Math OS Protocol — The Rulebook of Math Mastery

Unified Almost-Code Canonical Protocol Spec (Registry-Clean) v0.2

PAGE-ID: EDK-PROTO-MTH-LOOP-v0.2
Role: LAN.Protocol + DecisionPolicy + RepairLogic + ExamLoadStability
Binding: implements your math law: gaps compound; fix the broken link; mastery = stable method + transfer under time. (edukatesg.com)

0) Definition Lock

Math OS Protocol := the fixed execution rules that convert “I studied” into repeatable performance.

Lock: If you are not doing diagnosis → targeted repair → variation → timed stability → retest, you are not running Math OS.
(This is the Math version of your closed-loop OS enforcement across eduKateSG.)

1) The Only Approved Loop (MTH.OS.Loop)

MTH.OS.Loop :=
  Diagnose
→ Classify failure bucket
→ Repair weakest link
→ Link method (why / signals)
→ Train variation (transfer)
→ Timed run (pace + checking)
→ Review error log (one-line rule)
→ Retest ≤ 7 days

Reason: your approach page states gaps compound and “one broken link” collapses later topics; this loop prevents compounding by repairing upstream first. (edukatesg.com)

2) Failure Bucket Classifier (B1–B6) — LOCKED

Every mistake must be labelled as:

  • B1 Concept (don’t know the idea/definition)
  • B2 Manipulation (know idea, can’t execute fluently)
  • B3 Method Selection (don’t know which method)
  • B4 Representation (can’t translate from words/diagram to math form)
  • B5 Careless/Execution (slips, signs, arithmetic, copying, weak checking)
  • B6 Time/Pace (correct untimed, collapses timed)

Protocol rule: no “weak topic” language is allowed without a bucket.
This is what makes repair efficient instead of emotional.

3) Repair Logic (One-Bottleneck Rule) — LOCKED

If multiple failures exist:
  Fix the smallest upstream bottleneck that removes the most downstream errors.

Examples:

  • B2 manipulation leak often masquerades as B3 (method) because execution is too slow/ugly to reach the method step.
  • B4 representation leak makes every word problem feel “hard” even when math skill is fine.

This is the operational version of your “broken link” law. (edukatesg.com)

4) Method Linking Standard (Prevents Rote)

Rule: every solved question must include a one-line “method signal” statement:

Signal → Method
Because → Key property
Therefore → Steps

Example templates:

  • “This is quadratic because … therefore factorise / quadratic formula / complete square.”
  • “This is ratio because … therefore unit method / proportion.”

Why: prevents students from memorising steps without selection logic.

5) Variation Standard (Transfer Engine) — LOCKED

A skill is not learned until it survives form-change.

Variation levels

  • V0 same form (warm-up only)
  • V1 small surface change
  • V2 mixed context (same idea)
  • V3 multi-step / mixed topics
  • V4 exam-style unfamiliar variant

Protocol rule: you must reach V2 before you claim “can do”.

6) Timed Stability Standard (Performance Engine)

Timed stability = accuracy + pace + checking.
This is where most students collapse even if they “understand.”

Pace Budget Rule

  • define a time budget per question type
  • if exceeded, the student must trigger a fallback:
  • skip and return
  • simplify
  • partial method marks strategy (for secondary)

Checking Protocol (Mandatory)

Check :=
  arithmetic sanity
+ sign check
+ substitution check (when applicable)
+ reasonableness check (estimation)

Protocol rule: careless errors (B5) are treated as a system leak, not personality.

7) Retest Rule (Anti-Drift)

Retest ≤ 7 days for any bucket that appears ≥ 2 times in a week.

If retest is not done:

  • errors fossilise
  • confidence drops
  • student escalates volume instead of quality

8) Math OS Logging Standard (One-Line Rule Log)

For each mistake, log exactly one line:

Mistake → Bucket → Fix rule

Examples:

  • “Wrong sign when expanding → B5 → rewrite expansion line + sign scan.”
  • “Couldn’t form equation from statement → B4 → define variables + translate sentence-by-sentence.”

This keeps the system light enough for families to actually run.

9) Protocol Pass Conditions (P3 definition by stage)

Primary (PSLE)

  • representation stable (models/constraints)
  • accuracy stable
  • pace stable across word problems

Secondary E-Math

  • method selection stable across mixed sets
  • reduction in repeated error types
  • time budget stable

Secondary A-Math

  • algebra-first fluency stable
  • transformation chain clean
  • multi-step accuracy stable under time

10) Failure Mode Trace (Protocol-Specific)

Trace ID: EDK-TRACE-MTH-NOCLASSIFY-v0.2

Do papers
→ many mistakes
→ no bucket classification
→ no targeted repair
→ repeat same error type
→ time pressure worsens
→ “math is hard” narrative

Repair

Classify → One-bottleneck repair → Variation → Timed run → Retest
→ stability returns

Start here if you want the full sequence:

Vocabulary OS Series Index:
https://edukatesg.com/vocabulary-os-series-index/

Fence English Learning System: 

eduKateSG Learning Systems: 

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