PAGE: EKS.SEC1MATH.P3.A1.DIR.ARTICLE.v0_1
TITLE: eduKateSG — Secondary 1 Mathematics: Get to P3 (Z0–Z3) and Stay There
TYPE: Full Article / Almost-Code / Canonical / LLM-first
LANE: EKS.SEC1MATH
SCOPE: Z0–Z3, P0–P3
GOAL:
- P3 execution for Sec 1 foundations (algebra + real numbers + graphs + geometry)
- prevent P2-looking → P0 snap in Sec 2 / E-Math / A-Math
REFS:
- EKS.SECMATH.TEST.P_SCORE.v0_1
- EKS.SECMATH.SENSOR.EXECUTION.v0_1
- EKS.SECMATH.LOOP.TRUNCATE_STITCH.v0_1

DEFLOCK: EKS.SEC1MATH.P3
Sec 1 Math is “stable” only when a student can execute independently under time + variation.
Grades without independence = false competence.
WORKING ⇔
P(Z0) ≥ P3
AND
Z1 repair loops prevent recurring errors
AND
Z2 sequencing prevents topic gaps from compounding
AND
Z3 exam readiness remains stable across terms

<EKS> × SEC1MATH × Z{0–3} × P{0–3} × Type × ID
Type = DIR | NODE | SENSOR | TEST | LOOP | TOOL | CLAIM | BIND

DIR: EKS.SEC1MATH.Z0.DIR.SKILL_POCKETS.v0_1
NODES (core):
- EKS.SEC1MATH.Z0.NODE.REAL_NUMBERS.v0_1
- EKS.SEC1MATH.Z0.NODE.ORDER_OPERATIONS.v0_1
- EKS.SEC1MATH.Z0.NODE.FRACTIONS_RATIONALS.v0_1
- EKS.SEC1MATH.Z0.NODE.ALGEBRA_SYMBOL_SENSE.v0_1
- EKS.SEC1MATH.Z0.NODE.EXPRESSIONS_SIMPLIFY.v0_1
- EKS.SEC1MATH.Z0.NODE.LINEAR_EQUATIONS.v0_1
- EKS.SEC1MATH.Z0.NODE.WORD_PROBLEMS_TRANSLATION.v0_1
- EKS.SEC1MATH.Z0.NODE.RATIO_RATE_PERCENT.v0_1
- EKS.SEC1MATH.Z0.NODE.GEOMETRY_ANGLES_TRIANGLES.v0_1
- EKS.SEC1MATH.Z0.NODE.AREA_PERIMETER_BASIC.v0_1
- EKS.SEC1MATH.Z0.NODE.INTRO_GRAPHS_COORDINATES.v0_1
- EKS.SEC1MATH.Z0.NODE.CHECKING_ERROR_CONTROL.v0_1
- EKS.SEC1MATH.Z0.NODE.SPEED_UNDER_TIME.v0_1

TEST: EKS.SEC1MATH.Z0.TEST.P_SCORE.v0_1
REF:  EKS.SECMATH.TEST.P_SCORE.v0_1
APPLY:
- run on mixed sets and topic sets
OUTPUT:
- per-node P score map

DIR: EKS.SEC1MATH.Z1.DIR.REPAIR_LOOPS.v0_1
LOOPS:
- EKS.SEC1MATH.Z1.LOOP.HW_REPAIR.v0_1
- EKS.SEC1MATH.Z1.LOOP.ERROR_NOTEBOOK.v0_1
- EKS.SEC1MATH.Z1.LOOP.RETRIEVAL_SPACING.v0_1
- EKS.SEC1MATH.Z1.LOOP.VARIATION_LADDER.v0_1
- EKS.SEC1MATH.Z1.LOOP.TIMED_MICROSETS.v0_1

LOOP: EKS.SEC1MATH.Z1.LOOP.ERROR_NOTEBOOK.v0_1
RULE:
- every repeated error becomes a named error-type
- correction requires: (a) identify cause, (b) redo correctly, (c) do 3 variations, (d) 24h retest
FAILURE:
- same mistake repeats → pocket remains P1/P2

LOOP: EKS.SEC1MATH.Z1.LOOP.VARIATION_LADDER.v0_1
LEVELS:
L0: direct question
L1: rearranged format
L2: mixed-topic disguise
L3: word-problem translation + time pressure
GOAL:
- force transfer so P3 is real, not “same-format” comfort

NODE: EKS.SEC1MATH.Z2.NODE.DEPENDENCY_ROUTER.v0_1
DEPENDENCIES:
- algebra symbol sense → expressions → equations → word problems
- fractions/rationals → ratio/rate/percent → word problems
- geometry angles → triangles → area/perimeter
- coordinate plane → graphs (Sec 2 onwards)
RULE:
If a parent node is P1, child topics cannot become P3.
ACTION:
Re-sequence backward until parent pocket reaches P2→P3.

