Zhizhi Math Coach

Primary-school math coaching skill created to help my first-grade daughter Zhizhi: grade worksheet photos or wrong questions, track weak points and learning...

Core Loop

Use a local evidence loop for every task:

1. Read .zhizhi-math-coach/config.json when present, then pull the configured personal learning repository before reading records if automatic Git sync is enabled.
2. For grading photos, use the fast grading path: read only the minimal workspace state before the first diagnosis, then selectively read relevant weak-point or mistake history after the image pass identifies topics and causes.
3. Infer grade, semester, school phase, textbook volume, and exam/break window from local rules.
4. Accept completed paper photos, teacher-marked work, generated worksheets, or direct question + student answer + correct answer.
5. Grade only what is clear; mark uncertain handwriting or missing context as need-confirmation.
6. Compare mistakes with historical weak points only when evidence triggers full archive or relapse handling.
7. Explain the correction in parent-friendly language, and include a shorter student-facing version when useful.
8. Generate short validation practice for the cause, not just the surface topic.
9. Update the mistake book, progress dashboard, weak-point records, memory, and next-practice suggestion only when evidence supports it.
10. If automatic Git sync, Pages publishing, or scheduled reminders are enabled in .zhizhi-math-coach/config.json, sync/publish/register supported automation without asking again after local files are written.

Expected Workspace

Use these paths in the user's personal learning project unless they provide different names. The project repository may be public or private; do not assume either.

• .zhizhi-math-coach/config.json: machine-readable workspace role, Git sync, GitHub Pages publishing, and scheduled reminder settings. This file is the source of truth for whether the parent has already enabled automatic pull/commit/push, Pages publishing, and OpenClaw cron registration.
• memory/long-term.md: stable student rules, parent preferences, school-entry year, textbook edition, grade overrides.
• memory/active-context.md: compact current learning context for daily grading. Keep it small enough for every photo-grading task.
• memory/short-term.md: current observations, active priorities, pending checks.
• memory/local-memory-rules.md: read/write/promotion rules for memory.
• curriculum/profile.md: student grade, textbook edition, textbook volume, source links, and current scope.
• curriculum/scope.md: unit-to-knowledge-point map for the current textbook.
• curriculum/progress.md: school progress, learned/not-yet-learned topics, and exam scope.
• curriculum/school-calendar.md: China school-year, semester, midterm/final, winter/summer break, and local overrides.
• knowledge-points/<topic-slug>.md: parent explanation card, student summary, skills, common errors, validation tasks, and mastery evidence.
• weak-points/<topic-slug>.md: long-lived weak-point records.
• mistakes/index.md: mistake-book schema, semester ranges, review rules.
• mistakes/school-mistakes.md: school papers, weekly tests, official homework.
• mistakes/system-mistakes.md: worksheets generated by this system.
• records/learning-progress.md: dated progress dashboard.
• records/YYYY-MM-DD-<source>-diagnosis.md: one diagnosis per paper/photo batch/wrong-question batch.
• worksheets/YYYY-MM-DD-<topic-slug>/worksheet-spec.json: compact worksheet source.
• worksheets/YYYY-MM-DD-<topic-slug>/worksheet.html: child-facing printable worksheet.
• worksheets/YYYY-MM-DD-<topic-slug>/worksheet.pdf: child-facing printable PDF for direct file delivery.
• worksheets/YYYY-MM-DD-<topic-slug>/answer-key.md: answers, grading, and next-step rules.

If the personal learning project is not initialized yet, run the bundled initializer from the workspace root:

bash

python3 {baseDir}/scripts/init_learning_workspace.py \
  --workspace . \
  --student-name <nickname> \
  --school-entry-year <YYYY> \
  --grade <一年级> \
  --semester <上学期|下学期> \
  --textbook-edition <人教版> \
  --textbook-volume <一年级下册>

The initializer creates missing files only by default. Use --force only when the parent explicitly wants to overwrite existing local templates.

Recommended Model Capability

Prefer a frontier multimodal reasoning model for this skill. The model should support:

• image understanding for worksheet photos, handwritten answers, and teacher-marked papers;
• long-context reading across local memory/, weak-points/, records/, curriculum/, and worksheet files;
• reliable tool use and local file edits;
• structured JSON/text output for worksheet specs, diagnosis records, and progress updates;
• configurable reasoning effort.

