Canonical Gymnasium Mathematics Topic Workboard

Snapshot: 2026-04-05

Purpose:

• steer nationwide canonical math work by topic first
• use Bundeslaender as evidence and validation lanes, not as the pedagogical design driver
• make canonical gaps explicit before more state-local rollout work is done

Working rule:

1. pick one high-level topic
2. review the current canonical atom inventory for that topic
3. compare that topic against the reviewed Bundesland sources
4. classify each state cell
5. add canonical atoms only where multiple states or strong pedagogical structure justify them
6. only then deepen or widen state mappings for that topic

Coverage rule:

1. every top-level topic row now runs in all states required mode
2. a topic is not done until every Bundesland column is resolved once
3. seed, anchor, corr, gap, and loc count as resolved cells; only n/s means the topic has not yet been checked for that state
4. a frozen canonical package cut is therefore not enough for topic completion; nationwide coverage still has to be closed afterwards

Legend:

• seed: canonical topic already materially seeded from the Hessen legacy baseline
• anchor: only broad structural or area-level alignment exists
• corr: at least one reviewed corridor is already mapped for this topic
• gap: current reviewed source evidence suggests a canonical gap or unresolved atomic split
• n/s: not started
• loc: state-local packaging; do not automatically canonicalize

State columns use Bundesland abbreviations:

