Canonical Gymnasium Mathematics: Sek II Analysis Audit

Snapshot: 2026-04-05

Purpose:

• review the current canonical Sek II Analysis inventory after the lower-secondary packaging passes
• use already reviewed upper-secondary state evidence to test whether the current canonical analysis cuts are pedagogically stable
• define the next canonical work packages for Sek II Analysis

Scope

In scope:

• the canonical upper-secondary analysis topic surface in
• curricula/DE/Gymnasium/canonical/DE_DEU_S_GYM_CANONICAL_MATHEMATIK.de.json
• the already reviewed upper-secondary source and mapping evidence from
• BB
• BE
• BW
• BY
• HB
• HH
• HE
• MV
• NI
• NW
• RP
• SL
• ST
• SN
• SH
• TH

Out of scope:

• direct canonical JSON refactoring in this step
• learner-facing composition views
• upper-secondary stochastics, analytic geometry, and matrix corridors except where the current analysis packaging still mixes with them

Reviewed source evidence

Hessen (HE)

Observed signal:

• HE remains the mature donor baseline for E-phase analysis and later upper-secondary analysis progression
• the Hessen lane confirms that the canonical graph already has real material for derivative entry, function investigation, model work, and integral reasoning

Brandenburg and Berlin (BB, BE)

Observed signal:

• the currently reviewed BB and BE upper-secondary lanes already connect into the shared E-analysis baseline
• they validate a stable common core, but they do not yet force many additional visible subpackages on their own

Bremen (HB)

Observed signal:

• HB already connects reviewed upper-secondary analysis work into the shared E-analysis baseline and the broad integral corridor
• Bremen therefore pressure-tests late analysis packaging, especially around the transition from derivative work into integral work

Hamburg (HH)

Observed signal:

• HH already connects reviewed upper-secondary analysis work into the shared E-analysis baseline and the broad integral corridor
• the Hamburg lane increases pressure on whether the current visible split between E-foundations, model corridors, and the integral corridor is already sufficient

Nordrhein-Westfalen (NW)

Observed signal:

• NW now adds a reviewed mixed upper-secondary analysis lane with:
• an explicit E-phase derivative and first-curve parent
• a broad GK follow-on that mixes optimisation, exponential work, and integral understanding
• narrow LK integral strips and a late LK function-family strip
• Nordrhein-Westfalen confirms that the visible AN2-AN4 surface can absorb both broader parents and narrower late strips without forcing a new visible AN5 package.

Mecklenburg-Vorpommern (MV)

Observed signal:

• MV now adds a first reviewed upper-secondary analysis corridor on top of the newly activated broad qualification-phase snapshot lane
• the Mecklenburg-Vorpommern source still exposes analysis mainly as broad topic bands, but those bands now form a didactically coherent reviewed corridor across:
• Grenzwerte und Stetigkeit
• Ableitungen
• Untersuchungen von Funktionen und ihrer Graphen
• Anwendungen der Differentialrechnung
• Stammfunktionen
• Anwendungen der Integralrechnung
• Mecklenburg-Vorpommern therefore confirms that the frozen visible AN2-AN4 surface can already absorb a broad reviewed curriculum corridor even when the source has not yet been split into narrower late-analysis residues

Rheinland-Pfalz (RP)

Observed signal:

• RP now adds the first reviewed upper-secondary analysis corridor on top of the newly activated Grundfach / Leistungsfach snapshot lane
• the Rheinland-Pfalz source separates the functional-analysis corridor explicitly into:
• Grenzwerte
• Differentialrechnung
• Integralrechnung
• a Grundfach exponential strip and an Leistungsfach continuation strip
• Grundfach confirms the frozen visible AN2-AN4 surface with a clean split from derivative entry to integral understanding plus an explicit exponential-model lane
• Leistungsfach adds the expected late continuation pressure through the bundled continuation strip, but this still fits the existing visible late-analysis surface through a reviewed partial bridge onto Vertiefung der Analysis rather than forcing a visible AN5 package

Saarland (SL)

Observed signal:

• SL now adds a first reviewed upper-secondary analysis corridor on top of the newly activated Einführungsphase / G-Kurs / Leistungskurs snapshot lane
• the Saarland source separates the reviewed analysis lane into:
• Einführungsphase entry anchors for continuity / polynomial investigation, derivative rules, and exponential / differentiability follow-on
• G-Kurs strips for
  • Grundlegende Funktionen und Ableitungen
  • Integralrechnung
  • Die e-Funktion und die ln-Funktion
  • Modellieren
• matching Leistungskurs strips with the same visible surface but expected greater depth
• Saarland therefore confirms that the frozen visible AN2-AN4 surface can absorb both broad phase parents and explicit reviewed derivative / integral / e-ln / modelling strips without forcing a visible AN5 package

