BTT.MATH — BukitTimahTutor.com Math Lane Overlay (Z0–Z3)

(Almost-Code Canonical · Unified Spec v1.0)

This attaches Mathematics as a subject-lane implementation under BukitTimahTutor’s repair router, without changing the Education OS kernel.


BTT×MATH — Lane Registry

[SITE]
Domain: bukittimahtutor.com
Place: SGP.SG.BT
Lane: EDU.MATH
Role: Repair Router (Truncation + Stitching)
Zoom: Z0–Z3
v: v1.0

1) Math Lane Lock

[NODE]
SGP.SG.BT×EDU.MATH×Z3×V×LOCK×BTT.MATH.PURPOSE×v1.0:
txt: "BukitTimahTutor repairs mathematics capability by rebuilding symbol decoding, representation, error loops, and transfer—then reintroducing speed."
[EDGE]
binds_to:
SGP.SG.BT×EDU×Z3×R×PROTOCOL×BTT.REPAIR_ROUTING×v1.0
Z*×EDU×Z3×S×STACK×STUDY.SKILLS×v1.0

2) Math-Specific Capability Primitives (Below Topics)

These are the “pillars” that sit under algebra/geometry etc.

[NODE]
SGP.SG.BT×EDU.MATH×Z0×L×PRIM×MATH.SYMBOL_SYSTEM×v1.0:
def: "ability to decode and manipulate symbols (notation, operators, equality, functions)"
[NODE]
SGP.SG.BT×EDU.MATH×Z0×L×PRIM×MATH.REPRESENTATION×v1.0:
def: "ability to hold a mental model of quantity/structure (not just steps)"
[NODE]
SGP.SG.BT×EDU.MATH×Z1×L×PRIM×MATH.ERROR_LOOP×v1.0:
def: "ability to detect, locate, and correct errors independently"
[NODE]
SGP.SG.BT×EDU.MATH×Z2×L×PRIM×MATH.TRANSFER×v1.0:
def: "ability to apply principles under variation (twist questions)"
[NODE]
SGP.SG.BT×EDU.MATH×Z2×L×PRIM×MATH.TIME_CONTROL×v1.0:
def: "ability to execute within time constraints without collapse"

3) Math Phase Definitions (P0–P3) (Operational)

[NODE]
SGP.SG.BT×EDU.MATH×Z3×S×PHASE×P0P3.MATH×v1.0:
P3:
- "solves novel questions; explains reasoning; self-corrects; stable under time"
P2:
- "solves standard forms; brittle under twist/time; error loop partly external"
P1:
- "cram works short term; frequent slips; panic under time; high variance"
P0:
- "shutdown; cannot start; avoidance; identity damage around math"

4) Core Failure Mode Trace — Math (Required)

[NODE]
SGP.SG.BT×EDU.MATH×Z3×R×TRACE×BTT.MATH.FAILURE_MODE×v1.0:
chain:
- "Z0: weak symbol decoding (e.g., '=' treated as 'do something')"
- "Z0: steps memorised without representation"
- "Z1: error loop externalised (needs teacher to find mistakes)"
- "Z2: transfer breaks under variation"
- "Z2: time collapse → panic → blanking"
phase_drift:
- "P2 → P1 → P0 under acceleration mismatch"
repair_route:
- "reduce speed + rebuild primitives → restore transfer → add time last → P1→P2→P3"

5) Grade-Band Acceleration Map (PSLE → Sec → A-Math) (Abstract)

Primary / PSLE (Z1–Z2 pressure increase)

[NODE]
SGP.SG.BT×EDU.MATH×Z3×S×MODULE×MATH.PSLE.LOAD_JUMP×v1.0:
load_changes:
- "multi-step reasoning"
- "model drawing / representation demands"
- "time-pressure accuracy"
common_breaks:
- "representation gap"
- "error-repeat loops"
output_if_unrepaired:
- "careless cluster becomes chronic"

Secondary 1–2 (Symbol density + algebra)

[NODE]
SGP.SG.BT×EDU.MATH×Z3×S×MODULE×MATH.SEC12.LOAD_JUMP×v1.0:
load_changes:
- "algebraic symbolism"
- "equations/inequalities"
- "structured problem writing"
common_breaks:
- "symbol system weak → nonsense manipulation"
- "cannot start questions independently"

Secondary 3–4 / A-Math (Abstraction + speed)

