First Wrong Step

Inspiration

Most equation tutors tell a learner whether the final answer is right. That arrives too late. A learner can make one invalid transformation, continue flawlessly from the wrong equation, and still receive feedback that does not identify the misconception.

First Wrong Step changes the unit of feedback from the final answer to the first transformation that changes the equation's solution set. It is built for learners who type their own reasoning and for teachers who need a compact explanation of what happened—not another opaque score.

What it does

The learner selects a synthetic one-variable linear-equation example or edits the typed steps, then chooses Check my reasoning. The app:

parses supported integer and rational linear algebra; compares consecutive equations using exact rational arithmetic; stops at the first invalid transition instead of grading later work built on a broken premise; identifies the rule to inspect and shows one reviewed, answer-withholding hint; lets the learner repair the line and check again; unlocks a structurally equivalent transfer problem after a valid complete solution; and records deterministic mastery plus an immutable, read-only current-session evidence trail for a teacher or judge.

Three judge fixtures demonstrate distribution, equality preservation, and fully valid reasoning. The evidence view shows the submitted work, first-invalid diagnosis, hint provenance, repair attempts, transfer response, and mastery state. A separate Build view explains exactly how Codex and GPT-5.6 were used.

Why the approach is different

The novelty is the separation between mathematical authority and pedagogical assistance.

A project-owned exact rational algebra engine decides whether each transformation preserves the same solution set. GPT-5.6-assisted teaching copy was reviewed, versioned, and committed as static pedagogy assets. A constrained fallback remains available if reviewed pedagogy is unavailable. GPT-5.6 never decides whether a step is valid, whether the final response is correct, or whether mastery was achieved.

That boundary makes the demo reproducible without an API key, prevents a language model from becoming the correctness oracle, and keeps the learning loop usable even with no model network call.

How I used Codex and GPT-5.6

I first created and refined a reusable Greenfield Software Factory skill in Codex using GPT-5.6 Sol with ultra reasoning. The skill turns a product brief into a traceable workflow: baseline the PRD, choose an architecture, plan dependency-ordered vertical slices, assign bounded implementation work, freeze source fingerprints, collect independent review evidence, and route findings through repair.

I then invoked that skill to build First Wrong Step. Codex coordinated the factory run and maintained the durable task/evidence trail. GPT-5.6 Sol ultra helped reason through the product specification, exact-algebra architecture, privacy and failure boundaries, repair decisions, test design, and reviewed teaching copy. I made the central product and engineering decisions: focus feedback on the earliest broken transformation; keep exact algebra—not a model—as the authority; withhold answers in hints; use transfer to test mastery; and keep teacher evidence read-only and local to the current browser document.

Codex accelerated the work by converting those decisions into bounded tasks, testing adversarial algebra and UI states, surfacing defects, and iterating repairs. The repository includes the dated specification, architecture decisions, feature plan, traceability, and build documentation under .factory/.

Design and privacy

The interface is a complete diagnose → hint → repair → transfer → evidence loop, not a chat box or isolated model demo. It uses explicit step controls, clear first-error emphasis, keyboard-operable actions, responsive layouts, and visible provenance.

The public judge mode has no account, learner database, analytics, cookies, or live-model dependency. Work stays in memory for the current browser document and is cleared by reset or page lifecycle. The teacher view is current-session evidence, not a gradebook or shared student record. Judges should use only the bundled synthetic algebra examples and should not enter personal information.

Potential impact

The immediate audience is learners practicing introductory linear equations and teachers reviewing their reasoning. The core pattern can extend beyond algebra: identify the earliest invalid inference, provide the smallest useful nudge, require a repair, and verify learning on a new but equivalent task. That turns AI assistance from answer generation into a bounded coaching layer around independently checkable reasoning.

What is intentionally out of scope

This hackathon demo supports typed, one-variable linear equations with integers or rational constants, +, -, multiplication, division by a nonzero constant, parentheses, and equality. It does not support handwriting/OCR, nonlinear equations, accounts, classroom rosters, grades, analytics, or real student records. English/LTR is the current content scope.

Built during Build Week

First Wrong Step is a new Education project with its own repository, codebase, UX, data model, acceptance criteria, and learning workflow. It does not reuse CausalGate source, data, branding, or agent-governance workflow. The public repository commit and dated .factory/ artifacts document the Build Week work.

Try it

Live app: https://first-wrong-step-162314976173.us-central1.run.app Source: https://github.com/kenhuangus/first-wrong-step

No credentials or API key are required.

Greenfield Software Factory skill repository

The reusable Codex skill that governed this build is preserved in a private supporting repository: https://github.com/kenhuangus/greenfield-software-factory. It documents the factory workflow I created with GPT-5.6 Sol ultra and then used for requirements, architecture, dependency-ordered implementation, independent review, repair, and evidence-backed handoff. Judge access is provided separately because the repository is private. The runnable product source remains public at https://github.com/kenhuangus/first-wrong-step.

Built With

• codex
• google-cloud-run
• gpt-5.6
• node.js
• playwright
• react
• typescript
• vite
• vitest