Always on
Every tiny mistake becomes a cog
Built from the mistakes you make and fix.
- Sign lost on −3(x − 4) Merged into Negatives under an operation, 4 cogs 68%
- ÷ by −2, not flipped Merged into Negatives under an operation, 4 cogs 68%
- (−2)² written as −4 Merged into Negatives under an operation, 4 cogs 68%
- −b misread in the formula Merged into Negatives under an operation, 4 cogs 68%
- Values in too early Merged into Substituting too early, 2 cogs 44%
- Formula quoted, not derived Merged into Substituting too early, 2 cogs 44%
- cm dropped in the answer Merged into Units in the final line, 2 cogs 31%
- kg and g mixed in one sum Merged into Units in the final line, 2 cogs 31%
- Negatives under an operation Often confused with Substituting too early
- Negatives under an operation Appears alongside Units in the final line
- Substituting too early Appears alongside Units in the final line
- One moment, one mistake
- Merged into
- Often confused with
- Appears alongside
The lifecycle of a cog
Cogs do not pile up. They compound.
It notices. It remembers. It comes back to it.
Here’s what that looks like, stage by stage.
One example term · six weeks
What the stage produced
- 1, planned
Log
Every slip, hint and hesitation is captured, including the ones nobody in the room would notice.
1,284 captured
Tue class · a 41-second pause before the sign-diagram step
- 2, planned
Link
Related cogs connect. A sign error in algebra and a dropped negative in calculus become one thread.
612 linked
Friday's Q4 tied to the same slip in Monday's homework
- 3, next
Merge
Repeated cogs collapse into one stronger signal about a real weak spot, instead of four separate notes.
147 merged
Four sign slips became one weak spot worth a lesson
The four cogs behind "Negatives under an operation"
- Sign lost on −3(x − 4)14 Jul
- ÷ by −2, not flipped28 Jul
- (−2)² written as −405 Aug
- −b misread in the formula19 Aug
Strength rises each time the pattern repeats and falls each time it does not.
- 4, planned
Consolidate
Merged cogs become durable signals that survive between classes, so nothing has to be rediscovered.
38 held
Thursday's class opened on negatives, not on the next syllabus page
- 5, planned
Prune
Once something is genuinely known its cogs fade, so the model stays current instead of growing forever.
96 retired
Index laws · 9 of 9 correct across three weeks, so it faded
Micro-error intelligence
The six signals it reads
Signal
Where it showed up
-
Reasoning gap
A step skipped in the chain, even when the final answer is right.
Cleared6 of 6 on Tue
Chain rule · inner derivative stated
-
Recurring error
The same mistake on a different question.
Open4 since 14 Jul
Sign lost expanding brackets
-
Hint dependency
Answers arrive, but only after help arrives first.
Watching3 of 5 questions
Completing the square, Monday
-
Retention risk
Something known last month and quietly decaying now.
DueThu 3 Sep
Circle theorems · 3 of 8 recalled
-
Canvas hesitation
The pause before the pen moves, not the answer it eventually writes.
Noted41s median pause
Sign diagrams, six attempts
-
Misconception
The wrong mental model underneath a right-looking method.
Blocking3 topics behind it
Reads √(a² + b²) as a + b
What goes in, and what changes
Signals in
- Attempts and answers
- Recall and revision
- Live class and canvas work
Actions out
- Recovers weak concepts
- Adapts the next lesson
- Opens each class where you stopped
One learner model, not a session note.
Every signal on the left changes what the tutor does on the right, in the next class rather than at the end of term.
