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ROOT PAGE — BUKIT TIMAH PRIMARY MATHEMATICS CONTROL TOWER
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TITLE:
BukitTimahTutor Primary 1–6 + PSLE Mathematics Control Tower v1.0 (Bukit Timah OS)
SLUG:
bukit-timah-primary-mathematics-psle-control-tower-v1-0
VERSION:
BT_PRIM_MATH_PSLE_CT_v1_0
MODE:
Almost-Code / LLM-first / WordPress paste-ready
SCALE:
Human + District (Z0–Z2 execution) + National Exam Bind (Z6)
DOMAIN:
EducationOS + TuitionOS + MathOS (Primary Math lane)
CHRONOFLIGHT_LENS:
Structure × Phase × Time
(Time slices: weekly; Micro-returns: D+1/D+3/D+7/D+14/D+30)
PRIMARY_LOCAL_NODE:
BT.EDU.Z1.N.TUI.001
CONTROL_TOWER_COORDINATE (root):
BT.EDU.Z1.S.CTW.MTH.PRY.001
EXTERNAL_EXAM_NODE (bind target; do not rename):
SG.EDU.Z6.N.EXM.PSLE.001
PSLE_SUBJECT_BIND (syllabus lock):
SG.EDU.Z6.SYL.PSLE.MTH.0008.Y26
LOCAL_BINDS (Bukit Timah OS coupling):
- BT.FAM.Z0.P.LIF.001
- BT.FAM.Z0.S.TTC.001
- BT.TRN.Z2.B.MRT.DTL.06A
- BT.TRN.Z2.B.MRT.DTL.07A
- BT.EDU.Z2.N.PRI.001
- BT.EDU.Z2.P.SCH.001
TRACKS:
- P1–P4: Common syllabus
- P5–P6: Standard Mathematics OR Foundation Mathematics (subset corridor)
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0) CANONICAL FRAMING BOX
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PLACE: BT
LANE: EDU
ZOOM_BANDS:
- Z0 = micro-skill (single step, single representation, single heuristic move)
- Z1 = learner execution + tuition node control loop
- Z2 = district coupling (school pace + travel + family buffer)
PHASE GAUGE:
P0 random | P1 scaffolded | P2 independent | P3 timed-stable + self-correcting
GOAL:
P1–P4: P2 stability (no hidden holes)
P5: P2→P3 transition (model + speed + accuracy)
P6/PSLE: P3 reliability under exam format + low drift velocity
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1) CIVILISATION-GRADE DEFINITION (LOCK)
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DEFINITION:
BukitTimahTutor Primary Mathematics Control Tower is a closed-loop stability system
that builds “Mathematical Problem Solving” as the core capability by:
(1) instrumenting concepts + skills + processes + metacognition + attitudes,
(2) detecting drift early (before it becomes identity-level math fear),
(3) routing repairs into the smallest Z0 corridor,
(4) proving landing under the right load (age-appropriate timed slices),
(5) running maintenance returns on a fixed schedule,
while keeping family time-to-class (TTC) and learner energy inside a safe envelope.
THIS IS NOT:
- worksheet volume
- “finish the book”
- topic bingeing
THIS IS:
flight-control for capability through time.
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2) CURRICULUM KERNEL (MOE FRAMEWORK → CONTROL TOWER MAPPING)
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ID: BT_PRIM_MATH_CURRICULUM_KERNEL_01
CENTRAL_FOCUS:
Mathematical Problem Solving (MPS)
SUPPORT_COMPONENTS (must be explicitly instrumented):
C  = Concepts
S  = Skills
P  = Processes (reasoning, communication, applying/modeling)
M  = Metacognition (monitoring/regulating thinking)
A  = Attitudes (belief, confidence, perseverance)
CONTROL_TOWER_MAPPING:
- ESS_p (0–100) is a weighted function of {C,S,P,M,A} + exam-load truth checks.
- If M (metacognition) is missing, the learner cannot self-correct → drift accumulates.
