| 1 | # Mathematics pedagogy — fundamentals v1 |
| 2 | |
| 3 | **Мир:** `pedagogy.mathematics` |
| 4 | **Версия:** v1.0 · 2026-06-06 · **status:** draft |
| 5 | |
| 6 | --- |
| 7 | |
| 8 | ## Scope |
| 9 | |
| 10 | School mathematics: number sense, procedures, representations, problem solving. Out of scope v1: competition olympiad tactics, university proof courses. |
| 11 | |
| 12 | --- |
| 13 | |
| 14 | ## North star |
| 15 | |
| 16 | **Procedural + conceptual balance:** fluency on held-out items **and** explain/represent transfer, not speed drill alone. |
| 17 | |
| 18 | Evidence: [`kb-pedagogy-math-scientific-evidence-v1.md`](kb-pedagogy-math-scientific-evidence-v1.md). |
| 19 | |
| 20 | --- |
| 21 | |
| 22 | ## Four pillars (v1) |
| 23 | |
| 24 | | Pillar | Construct | Probe idea | |
| 25 | |--------|-----------|------------| |
| 26 | | M1 | Number / quantity sense | novel context, same structure | |
| 27 | | M2 | Procedural fluency | timed + untimed held-out | |
| 28 | | M3 | Representations (CRA) | concrete → pictorial → symbolic fade | |
| 29 | | M4 | Problem solving | multi-step, unfamiliar surface | |
| 30 | |
| 31 | --- |
| 32 | |
| 33 | ## School labels (authoring only) |
| 34 | |
| 35 | Арифметика, алгебра, геометрия, вероятность — **section tags**, not gate oracles. |
| 36 | |
| 37 | --- |
| 38 | |
| 39 | ## Cross-hub links |
| 40 | |
| 41 | - Rosenshine / CLT: [`../pedagogy-general/kb-pedagogy-evidence-global-v1.md`](../pedagogy-general/kb-pedagogy-evidence-global-v1.md) |
| 42 | - Transfer to physics quantity: [`../pedagogy-general/matrix-pedagogy-cross-subject-transfer-v1.md`](../pedagogy-general/matrix-pedagogy-cross-subject-transfer-v1.md) |
| 43 | |
| 44 | --- |
| 45 | |
| 46 | ## Anti-patterns |
| 47 | |
| 48 | - Procedure green = «understands math» |
| 49 | - CRA stuck on manipulatives forever |
| 50 | - Import physics intuition as math proof gate |
| 51 | |
| 52 | --- |
| 53 | |
| 54 | ## concept_id prefix (authoring) |
| 55 | |
| 56 | ```text |
| 57 | math.number.* |
| 58 | math.proc.* |
| 59 | math.repr.* |
| 60 | math.problem.* |
| 61 | ``` |
| 62 | |
| 63 | |