• BW BY BE BB HB HH HE MV NI NW RP SL SN ST SH TH

Topic board

Topic	Canonical	BW	BY	BE	BB	HB	HH	HE	MV	NI	NW	RP	SL	SN	ST	SH	TH	Open canonical gaps	Next action
Sek I Zahlen / Terme / Algebra	seed	corr	corr	anchor	anchor	anchor	anchor	seed	corr	corr	corr	corr	corr	corr	corr	corr	corr	visible A1-A4 packaging is in place, all Bundesland cells in this row are now resolved, and the reviewed BW/BY/MV/NI/NW/RP/SH/SL/SN/ST corridors together with the broader BE/BB lower-secondary algebra parents do not force a visible A5; the remaining late equation and quadratic/exponential tension stays on the accepted algebra/function boundary rather than opening a new shared lower-secondary algebra package	treat this row as coverage-closed for now, keep package churn frozen, and reopen only if a later reviewed lane or validator finding forces a real shared gap beyond the current A1-A4 surface
Sek I Funktionen / Zuordnungen	seed	corr	corr	corr	corr	corr	corr	seed	corr	corr	corr	corr	corr	corr	corr	corr	corr	visible F3-F5 packaging is now in place, all Bundesland cells in this row are resolved, and the reviewed BB/BE/BW/BY/HB/HH/HE/MV/NI/NW/RP/SH/SL/SN/ST/TH corridors confirm the existing F1/F2 surface, the accepted proportional bridge, the current F3/A4 boundary, the visible F4 quadratic boundary, and the broad J10 trigonometric/exponential continuation surface without forcing a new shared regression package, a standalone inverse-proportional package, a mixed function-equation package, a separate power-function package, or a sharper late-J10 split; the remaining broad overview lanes stay accepted as source-granularity residue rather than an open canonical gap	treat this row as coverage-closed for now, keep package churn frozen, and reopen only if a later reviewed lane or validator finding forces a real shared gap beyond the current F1-F5 surface
Sek I Geometrie / Raum	seed	corr	corr	corr	corr	corr	corr	seed	corr	corr	corr	corr	anchor	corr	corr	corr	corr	canonical G2-G7 packaging is now in place, all Bundesland cells in this row are resolved, and the reviewed HB/HH/MV/RP/SL/SN/ST/TH surface together with the widened BW/BY/BE/BB/NI/NW/SH lower-secondary lanes confirm the existing early geometry / space surface, the visible G2 congruence and construction cut, the visible G3 transformation/similarity cut, the visible G4 circle/Thales surface, the visible G5 Pythagoras cut, the existing G6 circle/body/solids surface, and the visible G7 trigonometric bridge without forcing another shared canonical package; the remaining breadth mismatches stay source-granularity residue rather than open packaging debt	treat this row as coverage-closed for now, keep geometry package churn frozen, and reopen only if a later reviewed lane or validator finding forces a real shared gap beyond the current G2-G7 surface
Sek I Daten / Zufall	seed	corr	corr	corr	corr	anchor	anchor	seed	corr	corr	corr	corr	anchor	corr	corr	corr	corr	canonical D1-D5 package surface is now explicit; the Sachsen K8 chance-experiment strip confirms the existing D2/D3/D5 surface, the Sachsen K10 discrete-random-variable strip confirms that later Sek-I random-variable work can still be carried by broad D3/D4-adjacent partial bridges without forcing a separate visible D6 package, and the Sachsen K9 descriptive-statistics plus earlier K7 data-display strips confirm the existing D4 surface while keeping histogram, manipulation, and diagram-reading residue on that same broad package instead of forcing a new visible critical-statistics or diagram-reading package; ST now adds a reviewed JG 7/8 chance corridor that keeps the broad random-events / frequencies strip on the existing Laplace bridge and keeps the multi-stage-experiment strip on the visible D3 surface without forcing a new mixed early-probability package, plus a reviewed JG9 frequency-distributions strip that sits on the visible D4 descriptive-statistics surface, and a reviewed JG10 random-variables strip that stays on the broad visible D1-D5 surface without forcing a separate visible D6 package, RP now also adds an explicit Klassenstufen 9 und 10 data/chance corridor in which Vierfeldertafeln, zweistufige Zufallsexperimente sit on the visible D3 surface and Wahrscheinlichkeiten durch Simulationen sit on the visible D2 bridge without forcing another package, and SL now also adds a first reviewed Klassenstufe 7 data/chance corridor plus first reviewed broad Klassenstufe 8, Klassenstufe 9, and Klassenstufe 10 data/chance corridors in which the current broad Daten und Zufall strips stay on the shared Sek-I data/chance surface without forcing sharper state-local splits, while MV now also adds a first reviewed Klassen 5/6 early data/chance corridor in which Statistische Erhebungen sit on the visible early data/chance surface and einstufige Zufallsexperimente sit on the visible early Laplace bridge without forcing a separate early diagram or early-probability package, a first reviewed Klasse 9 statistics corridor in which Haeufigkeiten/Mittelwerte/Streumasse and statistische Erhebungen both sit cleanly on the visible D4 descriptive-statistics surface without forcing a new survey- or critical-statistics package, and a first reviewed Klasse 10 later-probability corridor in which Zufallsexperimente mit und ohne Zuruecklegen sit on the visible D3 surface while the broad Zufallsgroessen/Binomialverteilung strip stays on the broad visible D1-D5 surface without forcing a separate visible D6 package; TH now also adds a first reviewed Klassenstufen 5/6 data/chance corridor in which early Daten erfassen und darstellen work stays on the visible early data surface while the mixed statistische Kenngroessen und mit Zufall experimentieren strip stays on the broad Sek-I data/chance surface without forcing a separate early diagram or early-probability package, plus a first reviewed broad Klassenstufen 7/8 data/chance corridor in which the archived Stochastik strip stays on the shared broad Sek-I data/chance surface without yet forcing a sharper reviewed split inside the lane, plus a first reviewed broad Klassenstufen 9/10 data/chance corridor in which the archived Stochastik strip likewise stays on the shared broad Sek-I data/chance surface without yet forcing a sharper reviewed split inside the lane, while the remaining Thueringen packaging pressure is now concentrated more clearly in the mixed 9/10 functions strip than in data/chance; BW now adds reviewed lower-secondary 3.1.5, 3.2.5, and 3.3.5 bridges on the visible early-data, descriptive-statistics, Laplace, conditional-probability, and later-random-variable surfaces, BY now adds reviewed M5-M10 data/chance leaves across counting, frequencies, arithmetic mean, descriptive statistics, Laplace, linked events, tree diagrams, simulation, and conditional-structure work, SH now contributes fully refined 5/6 and 7/8/9 data/chance lanes on the visible D1-D5 surface, NW now also adds an explicit lower-secondary data/chance corridor from 2.3, 2.4.1, and 2.4.2 on early data/statistics, Laplace, tree diagrams, simulation, data critique, conditional probability, independence, and combinatorics, BE/BB now also add a first explicit lower-secondary data/chance corridor on the shared BE/BB source with statistical surveys, frequencies, boxplots/histograms, data critique, Laplace, tree/vierfelder structure, and combinatorial probability bridges, and NI now also adds an explicit lower-secondary data/chance corridor from the five real Lernbereiche on statistical surveys, descriptive statistics, probability, multi-stage experiments, and tree/vierfelder work; all Bundesland cells in this row are therefore resolved once without forcing any reopen of the frozen D1-D5 cut	treat this row as coverage-closed for now, keep package churn frozen, and reopen only if a later reviewed lane or validator finding forces a real shared gap beyond the current D1-D5 surface
Sek II Analysis	seed	corr	corr	corr	corr	corr	corr	seed	corr	corr	corr	corr	corr	corr	corr	corr	corr	visible AN2-AN4 packaging is now in place, all Bundesland cells in this row are resolved, and the reviewed BB/BE/BW/BY/HB/HH/MV/NI/NW/RP/SH/SL/SN/ST/TH pressure tests do not force a visible AN5 package; late continuation remains accepted residue rather than an open canonical gap	treat this row as coverage-closed for now, keep package churn frozen, and reopen only if a later reviewed lane or validator finding forces a real shared gap beyond the current AN2-AN4 surface
Sek II Stochastik	seed	corr	corr	corr	corr	corr	corr	seed	corr	corr	corr	corr	corr	corr	corr	corr	corr	visible ST2, ST4, and ST5 packaging is now in place, ST3 remains an explicit LK-boundary marker, all Bundesland cells in this row are now resolved, and the reviewed BE/BB/BW/BY/HB/HH/HE/MV/NI/NW/RP/SH/SL/SN/ST/TH pressure tests do not force a new visible bridge package; the remaining hybrid residue stays source-granularity rather than an open canonical gap	treat this row as coverage-closed for now, keep package churn frozen, and reopen only if a later reviewed lane or validator finding forces a real shared gap beyond the current ST2-ST5 surface plus the explicit ST3 boundary
Sek II Analytische Geometrie / Vektoren	seed	corr	corr	corr	corr	corr	corr	seed	corr	corr	corr	corr	corr	corr	corr	corr	corr	visible AGV2-AGV5 packaging is now in place, all Bundesland cells in this row are now resolved, and the reviewed BE/BB/BW/BY/HB/HH/HE/MV/NI/NW/RP/SH/SL/SN/ST/TH pressure tests do not force a new shared package; the remaining tension stays source-granularity residue rather than an open canonical gap	treat this row as coverage-closed for now, keep package churn frozen, and reopen only if a later reviewed lane or validator finding forces a real shared gap beyond the current AGV1-AGV5 surface
Sek II Lineare Algebra / Matrizen	seed	corr	corr	corr	corr	corr	corr	seed	corr	corr	corr	corr	anchor	corr	anchor	anchor	corr	visible LM2-LM5 packaging is now in place, all Bundesland cells in this row are now resolved, and the reviewed BB/BE/BW/BY/HB/HH/HE/NI/NW/RP/SN corridors together with the broader MV/SH/SL/ST/TH overview lanes do not force another package-level bridge; the late LM5 continuation remains accepted as a real but sufficiently narrow matrix branch rather than a sign of missing shared packaging	treat this row as coverage-closed for now, keep package churn frozen, and reopen only if a later reviewed lane or validator finding forces a real shared gap beyond the current LM2-LM5 surface

