Scope

Defines the upgrade pathway from G1 Mathematics learning-state to G2 stability in Lower Secondary, including:

required capability increments
failure risks during transition
control loops that convert scaffolding-dependence into independent structure tracking

This is a capability bridge, not a motivational guide.

Target Outcome

			
UPO-G1G2:
- Student can handle mixed-format algebra questions
- Student can plan multi-step solutions without templates
- Student can transfer skills to new question shells
- Marks become stable under time constraints

		

Upgrade Gaps (What must change)

Gap Set A — Representation Shift

			
UG-A1: x is no longer a “blank”
UG-A2: expressions represent objects, not steps
UG-A3: student can translate words ↔ symbols reliably

Gap Set B — Structure Tracking

			
UG-B1: identify question type quickly
UG-B2: maintain step-to-step logical validity
UG-B3: reduce “random trial” behaviour

Gap Set C — Variation Immunity

			
UG-C1: same concept in different shells remains solvable
UG-C2: student does not freeze when layout changes

Transition Risks (If bridge is forced too early)

			
TR-G1G2-1: Confidence fracture (student feels “suddenly stupid”)
TR-G1G2-2: Memorisation escalation without grounding
TR-G1G2-3: Speed pressure causing error explosion

Bridging Control Protocol (BCP)

Phase 1 — Algebra Internalisation Lock

			
BCP-1.1: Arithmetic → Algebra translation drills
BCP-1.2: Inverse operations as “undo” logic (not rules)
BCP-1.3: Distribution + factorisation meaning checks
BCP-1.4: Verbal explanation for 70% of steps

Phase 2 — Structure Tracking Installation

			
BCP-2.1: 10-second question classification habit
BCP-2.2: Step checkpointing (“what must be true now?”)
BCP-2.3: One-concept sets → mixed-sets progression

Phase 3 — Variation Ladder (Transfer Training)

			
BCP-3.1: Same concept, 5 shells (layout changes)
BCP-3.2: Same shell, 5 variations (numbers/conditions change)
BCP-3.3: Reverse questions (work backwards)

Phase 4 — Time-to-Core (TTC) Compression

			
BCP-4.1: Short timed bursts with immediate feedback
BCP-4.2: Plan-first rule (outline steps before execution)
BCP-4.3: Reduce reliance on worked examples/templates

Readiness Indicators (When G2 stability is achieved)

			
RI-G1G2-1: Student identifies question type within 10–20 seconds
RI-G1G2-2: Student initiates first step correctly without prompt
RI-G1G2-3: Errors shift from “conceptual” → “minor”
RI-G1G2-4: Performance holds across 3 different shells of same concept

Success Definition (Bridge Completed)

			
SD-G1G2:
- Student can solve mixed-format algebra + number questions independently
- Student can explain why each operation is valid
- Marks stop swinging due to format dependence
- Confidence stabilises because competence is real, not scaffolded

		

Dependency Links

← G1 Cognitive Profile in Sec 1 Mathematics — Canonical
← G2 Cognitive Profile in Sec 1 Mathematics — Canonical
← Secondary 1 Mathematics under Full SBB (G1–G3) — Canonical
→ G2 → G3 Upgrade Path (Acceleration Controls) — Canonical
→ Parent-Readable: “From Struggling to Stable: What G1 Students Actually Need”

Non-Scope (Explicit)

Band-change policies (school admin rules)
Marketing / tuition claims
Full syllabus lists
Emotional coaching scripts

Status: Bridge Canonical
Version: v1.0 (Definition-Locked)
Update Rule: Clarify controls/indicators only

			
SERIES: EKS.SECMATH.v0_1SITE: eduKateSG.comMODE: Almost-Code / Canonical / LLM-firstCOORD_GRAMMAR:<EKS> × SECMATH × LEVEL × Z{0–3} × P{0–3} × Type × IDType = PAGE | DIR | NODE | BIND | LOOP | SENSOR | TEST | CLAIM | TOOL

0) Series Spine (Index)

			
PAGE: EKS.SECMATH.DIR.INDEX.v0_1TITLE: eduKateSG — Secondary Mathematics Directory IndexCONTENT:- EKS.SECMATH.DIR.LANE.v0_1- EKS.SEC1MATH.DIR.LANE.v0_1- EKS.SEC2MATH.DIR.LANE.v0_1- EKS.EMATH.DIR.LANE.v0_1- EKS.AMATH.DIR.LANE.v0_1- EKS.SECMATH.DIR.CORE_SKILLS.v0_1- EKS.SECMATH.DIR.TESTS.v0_1- EKS.SECMATH.DIR.BINDS.v0_1OUTPUT:- EKS.SECMATH.CLAIM.CANONICAL.v0_1