- If P (processes) is missing, non-routine problems collapse (PSLE kills you).
KEY FOCUS AREAS (system emphasis):
- processes supporting 21CC
- big ideas awareness (connections)
- metacognition emphasis (self-directed learning)
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3) CONTENT STRANDS (PRIMARY SYLLABUS ORGANISATION)
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ID: BT_PRIM_MATH_STRANDS_01
STRANDS (3):
- Number and Algebra
- Measurement and Geometry
- Statistics
NOTE:
These are content lanes. The Control Tower prioritises *problem solving* across lanes.
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4) METRICS (PRIMARY CONTROL TOWER SENSORS)
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ID: BT_PRIM_MATH_METRICS_LOCKBOX_01
CORE SPINE (same control architecture as Secondary):
- ESS_p (0–100)  : Primary Math Stability Score
- ESSp_Δ         : drift velocity (weekly)
- ECI_p          : error clustering index (repeat buckets)
- TR_p           : transfer ratio (unfamiliar variant / familiar)
- LCR_p          : load collapse ratio (timed / untimed)  [P5+ dominates]
- HY_p           : hysteresis (recovery time after stress)
- AO_p           : avoidance onset (skipped work, refusal, tears, procrastination)
- TTC_p, Θ_p, Λ_p: time-to-threshold, irreversibility ratio, enforcement lag
PRIMARY LEAF SENSORS (Z0–Z3):
NF   (Number Fluency)         : bonds, algorithms, mental math, accuracy
FL   (Fractions Ladder)       : part-whole, equivalence, operations (P3–P6)
PR   (Proportional Reasoning) : ratio/rate/percent; multiplicative thinking (P4–P6)
MF   (Model Fluency)          : bar model / unitary / diagrams (P2–P6)
RE_p (Representation Encode)  : word→equation/diagram/unit labelling
HS   (Heuristics Signal)      : choose strategy (draw model, table, guess-check, etc.)
RB   (Reasoning + Explanation): justify steps; communicate clearly (P3–P6)
MG   (Measure/Geometry)       : units, conversions, angle/shape reasoning
ST   (Statistics)             : read/interpret tables/graphs; data sense
AC_p (Audit/Checking)         : self-check routines; unit checks; estimation
PB_p (Pace Budget)            : time margin/deficit (P5–P6/PSLE)
NC_p (No-Calculator Mastery)  : accuracy without calculator (PSLE Paper 1)
NORMALISATION RULE:
Leaf sensors are weighted by level (P1–P2: NF+RE; P3–P4: MF+FL; P5–P6: TR/LCR/PB).
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5) CORE LAWS (CONTROL INEQUALITIES)
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ID: BT_PRIM_MATH_LAWS_01
LAW_01 (Regeneration):
RepairRate ≥ DriftRate under load
LAW_02 (True stability requires the right load):
If performance only exists with hints/untimed, stability is not real.
LAW_03 (Representation is a core engine):
If MF/RE fails, “word problems” are not solvable.
LAW_04 (Metacognition prevents drift):
If checking/self-monitoring is missing, careless + repeat buckets accumulate.
FENCE OVERRIDE:
If Θ_p < 1 → emergency truncate+stitch (smallest repair corridor only).
