Bridge to MATx — where to practise the solving

Why this bridge

The Progression matrix describes how a student learns to derive an equation from a word problem — 9 microskills define.tN.{add,mul,mix}. But deriving the equation is half the job. After that you have to solve it, which is a different domain altogether: the technical algebraic transformations.

MATx (Tom Kabel’s companion project) trains exactly that second half. Together you get a natural pipeline:

text ──▶ model (matx-hack)  ──▶ equation ──▶ solution (MATx)
          defining microskills              computing competencies

This page is the junction map: which of our microskills flows into which MATx competencies.

MATx coverage map

Tom Kabel’s MATx — TypeScript + React + Express + Postgres, Estonian mathematics for grades 7–9. Three topics, nine competencies:

Topic (slug)	Competencies
`abivalemid` (Korrutamise abivalemid)	summa ruut $(a+b)^2$ , vahe ruut $(a-b)^2$ , ruutude vahe $a^2 - b^2$
`protsendid` (Protsentarvutus)	osa leidmine, terviku leidmine, protsendi leidmine
`vorrandid` (Ühe tundmatuga võrrandid)	lihtsad ( $ax+b=c$ ), sulgudega, murdudega

The REST API is described publicly in shared/routes.ts; the DB schema lives in shared/schema.ts (models topics, competencies, questions, results).

Mapping table (our microskill → MATx competency)

Our microskill	MATx topic	Ready for competency	Logic
`define.t1.add` (T1 +/−)	`protsendid`	osa leidmine, protsendi leidmine	L1 (+/−) — abstract 2-quantity model `a = b + n`. A simple percentage is a special case.
`define.t1.mul` (T1 ×/÷)	`protsendid`	osa leidmine, protsendi leidmine	A percentage = a multiplicative relation with denominator 100. A direct continuation of L1 (×/÷).
`define.t1.mix` (T1 mix)	`protsendid`	osa leidmine, protsendi leidmine	After L1-mix, a simple percentage question is solved in the same language of relations.
`define.t2.add` (T2 +/− + context)	`protsendid`, `vorrandid`	terviku leidmine, lihtsad võrrandid	L2 (+/−) gives a 2-quantity narrative; the model lands on $ax+b=c$ .
`define.t2.mul` (T2 ×/÷ + context)	`protsendid`, `vorrandid`	terviku leidmine, lihtsad võrrandid	A multiplicative narrative → its inversion asks “find the whole”; the model → $ax=c$ .
`define.t2.mix` (T2 mix + context)	`protsendid`, `vorrandid`	terviku leidmine, lihtsad võrrandid	L2-mix lands consistently on $ax+b=c$ and on a narrative percentage.
`define.t3.add` (T3 +/− + 3+)	`vorrandid`	sulgudega võrrandid	3+ quantities through $x$ : substitutions yield an equation with parentheses.
`define.t3.mul` (T3 ×/÷ + 3+)	`vorrandid`	sulgudega võrrandid	Same for the multiplicative L3 — expand parentheses and collect like terms.
`define.t3.mix` (T3 mix + 3+)	`vorrandid`	murdudega võrrandid	The hardest tier of modeling; this is also the right place to drill fractional equations.

The bridge graph

On the left — our 9 modeling microskills, on the right — 9 MATx computation competencies. An arrow A → B reads as “after mastering A, the student is ready to practise B on the MATx side”.

graph LR
  classDef us fill:#bfdbfe,stroke:#1d4ed8,color:#0f172a;
  classDef pr fill:#fde68a,stroke:#a16207,color:#0f172a;
  classDef ls fill:#fecaca,stroke:#b91c1c,color:#0f172a;
  classDef mf fill:#e9d5ff,stroke:#7e22ce,color:#0f172a;

  subgraph US["matx-hack — defining (modeling)"]
    T1A["T1<br/>+/−"]:::us
    T1M["T1<br/>×/÷"]:::us
    T1X["T1<br/>mix"]:::us
    T2A["T2<br/>+/− + context"]:::us
    T2M["T2<br/>×/÷ + context"]:::us
    T2X["T2<br/>mix + context"]:::us
    T3A["T3<br/>+/− + 3+"]:::us
    T3M["T3<br/>×/÷ + 3+"]:::us
    T3X["T3<br/>mix + 3+"]:::us
  end

  subgraph MX["MATx — computing"]
    POSA["protsendid<br/>osa leidmine"]:::pr
    PTER["protsendid<br/>terviku leidmine"]:::pr
    PPRO["protsendid<br/>protsendi leidmine"]:::pr
    LLIH["vorrandid<br/>lihtsad"]:::ls
    LSUL["vorrandid<br/>sulgudega"]:::ls
    LMUR["vorrandid<br/>murdudega"]:::ls
  end

  T1A --> POSA
  T1A --> PPRO
  T1M --> POSA
  T1M --> PPRO
  T1X --> POSA
  T1X --> PPRO

  T2A --> PTER
  T2A --> LLIH
  T2M --> PTER
  T2M --> LLIH
  T2X --> PTER
  T2X --> LLIH

  T3A --> LSUL
  T3M --> LSUL
  T3X --> LMUR

The symmetry with the internal skill graph is visible: our vertical pyramid T1 → T2 → T3, when projected outward, rotates by 90° and becomes horizontal — a transition from modeling to computation.

Parallel prereq — abivalemid

Tom’s three formulas — summa-ruut, vahe-ruut, ruutude-vahe — are not directly tied to our modeling. They’re a low-level algebraic prereq for simplifying expressions: so the student doesn’t trip over $(a+b)^2$ technique while expanding parentheses in L3 models.

Recommended order: walk through abivalemid as a parallel track before reaching L3. They’re not shown as a separate column on the graph — it’s a horizontal base, not a vertical hand-off.

EU AI Act sub-thread

Our pipeline is deterministic at both ends: BKT per microskill (web/lib/bkt.ts) + template explanations (web/lib/explain.ts) + the numeric answer validation in MATx. Not a single LLM call in the production path.

Education / vocational training falls into the Annex III high-risk category under Regulation (EU) 2024/1689 (the EU AI Act) — obligations on traceability, documentation, human oversight and explainability come into force in stages from August 2026 to August 2027. Our side already meets those obligations by construction. If MATx wires in our bktUpdate (see the companion page), it inherits the same compliance profile automatically.

Source of truth

JSON: data/matx-bridge.json — a single file that contains:

the list of MATx topics and competencies (with trilingual names),
12 explicit bridge edges from_microskill → to_topic.competencies with rationale in three languages,
the parallel-prereqs block (abivalemid).

The same file is used to render the bridge UI widget (optional) and serves as the contract once MATx wires in our BKT engine.

What’s next

Companion page MATx — what MATx is, who’s behind it, where to try it.
Selector simulator — see how BKT picks the next defining microskill.
Glossary — definitions of the terms (microskill, competency, BKT etc).