1) Lane Family Root — Secondary Mathematics

			
PAGE: EKS.SECMATH.DIR.LANE.v0_1TITLE: Secondary Mathematics (Sec 1–4) — Lane Family DirectoryMISSION:- produce P3 execution under exam load across Z0–Z3- prevent false competence (P2-looking → P0 snap)LEVELS:- SEC1MATH, SEC2MATH, EMATH, AMATHOUTPUT:- EKS.SECMATH.Z3.P3.NODE.EXAM_STABILITY.v0_1

2) Shared Core Skills Directory (Used by all levels)

			
DIR: EKS.SECMATH.DIR.CORE_SKILLS.v0_1CORE_SKILLS:- EKS.SECMATH.Z0.NODE.ALGBRA_SYMBOL_SENSE.v0_1- EKS.SECMATH.Z0.NODE.ARITHMETIC_ACCURACY.v0_1- EKS.SECMATH.Z0.NODE.FRACTIONS_RATIO_RATE.v0_1- EKS.SECMATH.Z0.NODE.EQUATIONS_INEQUALITIES.v0_1- EKS.SECMATH.Z0.NODE.GRAPHS_FUNCTIONS.v0_1- EKS.SECMATH.Z0.NODE.GEOMETRY_ANGLES.v0_1- EKS.SECMATH.Z0.NODE.TRIG_FUNDAMENTALS.v0_1- EKS.SECMATH.Z0.NODE.PROB_STATS.v0_1- EKS.SECMATH.Z0.NODE.CHECKING_ERROR_CONTROL.v0_1- EKS.SECMATH.Z0.NODE.SPEED_UNDER_TIME.v0_1RULE:These Z0 nodes are reused across all sub-lanes as dependencies.

3) Universal Phase Test (Secondary Maths)

			
TEST: EKS.SECMATH.TEST.P_SCORE.v0_1P0: cannot solve independently; collapses under time/noveltyP1: solves with prompts; dependency; fragile confidenceP2: solves standard formats; breaks under variation/speedP3: solves independently under time + variation; bounded error tail

4) Universal Sensors (Same for Sec1–A-Math)

			
SENSOR: EKS.SECMATH.SENSOR.EXECUTION.v0_1MEASURES:- independent_success_rate (no hints)- time_to_solve_tail (slow tail kills grades)- recurring_error_types (same mistake repeats)- transfer_rate (new form, same concept)- careless_rate (often not careless: weak checking)

5) Universal Loop — Truncation & Stitching (Education Edition)

			
LOOP: EKS.SECMATH.LOOP.TRUNCATE_STITCH.v0_1TRUNCATE:- stop repeated error loops early (same mistake 3×)- cut dependency (remove hints, force retrieval)STITCH:- rebuild the missing Z0 pocket- re-run under time and variationGOAL:- push P1/P2 → P3 and prevent snap collapse at exams

6) Sub-Lane: Secondary 1 Mathematics

			
PAGE: EKS.SEC1MATH.DIR.LANE.v0_1TITLE: Secondary 1 Mathematics — Lane DirectoryFOCUS:- algebra entry + real numbers + foundations for all future mathZ0_NODES:- EKS.SEC1MATH.Z0.NODE.REAL_NUMBERS.v0_1- EKS.SEC1MATH.Z0.NODE.ALGEBRA_BASICS.v0_1- EKS.SEC1MATH.Z0.NODE.LINEAR_EXPRESSIONS.v0_1- EKS.SEC1MATH.Z0.NODE.BASIC_GEOMETRY.v0_1- EKS.SEC1MATH.Z0.NODE.INTRO_GRAPHS.v0_1Z1_LOOPS:- EKS.SEC1MATH.Z1.LOOP.HW_REPAIR.v0_1- EKS.SEC1MATH.Z1.LOOP.ERROR_NOTEBOOK.v0_1Z2_CONTROL:- EKS.SEC1MATH.Z2.NODE.MASTERY_SEQUENCING.v0_1Z3_OUTPUT:- EKS.SEC1MATH.Z3.P3.NODE.SEC1_FOUNDATION_LOCK.v0_1

7) Sub-Lane: Secondary 2 Mathematics

			
PAGE: EKS.SEC2MATH.DIR.LANE.v0_1TITLE: Secondary 2 Mathematics — Lane DirectoryFOCUS:- algebra expansion + functions/graphs + probability/stats; pre-O-level rampZ0_NODES:- EKS.SEC2MATH.Z0.NODE.ALGEBRA_EXPANSION_FACTORISATION.v0_1- EKS.SEC2MATH.Z0.NODE.FUNCTIONS_GRAPHS.v0_1- EKS.SEC2MATH.Z0.NODE.RATIO_RATE_SPEED.v0_1- EKS.SEC2MATH.Z0.NODE.PROB_STATS_CORE.v0_1- EKS.SEC2MATH.Z0.NODE.GEOMETRY_ADVANCE.v0_1Z1_LOOPS:- EKS.SEC2MATH.Z1.LOOP.TOPICAL_VARIATION.v0_1- EKS.SEC2MATH.Z1.LOOP.SPEED_BUILD.v0_1Z2_CONTROL:- EKS.SEC2MATH.Z2.NODE.EXAM_FORMAT_TRANSFER.v0_1Z3_OUTPUT:- EKS.SEC2MATH.Z3.P3.NODE.SEC2_STABILITY_LOCK.v0_1