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6) ONE-PAGE PANEL (WEEKLY)
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ID: BT_PRIM_MATH_PANEL_01
A) FLIGHT STATUS:
Phase + RouteState + TTC_p + Θ_p + Λ_p
B) STABILITY:
ESS_p + ESSp_Δ + TR_p + (LCR_p + PB_p if P5–P6)
C) DRIFT DRIVERS:
Top 3 repeat buckets (ECI_p)
Red sensors (NF/MF/RE/FL/PR/AC_p)
D) Z0 QUEUE (Top 5):
micro-skill | corridor | repair route | retest date
E) WEEK OUTPUTS:
- 1 timed slice landing (P3+; PSLE uses real format)
- 3 maintenance returns (D+1/D+3/D+7)
- 1 model/representation lab (MF/RE)
- 1 transfer set (TR_p) (P4+)
F) PARENT CONTROL TOWER:
sleep window locked
TTC friction reduced
overload trimmed
maintenance slots protected
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7) EXECUTION LOOP (Z0 TRUNCATE + STITCH)
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ID: BT_PRIM_MATH_Z0_LOOP_01
LOOP:
1) Sense: find the exact micro-failure (not “topic”)
2) Classify corridor:
   {concept | method | recall | representation | heuristic-choice | speed | stress | careless}
3) Micro-repair:
   1 clean example → 3 near reps → 3 variants → 1 anti-trap
4) Landing proof:
   short timed slice OR strict-marked mini set
5) Maintenance:
   D+1/D+3/D+7/D+14/D+30 (retrieval-first, 5–12 min)
RULE:
No fix is real unless it survives a timer appropriate to level.
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8) CHILD PAGES (P1–P6 + PSLE FINAL APPROACH)
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CHILD_1:  BT.EDU.Z1.S.CTW.MTH.PRY.P1.001  (P1)
CHILD_2:  BT.EDU.Z1.S.CTW.MTH.PRY.P2.001  (P2)
CHILD_3:  BT.EDU.Z1.S.CTW.MTH.PRY.P3.001  (P3)
CHILD_4:  BT.EDU.Z1.S.CTW.MTH.PRY.P4.001  (P4)
CHILD_5:  BT.EDU.Z1.S.CTW.MTH.PRY.P5.001  (P5 Standard/Foundation gates)
CHILD_6:  BT.EDU.Z1.S.CTW.MTH.PRY.P6.001  (P6 + pre-PSLE stabilisation)
CHILD_7:  BT.EDU.Z1.S.CTW.MTH.PRY.PSLE.001 (PSLE Final Approach, 0008 Y26 format)
VERSION LOCK:
BT_PRIM_MATH_PSLE_CT_v1_0 (forward-only upgrades; keep IDs stable)
END ROOT.

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CHILD PAGE — P1
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TITLE: BukitTimahTutor Primary 1 Mathematics Control Tower v1.0
SLUG:  bukit-timah-primary-1-mathematics-control-tower-v1-0
VERSION: BT_P1_MATH_CT_v1_0
COORD: BT.EDU.Z1.S.CTW.MTH.PRY.P1.001
PARENT: BT.EDU.Z1.S.CTW.MTH.PRY.001
TARGET (end-year):
P2 stability on NF + RE_p (basic representation + language)
WEIGHTS (ESS_p focus):
NF 0.40 | RE_p 0.20 | AC_p 0.15 | MF 0.10 | MG 0.10 | A/M 0.05
NON-NEGOTIABLES:
- place value + number sense
- addition/subtraction meaning + basic algorithms
- unit awareness (money/time/length basics)
TIMED LOAD:
light (short bursts only)
NEGATIVE VOID TRIGGERS:
- counting-based dependence persists (no number sense)
- reversals (misread, miscopy) → AC_p missing
OUTPUTS:
- daily 6–10 min NF maintenance
- weekly 1 mini landing proof (8–10 min)
END.

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CHILD PAGE — P2
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TITLE: BukitTimahTutor Primary 2 Mathematics Control Tower v1.0
SLUG:  bukit-timah-primary-2-mathematics-control-tower-v1-0
VERSION: BT_P2_MATH_CT_v1_0
COORD: BT.EDU.Z1.S.CTW.MTH.PRY.P2.001
PARENT: BT.EDU.Z1.S.CTW.MTH.PRY.001
TARGET:
P2 stability on NF + early MF (bar-model entry)
WEIGHTS:
NF 0.32 | MF 0.18 | RE_p 0.18 | AC_p 0.12 | MG 0.10 | ST 0.05 | A/M 0.05
NON-NEGOTIABLES:
- multiplication/division meaning + basic fluency
- model-first habit (draw/label before compute)
- graph reading basics (ST)
NEGATIVE VOID TRIGGERS:
- “can compute, cannot solve word problems” (MF/RE_p leak)
- careless drift begins (AC_p missing)
OUTPUTS:
- 3× model/representation micro-labs weekly
- 1 timed mini landing (10–12 min)
END.