Sachsen-Anhalt (ST)

Observed signal:

• ST now adds the first reviewed upper-secondary analysis corridor on top of the newly mapped GA / EA snapshot lane
• the Sachsen-Anhalt source separates both demand levels cleanly into:
• foundations of infinitesimal calculus
• differential calculus
• integral calculus
• GA confirms the frozen shared surface with a broad but clean progression from derivative entry to integral interpretation
• EA adds expected late depth through linear approximation, Newtonverfahren, Funktionsscharen, ln as antiderivative, and Rotationskoerper, but still fits into the existing visible AN2-AN4 surface via reviewed partial bridges rather than forcing a visible AN5 package

Sachsen (SN)

Observed signal:

• SN now adds a first reviewed upper-secondary analysis corridor on the broad upper snapshot itself
• the Sachsen Grundkurs split cleanly separates:
• derivative entry and derivative-based investigation
• model-heavy e/ln/trigonometric / regression work
• integral reconstruction, Hauptsatz, and area interpretation
• Sachsen therefore supports the frozen visible AN2-AN4 surface directly and does not create new pressure toward a separate visible AN5 package

Thueringen (TH)

Observed signal:

• TH now adds a first reviewed upper-secondary analysis corridor on top of the newly activated Klassenstufe 11 / 11/12 snapshot lane
• the Thueringen source is still broad, but it now exposes a didactically coherent reviewed bridge across:
• Klassenstufe 11: Funktionen
• Klassenstufen 11/12: Analysis
• Thueringen therefore confirms that the frozen visible AN2-AN4 surface can already absorb a reviewed broad corridor even when the current state packaging still mixes entry-phase function work and later upper-secondary analysis inside broad source bands

Current canonical analysis inventory

The canonical graph is already materially seeded here.

Important current package surfaces:

1. Grundlagen der Analysis und mathematische Modelle
2. Einstieg Ableitungsbegriff und Aenderungsraten
3. Ableitungen zur Funktionsuntersuchung und Optimierung nutzen
4. Natuerliche Exponentialfunktion, Logarithmus und Modelle
5. Periodische Funktionen und trigonometrische Ableitungen
6. Integralrechnung und Differenzialgleichungen (Sek II)
7. Funktionenscharen und Parameteruntersuchungen (Sek II) inside the broader Q4 mixed corridor

Audit judgment

The canonical Sek-II analysis topic is not missing a backbone. The main risk is packaging, not first missing content.

Three tensions are currently most relevant:

1. shared GK core versus LK-only enrichment is not yet checked explicitly enough
2. the integral corridor still looks broader than ideal because integral core and differential-equation continuation are bundled together
3. Q4 parameter families currently sit inside a mixed corridor together with non-analysis material

Findings

1. E-phase foundations and derivative entry should stay visible as a separate upper-secondary entry package

The reviewed state evidence supports a stable common entry corridor for:

• basic analysis foundations
• derivative entry
• early function investigation

This package surface should be treated as materially real, not as only a Hessen artifact.

2. Differential calculus and model corridors need an explicit shared-core check

The current canonical analysis surface already distinguishes between:

• derivative / optimisation work
• exponential and logarithmic models
• periodic / trigonometric model work

But the current state of the graph still needs an explicit audit of whether these visible cuts separate shared upper-secondary core from LK-depth consistently enough.

3. The current integral corridor is probably too broad for final steady state

Integralrechnung und Differenzialgleichungen (Sek II) is already useful as a visible corridor. But it likely still bundles:

• integral concept and reconstruction
• area and context interpretation
• later continuation toward differential equations

more broadly than we will want in the steady-state canonical packaging.

4. Q4 function families should not stay hidden inside a mixed late corridor forever

Funktionenscharen und Parameteruntersuchungen (Sek II) already exists as a reviewed analysis subtree. The open question is whether that is already enough as a visible analysis surface, or whether the broader mixed Q4 corridor still hides too much analysis-specific structure.

