SG Syllabus Lattice Directory v0.1 — MATH FIRST (Primary → Secondary → JC

TITLE: SG Syllabus Lattice Directory v0.1 — MATH FIRST (Primary → Secondary → JC)
VERSION: CivOS Unified Spec v1.x
MODE: Almost-Code / LLM-first / WordPress paste-ready
OWNER: eduKateSG Fence Learning Systems
SCOPE: Singapore Math syllabus as a runnable lattice (node registry + couplings + sensors + repair loops)
GOAL: Complete the “most used syllabus” first by publishing an executable Math directory:
      stable IDs, prerequisite graph, transfer tests, failure signatures, Fence repair routes.
CANONICAL CLAIM:
- Math success is not “more practice”. It is prerequisite stability + transfer reliability under time.
- This directory makes Math a computable repair system.
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0) DIRECTORY MAP (WHAT YOU PUBLISH)
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/sg/syllabus/math/                         (Hub)
/sg/syllabus/math/node-registry/           (All nodes, stable IDs)
/sg/syllabus/math/prereq-edges/            (Graph edges)
/sg/syllabus/math/sensor-pack/             (Micro-tests + metrics)
/sg/syllabus/math/failure-atlas/            (Error signatures)
/sg/syllabus/math/repair-protocols/         (Truncation + stitching)
/sg/syllabus/math/coupling-edges/           (Math↔Science↔English WP links)
/sg/exam-sim-os/                            (already built)
/sg/hgw-forecast/                           (already built)
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1) COORDINATE STANDARD (LOCKED)
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ID Grammar:
Place×Lane×Zoom×Role×Type×ID
Place: SG
Lane: MATH
Zoom: Z0 learner (directory is readable at Z1/Z2 as well)
Role: Learner/Tutor/Teacher/Operator
Type: Node/Edge/SensorPack/Protocol/Test/Atlas/Panel
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2) MATH “SPINE GRAPH” (HIGH-LEVEL)
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Spine (Primary → Secondary → JC):
NUM (number sense) →
FRAC (fractions) →
RATIO/% (rate/proportion/percent) →
ALG (algebra) →
FUNC/GRAPH →
GEOM/MEAS →
TRIG/CALC (JC) + STAT (if applicable)
Core coupling:
ENG inference → MATH word problems (H)
MATH ALG/GRAPH → PHY motion/electricity (VH)
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3) NODE REGISTRY (CORE SET v0.1)
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NodeRecord schema:
NodeRecord := {
  ID, LevelBand, Domain,
  Prereq[], Outputs[],
  PhaseTargets,
  TransferTests[],
  Sensors[],
  FailureSignatures[],
  RepairLoops[],
  FenceRules
}
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3.1 PRIMARY CORE NODES (P1–P6)
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Node: SG×MATH×Z0×Learner×Node×MATH-NUM-PLACEVALUE
LevelBand: P1–P3
Domain: Number Sense
Prereq: []
Outputs: [MATH-NUM-4OPS]
PhaseTargets: {P2 by P3}
TransferTests: {mental sums, regrouping, estimation}
Sensors: {RR-math-basic, SII-lite}
FailureSignatures: {PlaceValueSlip}
RepairLoops: {base-10 blocks → regroup drills → timed mini}
FenceRules: {if PlaceValueSlip repeats → truncate new topics; patch here first}
Node: SG×MATH×Z0×Learner×Node×MATH-NUM-4OPS
LevelBand: P1–P4
Prereq: [MATH-NUM-PLACEVALUE]
Outputs: [MATH-FRAC-BASICS, MATH-WP-READ]
PhaseTargets: {P2 by P4}
TransferTests: {multi-step, inverse ops}
Sensors: {TT1-basic}
FailureSignatures: {CarelessOps, WrongOperationChoice}
RepairLoops: {error-tag + 10-min mixed mini sets}
FenceRules: {if WrongOperationChoice → stitch WP structure, not more computation}
Node: SG×MATH×Z0×Learner×Node×MATH-FRAC-BASICS
LevelBand: P3–P6
Prereq: [MATH-NUM-4OPS]
Outputs: [MATH-FRAC-OPS, MATH-RATIO-PERCENT]
PhaseTargets: {P2 by P5}
TransferTests: {equivalent fractions, compare, simplify}
Sensors: {FRAC-10 (10-min fraction core)}
FailureSignatures: {DenominatorConfusion, SimplifyFail}
RepairLoops: {visual→number line→algorithm}
FenceRules: {if FRAC unstable → TRUNCATE ratio/% and many WP types}
Node: SG×MATH×Z0×Learner×Node×MATH-FRAC-OPS
LevelBand: P4–P6
Prereq: [MATH-FRAC-BASICS]
Outputs: [MATH-RATIO-PERCENT, MATH-WP-MULTISTEP]
PhaseTargets: {P2 by P6}
TransferTests: {add/sub unlike, multiply/div fractions}