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CHILD PAGE — P3
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TITLE: BukitTimahTutor Primary 3 Mathematics Control Tower v1.0
SLUG:  bukit-timah-primary-3-mathematics-control-tower-v1-0
VERSION: BT_P3_MATH_CT_v1_0
COORD: BT.EDU.Z1.S.CTW.MTH.PRY.P3.001
PARENT: BT.EDU.Z1.S.CTW.MTH.PRY.001
TARGET:
P2→P3 transition begins: MF + FL + HS become visible
WEIGHTS:
MF 0.22 | FL 0.18 | NF 0.18 | RE_p 0.14 | HS 0.10 | AC_p 0.10 | MG 0.05 | ST 0.03
NON-NEGOTIABLES:
- fractions ladder begins (equivalence + meaning)
- heuristic-choice becomes explicit (HS)
- multi-step survival starts (WB proxy via MF+AC_p)
NEGATIVE VOID TRIGGERS:
- fractions become memorised rules (no part-whole) → FL collapses later
- heuristic blindness (tries random operations)
OUTPUTS:
- weekly “model-first then solve” drill
- weekly “fractions ladder” drill
- timed slices start (12–15 min)
END.

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CHILD PAGE — P4
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TITLE: BukitTimahTutor Primary 4 Mathematics Control Tower v1.0
SLUG:  bukit-timah-primary-4-mathematics-control-tower-v1-0
VERSION: BT_P4_MATH_CT_v1_0
COORD: BT.EDU.Z1.S.CTW.MTH.PRY.P4.001
PARENT: BT.EDU.Z1.S.CTW.MTH.PRY.001
TARGET:
P3 readiness corridor: TR_p rising; PR begins to dominate
WEIGHTS:
PR 0.18 | MF 0.18 | FL 0.16 | TR_p 0.12 | AC_p 0.12 | NF 0.10 | RE_p 0.08 | MG 0.04 | ST 0.02
NON-NEGOTIABLES:
- proportional reasoning entry (multiplicative thinking)
- transfer practice weekly (TR_p)
- consistent checking routine (AC_p)
NEGATIVE VOID TRIGGERS:
- additive thinking used in multiplicative contexts (PR leak)
- transfer collapses when surface changes (TR_p low)
OUTPUTS:
- weekly transfer set (variants)
- timed mixed mini-sets (15–18 min)
END.

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CHILD PAGE — P5 (STANDARD + FOUNDATION GATES)
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TITLE: BukitTimahTutor Primary 5 Mathematics Control Tower v1.0
SLUG:  bukit-timah-primary-5-mathematics-control-tower-v1-0
VERSION: BT_P5_MATH_CT_v1_0
COORD: BT.EDU.Z1.S.CTW.MTH.PRY.P5.001
PARENT: BT.EDU.Z1.S.CTW.MTH.PRY.001
TARGET:
P2→P3 transition becomes real: LCR_p + PB_p + TR_p must be stable
WEIGHTS (Standard track):
LCR_p 0.18 | PB_p 0.14 | TR_p 0.14 | MF 0.14 | FL 0.12 | PR 0.10 | AC_p 0.10 | RE_p 0.08
FOUNDATION TRACK RULE:
Foundation = same control laws, narrower corridor:
- reduce novelty injection (ρ)
- increase maintenance returns
- prioritise NF + MF + FL core stability over breadth
NON-NEGOTIABLES:
- model fluency under time
- fractions/percent/ratio coherence (FL+PR)
- pace budgeting begins (PB_p)
NEGATIVE VOID TRIGGERS:
- timed collapse masked by homework (LCR_p low)
- error clusters repeat (ECI_p rising)
OUTPUTS:
- weekly timed landing proof (18–25 min)
- 2× model/transfer labs weekly
END.

