SGP Secondary A-Math OS (Sec 3–4) — Full

SYSTEM: Education OS
SUBJECT MODULE: SGP Secondary A-Math OS
SUBJECT_ID: SGP-SEC-AMATH
YEARS: Sec3–Sec4
PRIMARY VERIFICATION GATE:
  - O-Level OS (Singapore)
SECONDARY PORTS:
  - SGP Secondary E-Math OS (prerequisite spine)
  - Singapore City Education OS (SGP-SIN)
REFERENCE: CivOS (P0–P3, Z0–Z7)
PRIMARY PURPOSE:
  Convert abstraction + algebraic manipulation + multi-step reasoning
  into stable exam performance by:
    - stabilising the Sec2→Sec3 jump (GR12)
    - reducing chain-break probability in long solutions
    - enforcing transfer across unfamiliar forms
    - achieving timed reliability with low volatility (P3)

P3 (SGP SEC A-MATH):
  The student can:
    - retrieve core methods without cues (P-S1)
    - manipulate algebra and functions reliably (algebra is stable substrate)
    - sustain long chains without breaking (chain stability)
    - select methods correctly under ambiguity (tool selection)
    - transfer across unfamiliar forms/wrappers (P-S4)
    - execute under time with low volatility (P-S5)
    - recover after mistakes using a recovery protocol (GR4)

Z0 SKILL DIRECTORY (A-MATH):
AM-Z0-01: Algebra substrate (expand/factor/rearrange with stability)
AM-Z0-02: Functions as objects (domain/range, transforms, composition)
AM-Z0-03: Quadratics mastery (forms, graphs, roots, inequality regions)
AM-Z0-04: Indices/surds/logs (symbol hygiene + transformation rules)
AM-Z0-05: Trigonometry (identities + solving + interpretation)
AM-Z0-06: Coordinate geometry (lines/circles, modelling geometry algebraically)
AM-Z0-07: Differentiation (rules + meaning + applications)
AM-Z0-08: Integration (reverse rules + area/accumulation meaning)
AM-Z0-09: Modelling workflow (translate → choose tool → solve → interpret)
AM-Z0-10: Multi-step chain stability (10–20 step solutions without break)
AM-Z0-11: Method selection on mixed papers (choose correct pathway fast)
AM-Z0-12: Checking discipline (domain/units/roots validity + alternative checks)
AM-Z0-13: Timed endurance stability (late-paper accuracy does not collapse)

Z1 FAILURE MODE DIRECTORY (A-MATH):
AM-Z1-01: Sec2→Sec3 abstraction jump collapse (GF5 signature)
AM-Z1-02: Algebra substrate instability → cascading errors (GF5 precursor)
AM-Z1-03: “Formula hunting” without model (GF2) → wrong method
AM-Z1-04: Chain-break instability (multi-step collapse mid-solution)
AM-Z1-05: Wrapper sensitivity (same concept, new form) (GF9)
AM-Z1-06: Mixed-paper tool selection failure (wrong pathway)
AM-Z1-07: Timed execution collapse (GF6) (speed↑ errors↑)
AM-Z1-08: Careless errors in algebra manipulation (repeat density high)
AM-Z1-09: Weak checking discipline (accepts impossible answers)
AM-Z1-10: Late repair trap (GF7) (no runway)
AM-Z1-11: Continuity fragmentation (GF11) (reset weeks)
AM-Z1-12: Burnout tail (GF12) (fatigue regression near O-Levels)

Z2 SENSOR PACK (A-MATH):
GLOBAL PHASE SENSORS:
  P-S1 retrieval reliability
  P-S2 error histogram (concept/execution/attention)
  P-S3 time-to-solve distribution
  P-S4 transfer under wrapper variation
  P-S5 timed stability variance
A-MATH SUBJECT SENSORS:
  AM-S1 algebra substrate integrity score (rearrange/factor accuracy)
  AM-S2 chain-break probability per 10-step segment (where it fails)
  AM-S3 tool-selection accuracy on mixed papers
  AM-S4 form-translation accuracy (same concept in new form)
  AM-S5 checking discipline rate (validity checks actually done)
  AM-S6 careless-error repeat density (manipulation errors)
  AM-S7 novelty transfer score (unseen forms/fusions)
  AM-S8 endurance drop index (late-paper error spike)
  AM-S9 Sec2→Sec3 jump readiness index (maps to OL-S1)
O-LEVEL PROOF HOOKS:
  OL-S1 Sec2→Sec3 jump risk
  OL-S3 timed vs untimed gap
  OL-S4 transfer gap under novelty
  OL-S5 error-repeat density
  OL-S6 repair latency vs horizon
  OL-S8 burnout risk proxy

