BTT.SEC12_MATH — BukitTimahTutor.com Secondary 1–2 Mathematics Overlay

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

Secondary 1–2 is where many students look fine in Primary, then suddenly drift. Mechanically, this is a symbol-density jump + abstraction jump. This overlay formalises that in your BTT repair-router style.


BTT×SEC12_MATH — Lane Registry

[SITE]
Domain: bukittimahtutor.com
Place: SGP.SG.BT
Lane: EDU.MATH.SEC12
Role: Repair Router (Truncation + Stitching)
Zoom: Z0–Z3
v: v1.0

1) Sec 1–2 Math Lock

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z3×V×LOCK×BTT.SEC12.PURPOSE×v1.0:
txt: "Sec 1–2 Math is the symbol-and-structure gateway: algebra + number structure + representation. BTT prevents collapse by repairing decoding, representation, and error loops before speed."
[EDGE]
binds_to:
SGP.SG.BT×EDU×Z3×R×PROTOCOL×BTT.REPAIR_ROUTING×v1.0
SGP.SG.BT×EDU.MATH×Z3×S×PHASE×P0P3.MATH×v1.0

2) Sec 1–2 Capability Primitives (Below Topics)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z0×L×PRIM×SEC12.SYMBOL_DECODING×v1.0:
def: "read algebra correctly; interpret '='; interpret brackets; interpret indices; interpret fractions as structure"
[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z0×L×PRIM×SEC12.ALGEBRA_FOUNDATION×v1.0:
def: "treat letters as variables; manipulate expressions legally; maintain equivalence"
[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z0×L×PRIM×SEC12.NUMBER_STRUCTURE×v1.0:
def: "real numbers, integers, factors/multiples, rational structure; sign discipline"
[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z1×L×PRIM×SEC12.REPRESENTATION_MODELS×v1.0:
def: "translate word problems into structure; bar models evolve into algebraic models"
[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z1×L×PRIM×SEC12.ERROR_LOOP×v1.0:
def: "detect and localise errors independently in multi-step algebra"
[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z2×L×PRIM×SEC12.TRANSFER_STARTER×v1.0:
def: "start unfamiliar problems using decomposition templates"

3) Phase Definitions (Sec 1–2 Math)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z3×S×PHASE×P0P3.SEC12×v1.0:
P3:
- "algebra is natural language"
- "starts problems independently"
- "self-corrects signs/steps"
- "handles novel word problems"
P2:
- "can do standard forms"
- "brittle under word problems / mixed topics"
P1:
- "procedural memory; frequent sign errors"
- "slow; uncertain; depends on hints"
P0:
- "cannot start; avoidance; shutdown"

4) Core Failure Mode Trace (Sec 1–2)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z3×R×TRACE×BTT.SEC12.FAILURE_MODE×v1.0:
chain:
- "Z0: weak decoding of symbols (brackets/fractions/indices/signs)"
- "Z0: illegal algebra steps (equivalence broken)"
- "Z1: representation fails (word problems not translated)"
- "Z1: error loop externalised (needs teacher to locate mistakes)"
- "Z2: mixed-topic transfer fails; student freezes"
phase_drift:
- "P2 primary illusion → P1 secondary fragility → P0 under exam speed"
repair_route:
- "truncate speed → rebuild decoding → rebuild equivalence → rebuild representation → restore error loop → restore transfer → add time last"

5) Sec 1–2 Collapse Clusters (BTT Operational)

Cluster A — Sign & Structure Careless (S0 + Number Structure)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z0×R×TRACE×BTT.SEC12.CLUSTER.SIGN_STRUCTURE×v1.0:
symptoms:
- "sign flips incorrectly"
- "negative distribution errors"
- "fraction sign mistakes"
root:
- "number structure + symbol decoding weak"
fix:
- "sign discipline protocol + micro-drills + forced verbalisation of structure"

Cluster B — Equivalence Break (Illegal Algebra)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z0×R×TRACE×BTT.SEC12.CLUSTER.EQUIVALENCE_BREAK×v1.0:
symptoms:
- "cancels terms incorrectly"
- "moves terms with wrong operation"
- "changes expression meaning"
root:
- "equivalence concept missing"
fix:
- "equivalence guards: 'same value' checks; reverse-substitution verification"

Cluster C — Word Problem Freeze (Representation)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z1×R×TRACE×BTT.SEC12.CLUSTER.WORD_FREEZE×v1.0:
symptoms:
- "cannot start"
- "writes random equations"
root:
- "representation model missing"
fix:
- "decomposition templates: known/unknown/relations; convert language→structure"

Cluster D — Mixed Topics Collapse (Transfer Starter)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z2×R×TRACE×BTT.SEC12.CLUSTER.MIXED_TRANSFER×v1.0:
symptoms:
- "works in chapter practice, fails mixed tests"
root:
- "transfer starter missing"
fix:
- "mixed-topic sorting protocol + method-selection cues"

6) Sec 1–2 Math Repair Protocol (Strict Order)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z3×R×PROTOCOL×BTT.SEC12.REPAIR×v1.0:
TRUNCATE:
- "remove time pressure temporarily"
- "stop long mixed worksheets until decoding stable"
REBUILD_1 (S0 DECODING):
- "notation reading"
- "brackets/fractions/indices parsing"
- "sign structure discipline"
REBUILD_2 (EQUIVALENCE):
- "what operations preserve equality"
- "legal manipulation rules"
- "verification habit (substitute/check)"
REBUILD_3 (REPRESENTATION):
- "word→structure templates"
- "units/labels"
- "diagram-to-equation conversion"
REBUILD_4 (ERROR LOOP):
- "error detection"
- "error localisation"
- "self-correction scripts"
REBUILD_5 (TRANSFER STARTER):
- "problem decomposition"
- "mixed-topic method selection"
TIME (ONLY AFTER STABLE):
- "first-step speed"
- "accuracy under mild time"
SPEED LAST:
- "increase velocity only when variance low"

7) Sec 1–2 Sensors (What BTT Measures)

[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z0×R×METRIC×BTT.SEC12.SENSOR.DECODE_ERROR×v1.0:
def: "notation parsing error rate (brackets/fractions/indices/signs)"
[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z0×R×METRIC×BTT.SEC12.SENSOR.EQUIV_BREAK×v1.0:
def: "illegal-step frequency (equivalence broken)"
[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z1×R×METRIC×BTT.SEC12.SENSOR.START_LATENCY×v1.0:
def: "time to first meaningful equation/model on word problems"
[NODE]
SGP.SG.BT×EDU.MATH.SEC12×Z2×R×METRIC×BTT.SEC12.SENSOR.MIXED_TEST_DROP×v1.0:
def: "drop rate from chapter practice to mixed test performance"

8) Canonical Lock Block (Sec 1–2)

[LOCKBLOCK:BTT.SEC12_MATH.v1.0]
Sec 1–2 Math is the symbol gateway. Collapse usually starts at decoding + equivalence + representation.
BTT repairs in order: truncate → decode → equivalence → representation → error loop → transfer starter → time → speed last.
Target: P3 (independent start + self-correct + transfer), not P1 procedural cram.

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