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CHILD PAGE — P6 (PRE-PSLE STABILISATION)
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TITLE: BukitTimahTutor Primary 6 Mathematics Control Tower v1.0
SLUG:  bukit-timah-primary-6-mathematics-control-tower-v1-0
VERSION: BT_P6_MATH_CT_v1_0
COORD: BT.EDU.Z1.S.CTW.MTH.PRY.P6.001
PARENT: BT.EDU.Z1.S.CTW.MTH.PRY.001
BINDS_TO_EXAM: SG.EDU.Z6.N.EXM.PSLE.001
TARGET:
P3 corridor reliability before PSLE window (no late debt)
WEIGHTS:
LCR_p 0.20 | PB_p 0.16 | TR_p 0.14 | MF 0.14 | AC_p 0.12 | FL 0.10 | PR 0.08 | RE_p 0.06
FENCE OVERRIDE (near node):
If Θ_p < 1 OR TTC_p ≤ 8 weeks → truncate+stitch only (no new-topic binge)
NON-NEGOTIABLES:
- strict checking routine (AC_p)
- repeat bucket elimination (ECI_p downtrend)
- stable no-calc accuracy (NC_p rising)
OUTPUTS:
- paper-slice landings weekly (aligned to PSLE format)
- top-2 bucket repair rule
END.

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CHILD PAGE — PSLE FINAL APPROACH (0008, EXAM FROM 2026)
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TITLE:
BukitTimahTutor PSLE Mathematics Final Approach Control Tower v1.0 (0008 Y26)
SLUG:
bukit-timah-psle-mathematics-final-approach-control-tower-v1-0
VERSION:
BT_PSLE_MATH_FINAL_CT_v1_0
COORD:
BT.EDU.Z1.S.CTW.MTH.PRY.PSLE.001
EXAM BINDS:
SG.EDU.Z6.N.EXM.PSLE.001
SG.EDU.Z6.SYL.PSLE.MTH.0008.Y26
PURPOSE (LOCK):
Assess attainment at end of primary education with respect to Primary Mathematics objectives.
ASSESSMENT OBJECTIVES (AOs):
AO1 recall facts/concepts/rules/formulae; straightforward computations/procedures
AO2 interpret info; understand/apply concepts in various contexts
AO3 reason; analyse/make inferences; select strategies
EXAM FORMAT (HARD LOCK):
Two papers, three booklets, total 100 marks, total 2h 30m.
Paper 1 (1h 10m) — NO calculator:
Booklet A:
- MCQ: 10 questions × 1 mark = 10
- MCQ: 8 questions × 2 marks = 16
Booklet B:
- Short-answer: 12 questions × 2 marks = 24
Paper 1 total = 50 marks
Paper 2 (1h 20m) — calculator ALLOWED:
- Short-answer: 5 questions × 2 marks = 10
- Structured/Long-answer: 10 questions × 3/4/5 marks = 40
Paper 2 total = 50 marks
ITEM-TYPE MARKING IMPLICATIONS:
- short-answer can award method mark (when answer is wrong but method is correct)
- structured/long-answer requires clear working steps (working rent)
PSLE-SPECIFIC SENSORS (add-ons):
MCQ_p      : MCQ accuracy (Booklet A)
NC_p       : No-calc mastery (Paper 1)
CAL_p      : Calculator efficiency (Paper 2)
WA_p       : Working Awardability (examiner can award marks)
SW_p       : Switching control (topic switching under time)
FINAL APPROACH ENGINE (10–12 weeks typical):
- 1 full Paper 1 per week (strict timing, no-calc)
- 1 Paper 2 slice per week (structured Qs + working rent)
- alternate full Paper 2 bi-weekly → weekly near exam
- top-2 bucket elimination rule (ECI_p)
- rewrite weakest solution weekly (WA_p training)
FENCE RULE:
If Θ_p < 1 → stop breadth; repair only mark-lifting corridors.
END.