SGP Secondary E-Math OS (Sec 1–4) — Full

SYSTEM: Education OS
SUBJECT MODULE: SGP Secondary E-Math OS
SUBJECT_ID: SGP-SEC-EMATH
YEARS: Sec1–Sec4
PRIMARY VERIFICATION GATE:
  - O-Level OS (Singapore)
SECONDARY PORTS:
  - PSLE OS (Singapore) (foundation reference)
  - Singapore City Education OS (SGP-SIN)
REFERENCE: CivOS (P0–P3, Z0–Z7)
PRIMARY PURPOSE:
  Convert time into reliable mathematical execution by:
    - building algebra + representation spine
    - stabilising method selection on mixed papers
    - enforcing transfer across wrappers (worded/graphical/symbolic)
    - achieving timed reliability with low volatility (P3)

P3 (SGP SEC E-MATH):
  The student can:
    - retrieve core methods without cues (P-S1)
    - translate word problems into equations/diagrams correctly (transfer entry)
    - select the right method under mixed questions (method selection)
    - execute reliably under time (P-S5)
    - check answers intelligently (error containment)
    - transfer across wrapper variation (P-S4)
    - recover after mistakes using a recovery protocol (GR4)

Z0 SKILL DIRECTORY (E-MATH):
  EM-Z0-01: Algebra primitives (expand/factor/rearrange)
  EM-Z0-02: Fractions + indices + surds (symbol hygiene)
  EM-Z0-03: Ratios/rates/percentages (real-world translation)
  EM-Z0-04: Linear equations/inequalities (solve + interpret)
  EM-Z0-05: Graphs as objects (gradient/intercept/shape)
  EM-Z0-06: Geometry + mensuration (diagram reasoning)
  EM-Z0-07: Trigonometry (relationships + application)
  EM-Z0-08: Statistics/probability (data interpretation + inference)
  EM-Z0-09: Word-problem modelling workflow (diagram→variables→equations)
  EM-Z0-10: Mixed-paper method selection (choose correct tool fast)
  EM-Z0-11: Checking discipline (reasonableness + back-substitution)
  EM-Z0-12: Timed endurance stability (maintain accuracy late-paper)

Z1 FAILURE MODE DIRECTORY (E-MATH):
  EM-Z1-01: Algebra base gaps cause cascading failure (GF5 precursor)
  EM-Z1-02: Wrapper collapse on word problems (GF1+GF9)
  EM-Z1-03: Topic partitioning (can do topics, fails mixed papers) (GF9)
  EM-Z1-04: Method selection failure under ambiguity (wrong approach)
  EM-Z1-05: Timed execution collapse (GF6) (speed + errors spike)
  EM-Z1-06: Careless-error density high (checking absent)
  EM-Z1-07: Transfer failure under novelty (same concept, new form) (GF9)
  EM-Z1-08: Late repair trap (GF7) (no runway before O-Levels)
  EM-Z1-09: Practice without model (GF2) (volume, no spine)
  EM-Z1-10: Continuity fragmentation (GF11) (reset weeks)
  EM-Z1-11: Burnout tail (GF12) (fatigue regression)

Z2 SENSOR PACK (E-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
E-MATH SUBJECT SENSORS:
  EM-S1 algebra primitives integrity score (expand/factor/rearrange)
  EM-S2 method-selection accuracy on mixed sets
  EM-S3 worded-wrapper translation accuracy (diagram/variables correct)
  EM-S4 mixed-paper stability index (topics mixed under time)
  EM-S5 checking discipline rate (self-verification compliance)
  EM-S6 careless-error density (repeatable non-concept errors)
  EM-S7 novelty transfer score (same concept, new form)
  EM-S8 endurance drop index (late-paper error spike)
O-LEVEL PROOF HOOKS:
  OL-S2 multi-subject stability
  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 (E-MATH):
GR1 Buffer Build Loop (spine mastery):
  - lock algebra + representation primitives
  - small-set mastery + spaced retrieval
  - stop topic hopping
GR3 Transfer Loop (wrapper robustness):
  - same concept across worded/diagram/graph/symbol forms weekly
  - mixed sets to force method selection
GR2 Error-Log Closure Loop (repeat elimination):
  - tag errors: algebra / translation / method selection / careless / transfer
  - micro-drill root cause
  - retest until repeat rate collapses
GR4 Time-Pressure Loop (timed stability):
  - timed micro-sets → full papers
  - recovery protocol: skip/return + error containment + checking
  - train “stable speed,” not rushing
GR6 Continuity Loop (anti-reset):
  - weekly minimums + consolidation windows
  - prevent missing-week drift
GR8 Early-Warning Thresholds (pre-ramp triggers):
  - if timed gap or transfer gap persists → immediate repair
GR11 Pressure-Safety Scheduling (burnout control):
  - cap load below recovery capacity
  - protect consolidation
GR5 Language-Base Loop (when GF1 present):
  - teach word-problem parsing + key vocabulary + command words
GR12 Algebra Readiness Stabilisation (Sec2→Sec3 protection):
  - ensure algebra spine stable before jump-heavy years

FAILURE TRACE (E-MATH):
  EM-Z1-01 algebra gaps →
  EM-Z1-02 worded-wrapper collapse →
  EM-Z1-04 wrong method selection →
  EM-Z1-05 timed execution collapse →
  EM-Z1-06 careless errors spike →
  EM-Z1-08 late repair trap →
  O-Level underperformance + volatility

REPAIR TRACE (E-MATH):
  GR12 algebra readiness →
  GR1 spine mastery →
  GR3 wrapper audits + mixed papers →
  GR2 closure of repeats →
  GR4 timed stability + recovery protocol →
  GR6 continuity + GR11 pressure safety →
  P3 reliability on full papers

EARLY WARNING (E-MATH):
  Trigger repair immediately if any are true:
    - EM-S1 algebra integrity below threshold
    - EM-S2 method-selection accuracy low on mixed sets
    - EM-S3 translation errors frequent on word problems
    - OL-S3 timed gap widening (timed << untimed)
    - OL-S4 transfer gap persists across wrapper families
    - EM-S8 endurance drop index high (late-paper errors spike)
    - OL-S6 repair latency exceeds remaining runway

P3 PROOF (E-MATH):
  - EM-S1 algebra integrity stable
  - EM-S2 method-selection accuracy high on mixed papers
  - EM-S3 translation accuracy high on worded questions
  - EM-S6 careless-error density falling consistently
  - OL-S3 timed gap small (timed≈untimed)
  - OL-S4 transfer holds across 3 wrapper families
  - P-S5 volatility low across 3 full timed papers
  - EM-S8 endurance stable (no late-paper spike)

PORTS:
  - O-Level OS (Singapore)
  - Singapore Secondary Subject OS Directory (Hub)
  - Singapore City Education OS (SGP-SIN)
  - Singapore Nation Education OS (SGP)
  - PSLE OS (Singapore)
  - W4 GF Library
  - W5 GR Library