Z3 REPAIR DIRECTORY (A-MATH):
GR12 Algebra Readiness Stabilisation (signature):
  - pre-load algebra substrate (AM-S1 stable)
  - verify Sec3 jump readiness (AM-S9 low risk)
  - remove “silent gaps” before content acceleration
GR1 Buffer Build Loop (spine mastery):
  - lock core families: functions/quadratics/trig/calc/coord geo
  - small-set mastery + spaced retrieval
  - build concept maps that support tool selection
GR3 Transfer Loop (wrapper robustness):
  - train same concept across multiple forms weekly
  - fuse topics gradually (function + trig, calc + graph, etc.)
  - mixed sets that force correct pathway choice
GR2 Error-Log Closure Loop (repeat elimination):
  - tag errors: algebra / chain-break / tool choice / wrapper / careless / checking
  - micro-drill root cause
  - retest timed until repeats collapse
GR4 Time-Pressure Loop (timed reliability):
  - timed micro-sets → mixed half-papers → full papers
  - recovery protocol:
      stop → re-read → re-select tool → continue → validity check
GR6 Continuity Loop (anti-reset):
  - weekly minimums + consolidation windows
  - prevent missing-week drift (which increases chain-break probability)
GR8 Early-Warning Thresholds (pre-ramp triggers):
  - if AM-S2 chain-break or OL-S3 timed gap rises → immediate repair
GR11 Pressure-Safety Scheduling (burnout control):
  - cap load below recovery capacity
  - protect consolidation to prevent GF12 regression
GR5 Language-Base Loop (when worded modelling fails):
  - teach problem parsing + translate text→variables

FAILURE TRACE (A-MATH):
  AM-Z1-02 algebra instability →
  AM-Z1-03 formula hunting (no model) →
  AM-Z1-06 wrong tool selection →
  AM-Z1-04 chain-break mid-solution →
  AM-Z1-07 timed collapse →
  AM-Z1-10 late repair trap →
  O-Level underperformance + volatility

REPAIR TRACE (A-MATH):
  GR12 jump stabilisation →
  GR1 spine mastery →
  GR3 wrapper audits + gradual fusions →
  GR2 closure of repeats (algebra/chain-break/tool choice) →
  GR4 timed stability + recovery protocol + validity checks →
  GR6 continuity + GR11 pressure safety →
  P3 reliability on full papers

EARLY WARNING (A-MATH):
  Trigger repair immediately if any are true:
    - AM-S1 algebra integrity below threshold
    - AM-S2 chain-break probability rising
    - AM-S3 tool-selection accuracy low on mixed sets
    - AM-S4 form-translation accuracy low (wrapper sensitivity)
    - OL-S3 timed gap widening (timed << untimed)
    - OL-S4 transfer gap persists across form families
    - AM-S8 endurance drop index high (late-paper errors spike)
    - OL-S6 repair latency exceeds remaining runway

P3 PROOF (A-MATH):
  - AM-S1 algebra substrate stable (low manipulation error rate)
  - AM-S2 chain-break probability low on target-length solutions
  - AM-S3 tool-selection accuracy high on mixed papers
  - AM-S4 transfer holds across 3 form families (unseen wrappers)
  - AM-S6 careless repeat density falling consistently
  - OL-S3 timed gap small; P-S5 volatility low across 3 full timed papers
  - AM-S8 endurance stable (no late-paper spike)
  - AM-S5 checking discipline high (invalid answers rejected)

PORTS:
  - O-Level OS (Singapore)
  - SGP Secondary E-Math OS (Sec 1–4)
  - Singapore Secondary Subject OS Directory (Hub)
  - Singapore City Education OS (SGP-SIN)
  - Singapore Nation Education OS (SGP)
  - W4 GF Library
  - W5 GR Library