Math Academy-style pedagogy validation

Is the curriculum sound?

Each check below is a falsifiable claim about the prerequisite graph. Together they form a benchmark you can re-run after any edit to see whether the graph still holds up against the report’s recommendations.

Nodes

Edges

120

Hours

110h

Pass

Warn

Fail

Verdict

All hard checks pass — soft warnings remain.

Connectivity
No isolated nodes, no orphan leaves, every node reachable from a root, no cycles.
0 issues
Forward phase ordering
Every prereq comes from an earlier or same phase. Detects out-of-order edges that would gate a Week 1 skill on a Week 11 skill.
0 backward edges
Multiple entry points
At least three roots so a learner has multiple ways into the graph.
5 roots
Details
- Roots: practice-loop-habits, posture-bench-setup, keyboard-landmarks, pulse-finding, vocal-pitch-match
Capstone count
1–3 apex nodes mark the end of the curriculum; extras suggest missing edges.
1 apex
Details
- Apex: performance-runthrough
90-hour curriculum coverage
Sum of estimated hours across all KPs should reach the 3-month / 90-hour goal.
110.0h
Details
- 110.0h estimated · target 90h
Phase balance
Every 2-week phase should hold at least 4 KPs so the curriculum doesn't collapse onto one stretch.
6/6 phases ≥ 4
Details
- Weeks 1-2: orientation: 12 nodes
- Weeks 3-4: timing and pitch: 14 nodes
- Weeks 5-6: reading and touch: 16 nodes
- Weeks 7-8: harmony and scales: 10 nodes
- Weeks 9-10: two-hand coordination: 8 nodes
- Weeks 11-12: repertoire and performance: 7 nodes
No single-point bottleneck
Foundational nodes can gate up to 50% of downstream learning. Past 50% is a watch-list, past 80% is a chokepoint.
4 foundational nodes
Details
- keyboard-landmarks gates 75% of downstream nodes
- two-black-key-groups gates 58% of downstream nodes
- three-black-key-groups gates 58% of downstream nodes
- middle-c-orientation gates 57% of downstream nodes
Reasonable longest path
The deepest chain from a root shouldn't exceed ~14 nodes — too long means the user must master many things in serial before reaching anything new.
max depth 12
Details
- performance-runthrough: depth 12
- repertoire-piece-3: depth 11
- repertoire-piece-2: depth 10
Practice nodes reachable
Every interactive practice drill should sit within 12 steps of a root. The curriculum spans 12 weeks; capstone pieces can be deep, but no node should be unreachable.
all reachable
Details
- All practice nodes within 12 steps of a root.

Source: src/lib/learning/pedagogy-benchmark.ts