Mastery that forgets on purpose

Most learning apps treat "you learned this" as a permanent fact. You finished the lesson, the checkbox is ticked, done forever. That is fine for tracking what someone has seen. It is useless for tracking what they can still do, because people forget, and a model that never forgets will tell you a student is fine right up until they fail.

Lumen8 is a mastery-based maths platform for K-8, built to the NSW curriculum. It tracks two separate things on purpose, because they answer different questions.

Two signals, decoupled

Completion is binary and per-strategy: did you do it? It never decays. A teacher can toggle strategies on and off without corrupting the record of what was attempted.

Mastery is a score from 0 to 400, and it decays. This is the "how well, and how recently" signal. The two are deliberately decoupled so that fiddling with one never silently rewrites the other.

The score maps to tiers: Completion, Bronze, Silver, Gold, Diamond. Each tier has a floor, a decay rate, and a grace period before decay starts.

Decay toward the floor, not toward zero

The naive version of forgetting is "subtract a bit every day until zero." That is wrong, and it feels wrong to a student who worked hard to reach Gold and watched it evaporate. Lumen8 decays a percentage of the surplus above the tier floor:

baseDecay = (score - tierFloor) * tierDecayRatePerDay
newScore  = max(tierFloor, score - effectiveDecay)

So a Bronze student sitting at 150, inactive for five days, loses about 0.64 points a day. After a month they are around 131. After a hundred days they asymptotically approach the Bronze floor of 100 and stop. You drift back toward the floor of what you earned, you never crash through it. Reaching a tier means something.

Three modifiers that make it humane

The base decay is then bent by what the student is actually doing:

• Foundational depth. Root submodules (the Year 5 basics everything else builds on) decay up to 30 percent slower than the advanced Year 8 topics. The stuff you need most fades least.
• A related-activity shield. If any submodule within two hops on the prerequisite graph saw activity in the last three days, decay is halved. Working on algebra protects the connected number and fraction submodules, because in real learning they are not separate.
• Showing up. Any activity at all today halves the day's decay. Turning up is rewarded, even on the days the work is light.

None of this is the interesting-looking part of the product. There is no animation for it. But it is the difference between a progress bar and a model that actually tracks whether a kid can still do the maths, and that is the whole point of calling it mastery.