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Math OS Labs — The Practice Engine

Unified Almost-Code Execution Environment Spec (Registry-Clean) v0.2

PAGE-ID: EDK-LAB-MTH-EXEC-v0.2
Role: LAN.Labs + DrillEnvironments + TimedStability
Purpose: turn the Math OS Protocol into daily/weekly training blocks that directly repair sensor leaks and restore P3 stability.

0) Definition Lock

Math OS Labs := controlled drill environments that make the loop executable:

Diagnose → Repair → Link Method → Variation → Timed Run → Review → Retest

Labs are NOT “more practice papers.”
Labs are targeted environments that fix one leak fast.

1) Lab Architecture (Schema)

Every lab declares:

LabID
Target Sensor(s)
Target Bucket(s) (B1–B6)
Time Cap
Dataset Scope (question count)
Pass Condition
Retest Rule

2) The 6 Canonical Labs (matched to the 6 sensors)

LAB 1 — Foundation Fluency Lab

LabID: MTH-LAB-FOUND-FLUENCY
Targets: Sensor 1 (Foundation Fluency)
Buckets: B2 (Manipulation), sometimes B1
Time Cap: 10–15 min
Scope: 20–40 micro-questions

Drill

  • rapid simplification / expansion / factorisation micro-sets
  • fraction/ratio micro-sets (primary)
  • algebra manipulation chains (secondary)

Pass Condition

  • ≥ 90% accuracy at target micro-skill
  • hesitation drops (no “stuck” pauses)

Retest

  • next day + 7 days (delayed fluency stability)

LAB 2 — Method Signal Lab (Choose Without Solving)

LabID: MTH-LAB-METHOD-SIGNAL
Targets: Sensor 2 (Method Selection)
Buckets: B3
Time Cap: 10 min
Scope: 15–25 questions (signal-only)

Drill

For each question, write only:

  • Signal → Method (one line)

No full solutions allowed.

Pass Condition

  • ≥ 80% correct method choice within 15–20 seconds per item

Retest

  • mixed set weekly

LAB 3 — Representation / Encoding Lab

LabID: MTH-LAB-REP-ENCODE
Targets: Sensor 3 (Representation)
Buckets: B4
Time Cap: 15–20 min
Scope: 6–10 word problems

Drill

No solving at first. Only:

  • define variables
  • translate sentences → equations/constraints
  • draw bar model / diagram / table (as required)
  • list given vs unknown vs condition

Pass Condition

  • setup is correct ≥ 80% (even if final solution not done)

Retest

  • 48h later on new word-problem set

LAB 4 — Variation Ladder Lab (Transfer Engine)

LabID: MTH-LAB-VARIATION-LADDER
Targets: Sensor 6 (Transfer)
Buckets: B3 (often), hidden B1
Time Cap: 20–30 min
Scope: 12–18 questions across V-levels

Variation Levels

  • V0 same form (warm)
  • V1 small surface change
  • V2 different context
  • V3 mixed-step
  • V4 exam-style unfamiliar

Pass Condition

  • can clear V2 reliably before attempting V3–V4

Retest

  • weekly mixed set

LAB 5 — Timed Stability Lab (Pace + Checking)

LabID: MTH-LAB-TIMED-STABILITY
Targets: Sensor 5 (Pace Budget)
Buckets: B6 + B5 under pressure
Time Cap: 20–40 min
Scope: mini-paper (10–20 marks equivalent)

Drill

  • strict pace budget per item
  • mandatory checking protocol:
  • sign scan
  • substitution check (where applicable)
  • estimation sanity check

Pass Condition

  • finishes within budget
  • careless rate decreases week-to-week
  • no end-of-paper collapse

Retest

  • same format weekly (track time/accuracy)

LAB 6 — Error Repair & Retest Lab (Anti-Recurrence)

LabID: MTH-LAB-REPAIR-RETEST
Targets: Sensor 4 (Error Recurrence)
Buckets: any (but focuses repair discipline)
Time Cap: 10–15 min
Scope: 5–10 failed questions

Drill

For each failed question:

  1. label bucket (B1–B6)
  2. rewrite the critical line correctly
  3. write one-line rule:
  • “I must … because …”

Pass Condition

  • same error does not repeat in the next 7 days set

Retest

  • retest ≤ 7 days is mandatory

3) Default 14-Day Cycle (Minimal, Works for Families)

Days 1–3   → LAB1 Fluency + LAB2 Method Signal
Days 4–6   → LAB3 Representation + LAB4 Variation Ladder
Day 7      → Timed Mini (LAB5) + quick review
Days 8–10  → LAB6 Repair (weak set) + targeted lab repeats
Days 11–13 → LAB4 Variation (raise V-level) + LAB5 timed
Day 14     → Retest + update sensors

4) Scope Caps (Boot Safety Rules)

  • If Fluency sensor red → do not increase topic breadth
  • If Representation sensor red → do not spam papers
  • If Pace sensor red → reduce set size, add timed minis
  • Always fix one bottleneck first

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

5) Failure Mode Trace (Lab-Specific)

Trace ID: EDK-TRACE-MTH-LAB-WRONGDRILL-v0.2

student fails
→ chooses random drill type
→ works hard but wrong target
→ error recurrence remains high
→ time pressure worsens
→ belief “math is hard”

Repair

sensor identifies leak
→ correct lab selected
→ retest ≤ 7 days
→ 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: 

Recommended Internal Links (Spine)

Start Here for Lattice Infrastructure Connectors