Secondary Math OS Hub — E-Math + A-Math + O-Levels (Operator Master Page)

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

PAGE-ID: EDK-HUB-SEC-MTH-OS-v0.2
Role: HUB.Subject + Directory + Wrappers + OperatorGuide + LinkGovernance
Purpose: make eduKateSG’s Secondary Math “complete”: one master page that routes students/parents/tutors into the correct OS, sensors, labs, gauge, and exam wrappers—without topic-chasing.

0) Definition Lock

Secondary Math OS Hub := the master router that unifies:

  • Math OS Core (Boot / Protocol / Sensors / Labs / Gauge / Monitoring / Interface)
  • Secondary specialisations: E-Math vs A-Math
  • Exam wrappers: O-Level E-Math / O-Level A-Math
  • Kernel bottleneck pages (e.g., A-Math Fluency Kernel)

Lock: Students don’t fail Secondary Math because they didn’t “do enough.”
They fail because they repaired the wrong leak, at the wrong time, with the wrong load model.

1) Audience Router (Fast Entry)

Router A — Sec 1–2 (Foundation building)

Go to: Math OS Core + Foundation Fluency Lab + Representation Lab.

Router B — Sec 3–4 E-Math (O-Level readiness)

Go to: O-Level E-Math Wrapper + Method Signal + Mixed Mini Papers.

Router C — Sec 3–4 A-Math (Sec 3 jump / transformation chains)

Go to: A-Math Wrapper + A-Math Fluency Kernel + Trap Labs.

Router D — Parent Operator (no time, want clarity)

Go to: Sensors Directory → identify leak → run correct lab → retest ≤ 7 days.

2) Core Spine (Math OS — shared for both E/A)

S1 — Boot (M-GATE): install the model
S2 — Protocol: diagnose → repair → variation → timed stability → retest
S3 — Sensors Directory: 6 sensors (foundation, method, representation, errors, pace, transfer)
S4 — Labs: 6 labs matching sensors
S5 — Math Gauge: Precision/Bandwidth/Speed + DriftRisk
S6 — Monitoring Math Health: trend classifier M0–M4
S7 — Interface: Math ↔ Education OS: cross-subject learning velocity

This is the same “complete OS” structure you already locked for Vocabulary OS.

3) Split: E-Math vs A-Math (Definition Locks)

E-Math (Operational definition)

E-Math is the mixed-topic method selection + representation + pace exam.

Dominant failure modes:
B3 (method selection), B4 (representation), B6 (pace), B5 (careless).

A-Math (Operational definition)

A-Math is a transformation chain reliability exam.

Dominant failure modes:
B2 (manipulation fluency), chain break, traps (domain/extraneous), B6 pace.

4) Canonical Directories (What must exist under the hub)

4.1 E-Math Directory (Z0–Z3 skeleton)

Goal: method selection + representation + mixed set stability.

Z0 (Foundation): arithmetic, algebra basics, ratios/percentages
Z1 (Method signals): identify tool quickly
Z2 (Transfer): mixed sets, 2-step reasoning
Z3 (Timed): pace budget + audit routine

4.2 A-Math Directory (Z0–Z3 skeleton)

Goal: chain discipline + traps + timed stability.

Z0: algebra kernel
Z1: method signals + constraints
Z2: variation ladder (multi-step)
Z3: timed minis + trap audit

5) Exam Wrappers (O-Level)

Wrapper 1 — O-Level E-Math

What it enforces: mixed-topic switching control + pace + check discipline.

Wrapper 2 — O-Level A-Math

What it enforces: algebra-first + transformation chain discipline + trap prevention.

6) Kernel Bottleneck Pages (High leverage)

Kernel — A-Math Foundation Fluency Kernel (Sec 3 jump)

This must be featured prominently as the default fix for “Sec 3 collapse.”

Kernel law: if algebra fluency is weak, full papers are wasted until repaired.

7) Operator Decision Tree (1-minute routing)

Start → Run 10-min diagnostic
→ classify dominant bucket (B1–B6)
→ pick sensor + lab
→ run 7–14 day cycle
→ gauge test
→ retest ≤ 7 days for repeats
→ expand only after stability

8) “Complete Site” Link Governance (what this hub must link to)

This hub must link to (and each child page must link back up):

  • Math OS Boot (M-GATE)
  • Math OS Protocol
  • Math OS Sensors Directory
  • Math OS Labs
  • Math Gauge + Reading the Math Gauge
  • Monitoring Math Health
  • Interface: Math ↔ Education OS
  • O-Level E-Math Wrapper
  • O-Level A-Math Wrapper
  • A-Math Fluency Kernel
  • (Optional) PSLE Math Wrapper (for cross-grade continuity)

9) Failure Mode Trace (Secondary hub-specific)

Trace ID: EDK-TRACE-SEC-MTH-TOPICCHASE-v0.2

student chases topics
→ gaps compound
→ mixed sets expose method confusion
→ time pressure rises
→ careless spikes
→ grade collapses

Repair

use hub routing
→ sensors identify leak
→ correct lab
→ gauge + monitoring
→ stable growth

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