[NODE]
SGP.SG.BT×EDU.MATH×Z3×S×MODULE×MATH.SEC34_AMATH.LOAD_JUMP×v1.0:
load_changes:
- "functions, graphs, transformations"
- "proof-like reasoning / identity manipulation"
- "higher time compression"
common_breaks:
- "transfer collapse under variation"
- "time-control collapse"
risk:
- "P2 brittle → P1 panic under exams"

6) Math Collapse Clusters (BTT Diagnostic Router)

Cluster A — Careless/Accuracy (often S0 + S3)

[NODE]
SGP.SG.BT×EDU.MATH×Z0×R×TRACE×BTT.MATH.CLUSTER.ACCURACY×v1.0:
symptoms:
- "sign errors"
- "copying errors"
- "missed constraints"
root:
- "S0 input + S3 error loop weak"
fix:
- "precision rituals + error localisation training"

Cluster B — Cannot Start (often S1)

[NODE]
SGP.SG.BT×EDU.MATH×Z0×R×TRACE×BTT.MATH.CLUSTER.CANNOT_START×v1.0:
symptoms:
- "stares at question"
- "waits for hints"
root:
- "representation gap + decomposition gap"
fix:
- "starter templates + decomposition drills"

Cluster C — Twist Questions (S4 transfer)

[NODE]
SGP.SG.BT×EDU.MATH×Z2×R×TRACE×BTT.MATH.CLUSTER.TRANSFER_BREAK×v1.0:
symptoms:
- "can do drills, fails unfamiliar"
root:
- "principle extraction missing"
fix:
- "variation ladder + principle-first training"

Cluster D — Time Collapse (S5 + S6)

[NODE]
SGP.SG.BT×EDU.MATH×Z2×R×TRACE×BTT.MATH.CLUSTER.TIME_COLLAPSE×v1.0:
symptoms:
- "slow"
- "panic"
- "blanking"
root:
- "meta-control + stability weak; acceleration mismatch"
fix:
- "time budgeting + staged speed reintroduction"

7) BukitTimahTutor Math Repair Protocol (Strict Order)

[NODE]
SGP.SG.BT×EDU.MATH×Z3×R×PROTOCOL×BTT.MATH.REPAIR×v1.0:
Step0 TRUNCATE:
- "stop runaway workload; remove speed pressure"
- "prevent identity damage: 'math failure' → 'missing primitive'"
Step1 S0 SYMBOL + INPUT:
- "decode notation"
- "read constraints precisely"
- "units/labels discipline"
Step2 S1 REPRESENTATION:
- "build mental model"
- "derive steps from meaning, not memory"
Step3 S3 ERROR LOOP:
- "error detection"
- "error localisation"
- "self-correction protocol"
Step4 S4 TRANSFER:
- "variation ladder"
- "principle extraction"
- "twist question training"
Step5 S5 TIME CONTROL:
- "time budgeting"
- "first-step speed"
- "accuracy under mild time"
Step6 SPEED (ONLY LAST):
- "raise velocity gradually"
- "monitor variance + stress"

8) Sensors (Math Lane)

[NODE]
SGP.SG.BT×EDU.MATH×Z0×R×METRIC×BTT.MATH.SENSOR.ERROR_REPEAT×v1.0:
def: "same error recurrence frequency per 10 questions"
[NODE]
SGP.SG.BT×EDU.MATH×Z0×R×METRIC×BTT.MATH.SENSOR.START_LATENCY×v1.0:
def: "time to first correct step"
[NODE]
SGP.SG.BT×EDU.MATH×Z2×R×METRIC×BTT.MATH.SENSOR.TRANSFER_BREAK×v1.0:
def: "failure probability under format variation"
[NODE]
SGP.SG.BT×EDU.MATH×Z2×R×METRIC×BTT.MATH.SENSOR.TIME_VARIANCE×v1.0:
def: "performance variance under timed vs untimed conditions"

9) Outcomes Lock (What “A1 / Strong Math” Means Here)

[NODE]
SGP.SG.BT×EDU.MATH×Z3×V×LOCK×BTT.MATH.A1_MEANING×v1.0:
txt: "A1 is not memorisation. A1 = stable primitives + robust transfer + self-correction + time control (P3)."

10) Canonical Copy/Paste Block (Math Lane)

[LOCKBLOCK:BTT.MATH.v1.0]
Math success is primitives, not topics:
symbol_system + representation + error_loop + transfer + time_control.
BTT repairs in order: truncate → symbols → representation → error loop → transfer → time → speed.
Target: P3 (robust under novelty and time), not P1 cram.

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