Proposed canonical work packages

For Sek II Analysis, use these work packages:

1. AN1 E-phase analysis foundations and derivative entry

Residue update: NI late-continuation pressure test

The reviewed NI upper-secondary lane adds the strongest current pressure test for the open late-continuation question because it contains explicit evidence for both sides of the corridor:

1. differential-equation continuation and solution checking
2. function families and parameter fitting

Current reviewed NI mapping evidence does not force a new visible AN5 package:

1. differential-equation continuation items already land on a shared canonical differential-equation target
2. parameter-fitting and function-family items already land on distinct canonical late-analysis targets

Judgment:

1. keep the visible package surface at AN2-AN4
2. treat AN5-late-continuation as accept for now
3. reopen only if another reviewed lane shows a shared late-continuation split that cannot be absorbed by the existing atomic targets
4. basic analysis foundations
5. derivative entry

6. first function investigation routines

7. AN2 Differential calculus, investigation, and optimisation

8. derivative-based analysis
9. monotonicity, extrema, optimisation

10. core shared calculation and interpretation routines

11. AN3 Exponential, logarithmic, and periodic models

12. natural exponential function
13. logarithmic understanding and modelling

14. periodic / trigonometric model work

15. AN4 Integral concepts, reconstruction, and context interpretation

16. integral concept
17. bestandsrekonstruktion / Hauptsatz bridges

18. area and context interpretation

19. AN5 Differential equations and late parameter families

20. differential-equation continuation
21. function families / parameter investigations
22. keep explicitly open until the shared-core versus LK-depth boundary is tested harder

Design step executed

The first canonical Sek-II analysis packaging pass is now in place.

Accepted package surface:

1. AN2 is now visible as Differentialrechnung, Untersuchung und Optimierung.
2. AN3 is now visible as Exponential-, logarithmische und periodische Modelle (Sek II).
3. AN4 is now visible as Integralbegriffe, Rekonstruktion und Kontextdeutung (Sek II).

Important boundary decision:

1. the broad integral corridor no longer carries ordinary differential equations directly
2. late continuation stays reachable above AN4
3. no separate visible AN5 package is currently justified; differential-equation continuation and late parameter work are absorbed by the existing late-analysis atoms

Recommendation

Freeze Sek-II analysis package churn. Additional reviewed state work should only serve residue control, not reopen the package cut without clear contrary evidence.

Open questions now reduced to:

1. Does another reviewed lane expose a shared canonical gap beyond the current late-continuation atoms?
2. Is the shared-core versus LK-depth boundary inside the late continuation corridor still stable under broader reviewed evidence?

Recommended next concrete step

Do not schedule a dedicated next package step for Sek-II analysis. Keep the current surface frozen and only reopen it if a later validator finding or reviewed lane produces a concrete shared mismatch.

Close-out judgment (2026-04-05)

The current Sek-II analysis sweep can now be treated as closed.

Why this is now strong enough:

1. the accepted visible package surface stays at AN2-AN4
2. late continuation is explicitly downgraded to accepted residue instead of an open package blocker
3. the corresponding workboard row now has no remaining n/s cells
4. no reviewed state lane currently forces a new shared canonical analysis package

Operational consequence:

1. keep Sek II Analysis in residue-control mode only
2. do not schedule another dedicated package pass for this topic
3. reopen only if a later reviewed lane or validator finding exposes a real shared canonical gap

Baden-Wuerttemberg upper-secondary integral-application parents connected (2026-04-04)

Observed signal:

• BW now also carries the broad upper-secondary parent corridor Integralgrenzwert, Flaechen und Rotationskoerper
• the broad course-stage parent sits on the shared Integralbegriffe, Rekonstruktion und Kontextdeutung (Sek II) surface
• the Basisfach parent sits on Flaechen und Kontextdeutung mit Integralen
• the Leistungsfach parent sits on Vertiefung der Analysis

Interpretation:

• Baden-Wuerttemberg therefore confirms once more that the frozen visible AN2-AN4 surface is sufficient even for the remaining broad integral-application parents
• the late Leistungsfach continuation can stay above AN4 without forcing a separate visible AN5 package

Baden-Wuerttemberg upper-secondary broad analysis parents closed (2026-04-04)

Observed signal:

• BW now also carries the broad first and second course-stage analysis parents on the shared Sek-II analysis surface
• the linked Basisfach and Leistungsfach parent strips now sit on the shared integral / late-analysis surfaces
• the retained natural-exponential split leaf and the two retained broad integral-idea leaves are now also connected to the shared exponential and integral surfaces

Interpretation:

• Baden-Wuerttemberg no longer keeps any unmapped broad upper-secondary analysis residue inside the active pilot snapshot
• the current frozen visible AN2-AN4 package cut still absorbs these mixed BW parent bands without forcing a new visible bridge package

Exit criteria for this audit

This topic audit is complete when:

1. the canonical subpackage boundaries above are either accepted or revised
2. the canonical graph has a stable Sek-II analysis packaging
3. reviewed BB, BE, BW, BY, HB, HH, HE, NI, NW, RP, SN, and SH evidence can be described as aligned to the revised packaging or intentionally broader because of source granularity
4. the late-continuation question stays frozen unless new reviewed residue forces further canonical restructuring