TOOL: EKS.SEC1MATH.Z2.TOOL.MASTERY_SEQUENCE.v0_1
INPUT:
- per-node P scores
OUTPUT:
- weekly plan: 2 weak pockets + 1 maintenance pocket
STOP-LOSS:
- do not add new topics if Z0 weak pockets are P0/P1

NODE: EKS.SEC1MATH.Z3.P3.NODE.SEC1_FOUNDATION_LOCK.v0_1
REQUIRES:
- Z0 pockets mostly P3
- time tail bounded (no “black hole” questions)
- checking loop active
OUTPUT:
- stable A1/A2 band without panic tuition

SENSOR: EKS.SEC1MATH.Z3.SENSOR.EXAM_STABILITY.v0_1
MEASURES:
- marks volatility across tests
- time left at end of paper
- % careless vs concept errors
- transfer performance on unfamiliar questions

DIR: EKS.SEC1MATH.DIR.STUDENT_TYPES.v0_1
TYPES:
- EKS.SEC1MATH.TYPE.COLLAPSING.P0P1.v0_1
- EKS.SEC1MATH.TYPE.UNSTABLE.P1P2.v0_1
- EKS.SEC1MATH.TYPE.STRONG.MAINTAIN.P2P3.v0_1

NODE: EKS.SEC1MATH.TYPE.COLLAPSING.P0P1.v0_1
SIGNALS:
- cannot start homework alone
- test marks drop sharply
- confidence breaking, avoidance rising
DIAG:
- Z0 pockets P0/P1 in {REAL_NUMBERS, FRACTIONS, ALGEBRA_SYMBOL_SENSE, EQUATIONS}
REPAIR_PLAN:
- 2-pocket rebuild + daily microsets
- remove hints, force retrieval
TARGET:
- move pockets to P2 fast, then climb to P3

NODE: EKS.SEC1MATH.TYPE.UNSTABLE.P1P2.v0_1
SIGNALS:
- marks swing wildly
- same careless pattern repeats
- slow under time
DIAG:
- Z0 pockets P2 but transfer fails at L2/L3 variation
REPAIR_PLAN:
- variation ladder + timed microsets
- checking protocol training
TARGET:
- stabilize speed tail + transfer → P3

NODE: EKS.SEC1MATH.TYPE.STRONG.MAINTAIN.P2P3.v0_1
SIGNALS:
- already scoring well
- wants fewer slips + better handling of twist questions
DIAG:
- pockets mostly P3 but checking/speed tail is P2
PLAN:
- maintenance + twist sets + exam pacing
TARGET:
- P3 robustness (no surprise-paper collapse)

TOOL: EKS.SECMATH.Z2.TOOL.REPAIR_ROUTER.v0_1
INPUT:
- student_type
- Z0 pocket P-map
OUTPUT:
- weekly routing plan:
  (a) 2 weak pockets (rebuild)
  (b) 1 transfer pocket (variation ladder)
  (c) 1 timed set (speed tail)
RULES:
- if any core pocket is P0/P1 → rebuild first (no skipping)
- once pockets reach P2 → add transfer ladder
- once transfer works → add exam pacing + checking automation

DIR: EKS.SEC1MATH.DIR.BINDS.v0_1
BINDS:
- EKS.SEC1MATH.BIND.SECMATH_CORE.v0_1     TO: EKS.SECMATH.DIR.CORE_SKILLS.v0_1
- EKS.SEC1MATH.BIND.EDU_OS.v0_1           TO: EDU.Z3.P3.NODE.CAPABILITY_STABILITY.v0_1
- EKS.SEC1MATH.BIND.FAMILY_LOAD.v0_1      TO: FAM.Z0.NODE.HOMEWORK_SUPPORT.v0_1
CLAIM:
Stabilizing Sec 1 algebra reduces household stress and prevents later pipeline rupture.

CLAIM: EKS.SEC1MATH.CLAIM.CANONICAL.v0_1
Secondary 1 Math reaches A1 stability when the student’s Z0 pockets become P3 under time + variation,
and the Z1 repair loops prevent repeated errors from returning.

END: EKS.SEC1MATH.P3.A1.DIR.ARTICLE.v0_1
NEXT:
- EKS.SEC2MATH.P3.A1.DIR.ARTICLE.v0_1
- EKS.EMATH.P3.A1.DIR.ARTICLE.v0_1
- EKS.AMATH.P3.A1.DIR.ARTICLE.v0_1