Math Gauge — The Telemetry Tool to Measure Math Reliability

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

PAGE-ID: EDK-MET-MTH-GAUGE-PBS-v0.2
Role: LAN.Measurement + Scorecard + DriftAlarm
Purpose: convert “I think I can do it” into measurable stability under variation and time.

0) Definition Lock

Math Gauge := the measurement layer of Math OS that scores a learner on:

  • Precision (accuracy + correctness)
  • Bandwidth (structure recognition / compression ability)
  • Speed (pace stability under time)
  • DriftRisk (silent collapse risk under pressure)

Lock: A topic is “learned” only if it survives variation + timed conditions, not just homework form.

1) The Four Core Metrics (LOCKED)

Metric P — Precision Score (0–5)

Meaning: correctness, clean steps, correct method execution.

ScoreMeaning
0cannot solve / random
1partial but unstable
2solves only in one form
3usually correct, minor slips
4correct across forms
5correct + explains + checks reliably

Feeds from sensors: Foundation Fluency, Error Recurrence.

Metric B — Bandwidth Score (0–5)

Meaning: “how much structure you see” per glance; speed of recognising the type and reducing it.

ScoreMeaning
0cannot classify
1slow recognition
2recognises with hints
3recognises independently
4fast recognition + clean plan
5can compress & generalise patterns

Feeds from sensors: Method Selection, Transfer/Variation.

Metric S — Speed Score (0–5)

Meaning: pace stability, time-to-solution under exam-like conditions.

ScoreMeaning
0cannot finish
1severe time collapse
2finishes but rushed errors
3pace acceptable
4fast + stable
5reflex-level stable under pressure

Feeds from sensors: Pace Budget, Fluency.

DriftRisk — {Low, Medium, High}

Meaning: probability of silent failure under load even when the student “can do” untimed.

High DriftRisk indicators:

  • careless spike under timing
  • method switching / panic
  • large variance between practice and test
  • end-of-paper collapse

Feeds from sensors: Pace Budget + Error Recurrence + Transfer.

2) Math Gauge Scorecard (Topic-Level)

Each topic family gets a scorecard:

  • Precision __ / 5
  • Bandwidth __ / 5
  • Speed __ / 5
  • DriftRisk: Low / Medium / High
  • Notes: top 1 failure bucket (B1–B6)

3) Certification Ladder (Optional, mirrors Vocabulary Gauge)

  • Bronze: Foundation stable (P≥2 and DriftRisk not High)
  • Silver+: Precision ≥ 3
  • Gold+: Bandwidth ≥ 3
  • Professional+: Speed ≥ 4
  • Critical+: passes trap suite (mixed set + timed, low drift)

4) Minimal Test Protocol (How to produce the numbers)

To compute P/B/S without over-testing:

Test Set A — Accuracy (Precision)

  • 8–12 questions in one family, include 2 variants (V1/V2)

Test Set B — Recognition (Bandwidth)

  • 10 “signal-only” items (choose method without solving)

Test Set C — Timed Mini (Speed)

  • 15–25 minutes, mixed set (small paper)
  • enforce pace budget + checking protocol

Then compute:

  • Precision = accuracy + step quality
  • Bandwidth = method recognition speed/accuracy
  • Speed = completion + stability under time
  • DriftRisk = variance + careless spike rate

5) Reading the Math Gauge — Decision Policy

Unified Almost-Code Interpretation Spec v0.2

PAGE-ID: EDK-STD-MTH-GAUGE-READING-v0.2

5.1 The One Rule

The lowest metric determines the next action.

Case A — Precision low (0–2)

Action: Fluency Lab + Repair Lab
Do not: timed papers yet.

Case B — Bandwidth low (0–2)

Action: Method Signal Lab + Variation Ladder
Do not: memorise steps.

Case C — Speed low (0–2)

Action: Timed Stability Lab with smaller scope
Do not: increase breadth.

Case D — DriftRisk High (any score)

Action: freeze new topics; isolate weak buckets; repair + retest ≤ 7 days.

6) Failure Mode Trace (Gauge-Specific)

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

no measurement
→ “can do” illusion
→ weak transfer
→ timed collapse
→ repeated errors

Repair

apply Math Gauge
→ read the Gauge
→ run the right Lab
→ retest

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