8) Sub-Lane: E-Mathematics (O-Level)

			
PAGE: EKS.EMATH.DIR.LANE.v0_1TITLE: E-Mathematics — O-Level Lane DirectoryFOCUS:- full-syllabus execution + exam strategy + speed + checkingZ0_NODES:- EKS.EMATH.Z0.NODE.ALGEBRA_SYSTEMS.v0_1- EKS.EMATH.Z0.NODE.GRAPHS_FUNCTIONS.v0_1- EKS.EMATH.Z0.NODE.GEOMETRY_TRIG.v0_1- EKS.EMATH.Z0.NODE.MENSURATION.v0_1- EKS.EMATH.Z0.NODE.PROB_STATS.v0_1- EKS.EMATH.Z0.NODE.MODELLING_WORD_PROBLEMS.v0_1Z1_LOOPS:- EKS.EMATH.Z1.LOOP.TEN_YEAR_SERIES.v0_1- EKS.EMATH.Z1.LOOP.CARELESSNESS_ZEROING.v0_1Z2_CONTROL:- EKS.EMATH.Z2.NODE.PAPER_ROUTING.v0_1  (Paper 1 vs Paper 2 tactics)Z3_OUTPUT:- EKS.EMATH.Z3.P3.NODE.OLEVEL_A1_STABILITY.v0_1

9) Sub-Lane: A-Mathematics (O-Level)

			
PAGE: EKS.AMATH.DIR.LANE.v0_1TITLE: A-Mathematics — O-Level Lane DirectoryFOCUS:- algebraic power + calculus + trig identities; high-precision executionZ0_NODES:- EKS.AMATH.Z0.NODE.ALGEBRA_TECHNIQUE.v0_1- EKS.AMATH.Z0.NODE.TRIG_IDENTITIES_EQUATIONS.v0_1- EKS.AMATH.Z0.NODE.LOGS_EXPONENTIALS.v0_1- EKS.AMATH.Z0.NODE.CALCULUS_DIFF.v0_1- EKS.AMATH.Z0.NODE.CALCULUS_INTEGRATION.v0_1- EKS.AMATH.Z0.NODE.PROOF_CHAINING.v0_1Z1_LOOPS:- EKS.AMATH.Z1.LOOP.SKILL_DRILLS_TO_VARIATION.v0_1- EKS.AMATH.Z1.LOOP.EXAM_SPEED_PRECISION.v0_1Z2_CONTROL:- EKS.AMATH.Z2.NODE.TOPIC_DEPENDENCY_ROUTER.v0_1Z3_OUTPUT:- EKS.AMATH.Z3.P3.NODE.OLEVEL_AMATH_A1_STABILITY.v0_1

10) Tests Directory (Reusable)

			
DIR: EKS.SECMATH.DIR.TESTS.v0_1TESTS:- EKS.SECMATH.TEST.P_SCORE.v0_1- EKS.SECMATH.TEST.INDEPENDENCE.v0_1- EKS.SECMATH.TEST.SPEED_TAIL.v0_1- EKS.SECMATH.TEST.TRANSFER.v0_1- EKS.SECMATH.TEST.ERROR_REPEAT.v0_1

			
TEST: EKS.SECMATH.TEST.INDEPENDENCE.v0_1PASS: ≥80% correct with zero hints on mixed setFAIL: needs prompts/rescues or only works on “same-format” questions

			
TEST: EKS.SECMATH.TEST.SPEED_TAIL.v0_1PASS: tail time bounded (no time sink questions)FAIL: a few questions consume most time → paper collapses

11) Binds Directory (How everything stitches into CivOS/EducationOS)

			
DIR: EKS.SECMATH.DIR.BINDS.v0_1BINDS:- EKS.SECMATH.BIND.EDU_CORE.v0_1      TO: EDU.Z3.P3.NODE.CAPABILITY_STABILITY.v0_1- EKS.SECMATH.BIND.FAM_LOAD.v0_1      TO: FAM.Z0.NODE.HOMEWORK_SUPPORT.v0_1- EKS.SECMATH.BIND.HLT_STRESS.v0_1    TO: HLT.Z0.NODE.PATIENT_MONITORING.v0_1CLAIM:Secondary Maths stability reduces household load and prevents P0 education collapse.

12) Canonical Claim (Series)

			
CLAIM: EKS.SECMATH.CLAIM.CANONICAL.v0_1Secondary Mathematics works when Z0 execution becomes P3 under time + variation,and repair loops prevent false competence from snapping into exam collapse.

G1 → G2 Upgrade Path (Bridging Controls) — Canonical (Almost-Code)