Math OS Boot — M-GATE (Start Here)

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

PAGE-ID: EDK-BOOT-MTH-MGATE-v0.2
Role: LAN.Boot + Router + SafetyRules
Binding: installs the Math OS mental model so parents/students stop “covering topics” and start building stable capability (Foundation→Connection→Performance). (edukatesg.com)

0) Definition Lock

Math OS Boot (M-GATE) := the onboarding gateway that installs 5 truths:

  1. Math is a system, not a chapter list.
  2. Most “math weakness” is a broken link, not low IQ. (edukatesg.com)
  3. Practice only works after you repair the weakest link.
  4. Transfer matters (variants), not repetition of the same form.
  5. Timed stability matters (pace + checking), not untimed comfort.

1) Router (Choose Your Path)

Router A — Primary (PSLE)

Goal: number sense + models + word-problem decoding + pace.

Router B — Secondary E-Math

Goal: method selection + mixed-topic stability + exam pace.

Router C — Secondary A-Math

Goal: algebra-first fluency + transformation speed + multi-step accuracy.

Router D — Parent Operator

Goal: identify broken link fast; stop wasting time on the wrong drills.

2) The 3-Layer Install (the only model you need)

MTH.OS.Stack :=
  Foundation → Connection → Performance

Foundation examples: manipulation fluency, fraction handling, algebra rules.
Connection examples: linking factorisation ↔ equations ↔ graphs; seeing families of methods.
Performance examples: speed, checking, pace budget, exam judgement. (edukatesg.com)

3) The Boot Diagnostic (10-minute “Where are you leaking?”)

Diagnostic ID: MTH.BOOT.DIAG.10

Run 10 minutes and label every miss as one of 6 buckets:

  • B1 Concept (doesn’t know what the idea is)
  • B2 Manipulation (knows idea, can’t execute fluently)
  • B3 Method Selection (doesn’t know which method)
  • B4 Representation (can’t translate word problem to math form)
  • B5 Careless/Execution (slips, signs, copying, arithmetic)
  • B6 Time/Pace (correct untimed, collapses timed)

Boot rule: you are not allowed to say “I’m weak in math” without a bucket label.

4) The One-Bottleneck Rule (Boot Safety)

Fix one bottleneck first.

If you fix the wrong thing (e.g., spam papers when it’s a manipulation leak), you get:

  • slow speed
  • repeated errors
  • lost confidence
    (which your approach page describes as “gaps compounding.”) (edukatesg.com)

5) Minimal Loop Install (7-Day Starter)

Objective: prove Math OS works in one week using a tiny scope.

Daily (10–20 min)

Day loop:
  Diagnose (2–3 questions)
→ Repair (micro-skill drill)
→ Link (why method)
→ Variation (2 forms)
→ Mini-timed (3–5 min)
→ Log error rule (1 line)

Scope cap

  • Primary: 1 micro-skill + 1 word-problem pattern only
  • Secondary: 1 technique family only (e.g., factorisation family, linear equations family)

6) First Measurement (Day 7: Mini Gauge)

You don’t need a full “Math Gauge page” yet—Boot only needs a mini scorecard:

  • Precision: % correct on a mixed mini-set
  • Bandwidth: method recognition speed (how fast you see structure)
  • Speed: time per question type
  • DriftRisk: did careless errors spike under time?

Boot pass condition (default):

  • Precision ≥ 70% on the target family
  • Speed improves (or time budget meets target)
  • DriftRisk not High (careless not dominating)

7) Boot Graduation Criteria

You pass M-GATE when:

  • you can classify errors into buckets without guessing
  • you can execute One-Bottleneck repair
  • you can do a mini timed run without panic collapse
  • your pace is improving week-to-week

8) Mandatory Links (Boot must route into the stack)

After Boot, the page must route to the Math OS ladder:

  1. Math OS Protocol (rulebook)
  2. Math OS Labs (drill environments)
  3. Math OS Sensors Directory (instrument panel)
  4. Math Gauge (full PBS + DriftRisk)
  5. Reading the Math Gauge
  6. Monitoring Math Health
  7. Interface: Math OS ↔ Education OS
  8. Math Learning System Hub (canonical subject hub) (edukatesg.com)

9) Failure Mode Trace (Boot-Specific)

Trace ID: EDK-TRACE-MGATE-PAPERSPAM-v0.2

start with full papers
→ many errors
→ no classification
→ no targeted repair
→ repeated same mistake type
→ time pressure increases
→ confidence collapses

Repair

bucket the errors
→ fix one bottleneck
→ variation
→ mini timed
→ retest ≤ 7 days

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)

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