Sensors: {TT1-frac}
FailureSignatures: {LCDFail, InvertMistake}
RepairLoops: {LCD drill + step-check + timed ramps}
FenceRules: {if LCDFail → reduce question variety, rebuild LCD stability}
Node: SG×MATH×Z0×Learner×Node×MATH-RATIO-PERCENT
LevelBand: P5–Sec2
Prereq: [MATH-FRAC-OPS]
Outputs: [MATH-RATE, MATH-ALG-LINEAR]
PhaseTargets: {P2 by Sec1}
TransferTests: {% of %, speed, best buy}
Sensors: {RPP-15 (ratio/percent/proportion)}
FailureSignatures: {UnitRateConfusion, WrongBasePercent}
RepairLoops: {bar model→unit method→equation}
FenceRules: {if WrongBasePercent repeats → force “base quantity” annotation}
Node: SG×MATH×Z0×Learner×Node×MATH-WP-READ
LevelBand: P3–Sec
Prereq: [ENG-READ-COMP-INF (coupling)]
Outputs: [MATH-WP-BARMODEL]
PhaseTargets: {P2 by P6}
TransferTests: {identify givens, constraints, unknowns}
Sensors: {WP-UNDERLINE protocol}
FailureSignatures: {MisreadConstraint, WrongReferent}
RepairLoops: {3-pass read→restate→bar}
FenceRules: {if MisreadConstraint → truncate WP variety; stitch reading loop}
Node: SG×MATH×Z0×Learner×Node×MATH-WP-BARMODEL
LevelBand: P4–Sec1
Prereq: [MATH-WP-READ, MATH-RATIO-PERCENT]
Outputs: [MATH-WP-EQUATION]
PhaseTargets: {P2 by Sec1}
TransferTests: {model→equation translation}
Sensors: {WP-15 timed}
FailureSignatures: {ModelWrongSegments}
RepairLoops: {bar templates + compare cases}
FenceRules: {if ModelWrongSegments → freeze algebra intro until stable}
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3.2 SECONDARY CORE NODES (Sec1–Sec4/5)
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Node: SG×MATH×Z0×Learner×Node×MATH-ALG-LINEAR
LevelBand: Sec1–Sec3
Prereq: [MATH-RATIO-PERCENT, MATH-WP-EQUATION]
Outputs: [MATH-ALG-SIMUL, MATH-FUNC-GRAPH]
PhaseTargets: {P2 by Sec2}
TransferTests: {form equation, solve, interpret}
Sensors: {ALG-15}
FailureSignatures: {SignError, TransposeFail}
RepairLoops: {algebra hygiene rules + short drills + unit check (VL-05 optional)}
FenceRules: {if TransposeFail → truncate new topics; stitch rearrangement}
Node: SG×MATH×Z0×Learner×Node×MATH-ALG-SIMUL
LevelBand: Sec2–Sec4
Prereq: [MATH-ALG-LINEAR]
Outputs: [MATH-FUNC-GRAPH]
PhaseTargets: {P2 by Sec3}
TransferTests: {substitution/elimination + interpretation}
Sensors: {SIMUL-15}
FailureSignatures: {ElimSetupWrong}
RepairLoops: {alignment templates + check by substitution}
FenceRules: {if setup wrong → force “equation labelling” protocol}
Node: SG×MATH×Z0×Learner×Node×MATH-FUNC-GRAPH
LevelBand: Sec2–JC
Prereq: [MATH-ALG-LINEAR]
Outputs: [MATH-TRIG, MATH-CALC, PHY-MOTION coupling]
PhaseTargets: {P2 by Sec4, P3 top band}
TransferTests: {gradient meaning, intercept, transformation}
Sensors: {GRAPH-15}
FailureSignatures: {GraphAsPicture, GradientMeaningWrong}
RepairLoops: {table→equation→graph→story mapping}
FenceRules: {if GraphAsPicture → truncate variation; stitch meaning mapping}
Node: SG×MATH×Z0×Learner×Node×MATH-GEOM-CORE
LevelBand: P4–Sec4
Prereq: [MATH-NUM-4OPS]
Outputs: [MATH-TRIG, MATH-MEASURE]
PhaseTargets: {P2 by Sec2}
TransferTests: {angle rules, similarity, area/volume}
Sensors: {GEOM-15}
FailureSignatures: {AngleRuleMemoryOnly}
RepairLoops: {diagram marking protocol + reason chain}
FenceRules: {if memory-only → enforce “because” line per step}
Node: SG×MATH×Z0×Learner×Node×MATH-TRIG
LevelBand: Sec3–JC
Prereq: [MATH-GEOM-CORE, MATH-FUNC-GRAPH]
Outputs: [MATH-CALC, PHY waves coupling]
PhaseTargets: {P2 by JC1}
TransferTests: {solve triangles, trig graphs, identities}
Sensors: {TRIG-15}
FailureSignatures: {ModeConfusion, IdentityBlind}
RepairLoops: {unit circle meaning + graph link + identity drills}
FenceRules: {if ModeConfusion → truncate to meaning+graph before identities}
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3.3 JC EXTENSIONS (JC1–JC2)
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Node: SG×MATH×Z0×Learner×Node×MATH-CALC
LevelBand: JC1–JC2
Prereq: [MATH-FUNC-GRAPH, MATH-ALG-LINEAR, MATH-TRIG]
Outputs: [MATH-APPL, PHY calculus coupling]
PhaseTargets: {P2 by JC2, P3 top band}
TransferTests: {differentiate/integrate + interpret + application}
Sensors: {CALC-20}
FailureSignatures: {ProcedureNoMeaning, StationaryPointMisread}