Current recommendation

Active next focus:

1. no new top-level package pass
2. keep Sek II Analysis, Sek II Stochastik, Sek II Analytische Geometrie / Vektoren, Sek II Lineare Algebra / Matrizen, Sek I Zahlen / Terme / Algebra, Sek I Funktionen / Zuordnungen, and Sek I Geometrie / Raum closed and in residue-control mode
3. keep Sek I Daten / Zufall closed as well and move active completion work to applicability, learner-facing scope stabilization, and P6/F6 cutover cleanup

Active coordination artifact:

1. docs/dev/canonical-gymnasium-math-topic-workboard.md

Supporting audit artifacts:

1. the existing topic audits as support for all-state closure and reopen decisions only

Why:

• the first canonical packaging passes for the current top-level math topics are now in place
• all four Sek-II rows plus all four Sek-I rows now have no remaining n/s cells and no currently open shared package blocker
• the reviewed upper-secondary pressure tests across BB, BE, BW, BY, HB, HH, NI, NW, SH, and ST still do not force another top-level package split
• the next nationwide gain now comes from finishing applicability, learner-facing scope, and cutover work on top of the now coverage-closed topic board

Coverage queue:

1. no open top-level topic row remains

Current blocker note:

1. no n/s cells remain on the top-level topic board; the remaining national work now sits in applicability, learner-facing scope stabilization, and broader P6/F6 cutover tasks rather than in topic-row breadth debt

Definition of done for one topic:

1. the canonical atom inventory is reviewed and, where needed, tightened
2. reviewed state evidence no longer forces obvious new shared atoms
3. every Bundesland cell in that topic row is resolved once, i.e. no n/s cells remain
4. state mappings for the resolved states are consistent with the revised canonical cuts
5. state-local leftovers are explicitly marked as loc or kept out of the canonical core