oversized or deliberately malformed link is refused instead of opened. Opening a link someone sent you will not change your own saved graph.

Only in this browser, on this device, using its own storage. Nothing is sent to us or anyone else, so it will not follow you to another browser or computer. Use “Forget my saved graph” under the title to remove it, or clear this site’s data in your browser settings.

The demo is a real learner’s journey, shown by day only. Unofficial community project; not affiliated with Math Academy.