RepairLoops: {meaning-first: rate/area + worked variation}
FenceRules: {if no meaning → truncate procedures; stitch interpretation tasks}
Node: SG×MATH×Z0×Learner×Node×MATH-STAT-PROB
LevelBand: Sec3–JC
Prereq: [MATH-RATIO-PERCENT]
Outputs: [MATH-APPL, decision reasoning]
PhaseTargets: {P2 by JC2}
TransferTests: {interpret, compute, explain}
Sensors: {STAT-15}
FailureSignatures: {ConditioningConfusion}
RepairLoops: {tree/venn templates + check totals}
FenceRules: {if conditioning confusion → enforce diagram-first}
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4) PREREQUISITE EDGES (GRAPH) — v0.1 (CORE)
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Edge format:
Edge := {FromID, ToID, Weight(VH/H/M), SignatureLink}
Edges (selected):
- MATH-NUM-PLACEVALUE → MATH-NUM-4OPS (VH)
- MATH-NUM-4OPS → MATH-FRAC-BASICS (H)
- MATH-FRAC-BASICS → MATH-FRAC-OPS (VH)
- MATH-FRAC-OPS → MATH-RATIO-PERCENT (VH)
- ENG-READ-COMP-INF → MATH-WP-READ (H) [COUP-SG-01]
- MATH-WP-READ → MATH-WP-BARMODEL (H)
- MATH-RATIO-PERCENT → MATH-ALG-LINEAR (H)
- MATH-ALG-LINEAR → MATH-FUNC-GRAPH (VH)
- MATH-FUNC-GRAPH → MATH-CALC (VH)
- MATH-ALG-LINEAR + MATH-FUNC-GRAPH → PHY-MOTION (VH) [COUP-SG-02]
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5) SENSOR PACK (MICRO-TESTS) — v0.1
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SensorPack: SG×MATH×Z0×Tutor×SensorPack×SENS-SG-MATH-v0.1
Weekly minimum (15–30 min total):
- TT1-Core (10–15 min): mixed prerequisite set
- Topic Probe (10 min): weakest node only
- WP-5 (5 min): one word problem with mandatory underline + bar/equation
Metrics:
- TR-math (transfer reliability)
- SII-math (speed instability index)
- ERC (error-repeat count)
- CompletionRate
Fence triggers:
- TR < 70% for 2 cycles → treat as P1 masquerading as P2
- ERC same error 2 weeks → mandatory repair loop
- CompletionRate drops under time → SSL ladder
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6) FAILURE ATLAS (SIGNATURES) — v0.1 (MATH)
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MATH-SIG-01: Wrong Base in Percent (ties to MATH-RATIO-PERCENT)
MATH-SIG-02: LCD Failure (ties to FRAC-OPS)
MATH-SIG-03: Transpose Fail (ties to ALG-LINEAR)
MATH-SIG-04: Graph as Picture (ties to FUNC-GRAPH)
MATH-SIG-05: WP Misread Constraint (ties to WP-READ) [COUP-SG-01]
MATH-SIG-06: Finish-ability crash (SpeedCollapse) [FM-1]
Each signature links to:
- predicted next failure
- truncation action
- stitching repair loop
- re-test
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7) REPAIR PROTOCOLS (TRUNCATION + STITCHING) — v0.1
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Protocol: SG×MATH×Z0×Operator×Protocol×MATH-FENCE-v0.1
Truncation Rules:
- If FRAC unstable → pause ratio/% + many WP types
- If ALG rearrangement unstable → pause new algebra topics + reduce physics coupling risk
- If WP misread repeats → pause variety; enforce 3-pass read + bar only
Stitching Order:
1) Upstream prerequisite node
2) One repair loop (template)
3) Timed re-test
4) Only then widen variation
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8) WORDPRESS PASTE-READY STRUCTURE
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H1: SG Syllabus Lattice Directory (Math First) — Runnable Math Graph for Singapore
H2: Directory map + how to use it
H2: Math spine graph (Primary→Secondary→JC)
H2: Node Registry (core set v0.1)
H2: Prerequisite edges + coupling edges
H2: Sensor pack (weekly micro-tests)
H2: Failure atlas (math signatures)
H2: Repair protocols (truncation + stitching)
H2: Failure trace + repair trace
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9) REQUIRED FAILURE TRACE (MATH DIRECTORY)
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Trace:
Fractions unstable →
ratio/% + WP become brittle →
algebra built on weak base →
graphs meaningless →
time collapse →
P2→P0 exam shock.
Fence Repair:
Detect via sensors →
truncate breadth →
stitch prerequisite nodes →
timed re-test →
restore transfer →
stable flight.
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END: SG Syllabus Lattice Directory v0.1 — MATH FIRST
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