Pondera
Learning systems laboratory
Graph-first maths project

Pondera turns curriculum into a navigable knowledge constellation.

A private K–12 mathematics system that maps prerequisite knowledge, interprets diagnostic evidence and selects the next useful learning step. A working fractions slice is now ready for testing in our home-education setting.

Explore the graph Read the build note
Graph skills and prerequisites
Evidence from every answer
Review AI kept on rails

The learner-facing card is not the product boundary. The durable core is the connected map: skills, prerequisites, misconceptions, evidence, and review paths.

Graph workbench Ontology / evidence / review
Maths / Number / Fractions Search nodes...

Equivalent fractions active

A graph explorer centred on equivalent fractions, showing prerequisites, practice targets, evidence, and review paths. Generate equivalent fractions Equivalent scaling Compare Common denom. Simplify fractions Mixed numbers Area models Unit notation Equivalent fractions
2,600+ nodes
4,400+ edges
K-12 graph
What the graph sees

Same answer. Three very different systems.

A learner answers 3/8 to 1/4 + 2/4. Pondera treats that as a small diagnostic event: what did the learner probably believe, and what should be repaired next?

Bad system
1/4 + 2/4 = 3/8

Incorrect.

The system only knows the answer was wrong. The next activity is guesswork or a generic retry.

Reasonable system
topic: adding fractions

More practice needed.

The system knows the broad topic is shaky, but it does not know which idea inside the topic broke.

Pondera
signal: added denominators

Repair denominator meaning.

The graph points to a likely misconception: the learner counted shaded pieces but treated denominators as addable counts.

A three-band diagnostic graph showing prerequisite knowledge, this attempt, and diagnosis plus remediation. Prerequisite knowledge This attempt Diagnosis + remediation Unit fractions Denominator meaning Add same denominators key fix identified many prerequisites, one identified as key 1/4 + 2/4 response 3/8 given checked against 3/4 correct diagnostic signal Adds denominators (misconception) Fraction-bar repair remediation path requires / targets knowledge diagnostic signal remediation path
Traversal, not worksheets

Ready students should not wait for the calendar.

A broad graph lets Pondera move quickly through secure territory, pause on shaky edges, and route around a precise misconception when a wrong answer reveals one. The path is not fixed by a workbook order.

01 Observe

Evidence arrives

A check records what a learner did, not just whether the answer was right.

02 Locate

Find the node

The event attaches to a knowledge point, prerequisite, or misconception.

03 Infer

Update state

Mastery, confidence, and likely blockers shift in the local graph.

04 Route

Choose the next star

The next step can accelerate forward, review, or remediate.

05 Review

Keep it inspectable

AI-assisted content is checked against graph facts and deterministic rules.

Diagnostic evidence

The interface can change. The evidence trail should survive.

Different clients may want different learner surfaces. The durable part is the model beneath them: a wrong answer becomes evidence, evidence updates the graph-local learner state, and the graph picks a reasoned next move.

checked_learning_event
domain: mathematics
local_area: fractions
prompt: 1/4 + 2/4
answer: 3/8
verdict: incorrect
signal: likely_added_denominators
next: denominator_meaning_repair
audit: inspectable
Ontology

Structure first

Curriculum standards are useful, but Pondera's primary unit is the teachable, diagnosable knowledge node.

Diagnostics

Errors have shape

A mistake can point to a misconception, a missing prerequisite, or a fragile representation.

Review

AI stays bounded

Hints and wording can vary, but graph IDs, checker logic, and evidence rules stay validated.

Build note

Maths learning should move at the speed of actual understanding.

Pondera grew out of a problem I kept coming back to for years: how do you help a child move through maths at the speed of their actual understanding, without turning learning into either a worksheet conveyor belt or a black-box AI chat?

I have a maths background, and I am building this first for home-education use because I wanted something better for my own kids: a system that can see the structure underneath a mistake, explain why the next step makes sense, and keep the learning path inspectable.

What exists today: a schema-validated curriculum graph, graph explorer, diagnostic and evidence model, bounded AI-assisted authoring checks, and a focused fractions slice ready for learner testing. Broader curriculum coverage and product packaging remain in development.

Lachlan Bridges, Founder

Project status

Early alpha, ready to test a focused slice.

Pondera is currently a private internal tool. The fractions slice is ready for hands-on testing with my children; broader curriculum coverage, learner flows and product packaging remain active work. The long-term path may be a paid product, a sale, or an open-source release, so the implementation and curriculum data stay private while that direction develops.

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