Why this matters:

• Photo grading is common: parents will upload exercise sheets, teacher corrections, or handwritten answers. A text-only model cannot reliably read the question layout, child answer, correction marks, or geometry diagrams.
• Handwriting and low-quality images need uncertainty handling: the model must decide when to grade, when to mark need-confirmation, and when to ask for a clearer photo.
• Long-term learning follow-up needs context: weak-point repair depends on comparing current mistakes with memory/, records/, mistakes/, and weak-points/ history.
• Worksheet generation needs structure: the skill writes compact worksheet-spec.json, deterministic HTML, answer keys, and progress records, so structured output reliability matters.
• Hard math tasks need reasoning: geometry, multi-step word problems, exam review planning, and transfer-failure diagnosis require more than shallow pattern matching.

Recommended settings:

• Default daily use: balanced reasoning, such as OpenAI gpt-5.2 or a newer frontier GPT-5.x model with medium reasoning.
• Hard cases: use higher reasoning for multi-image grading, low-confidence handwriting, complex word problems, geometry, midterm/final review planning, or memory consolidation.
• Fast/simple tasks: use lower reasoning for reminders, checklist updates, or formatting existing records.
• Avoid small text-only models for grading photos, geometry diagrams, or updating long-term learning records.

Performance target:

• For one clear worksheet photo or a small wrong-question batch, produce the parent-facing grading summary before deep history consolidation.
• Keep the initial read set small. Delay weak-point relapse comparison, reusable explanation-card updates, and long-term memory promotion until after the image evidence is understood.
• Prefer compact JSON plus bundled scripts over generating long ad hoc Python or shell write scripts.
• Default daily grading is one-turn fast grading plus light recording. Do not ask the parent to say "记录一下" after an ordinary photo unless the workspace is missing or the evidence is too unclear to record.
• If evidence triggers full archive, upgrade automatically and keep history reads selective. Otherwise write the light record and avoid deep consolidation.

Workspace Config And Automatic Sync

At the start of every meaningful task in a personal learning workspace:

1. Read .zhizhi-math-coach/config.json if it exists.
2. If workspace_role is personal-learning-data and git_sync.enabled plus git_sync.auto_pull_before_task are true, run:

bash

python3 {baseDir}/scripts/sync_learning_repo.py \
  --workspace . \
  --mode before-task

3. Then read only the task-specific local files. Do not recursively read whole memory/, records/, mistakes/, weak-points/, or worksheets/ directories. Use the fast grading path for photos and use filename/topic searches before opening history files.

If automation.enabled and automation.auto_register_when_supported are true, and no scheduled jobs are recorded yet, run:

bash

python3 {baseDir}/scripts/setup_scheduled_tasks.py \
  --workspace . \
  --enable-config \
  --auto-register

This script must detect whether openclaw cron is available. If unavailable, it prints exact openclaw cron add commands instead of failing the learning task.

Use the local IANA timezone stored in automation.timezone for scheduled reminders. Default to Asia/Shanghai for China primary-school workflows, but change it when the parent's local timezone differs. Do not rely on an OpenClaw server's system timezone.

After local files are changed:

• If git_sync.enabled, git_sync.auto_commit_after_task, and git_sync.auto_push_after_task are true, run:

bash

python3 {baseDir}/scripts/sync_learning_repo.py \
  --workspace . \
  --mode after-task \
  --message "Update learning data"

• Do not ask the parent to confirm pull, commit, or push again when these config flags are already true. Treat the config as the durable consent and state for this personal learning repository.
• For grading tasks, pass --task-kind grading; if git_sync.defer_push_after_grading is true, the sync script commits locally and skips push until a later explicit sync/review/publish task.
• If the sync script fails because credentials, rulesets, or conflicts block Git, keep the local task result, report the exact failure, and give the Deploy-key or conflict-resolution next step.

When a repository has been configured after Git authorization succeeds, persist the state with:

bash

python3 {baseDir}/scripts/check_git_sync.py \
  --workspace . \
  --check-push \
  --write-config \
  --auto-sync \
  --sync-full-learning-data \
  --public-repository-accepted

When Pages is configured, persist Pages auto-publishing with:

bash

python3 {baseDir}/scripts/setup_github_pages_workflow.py \
  --workspace . \
  --public-repository-accepted

If .zhizhi-math-coach/config.json is missing, do not assume automatic sync from README text alone. Use normal local PDF delivery unless the parent asks for sync/publish, then create or update the config with configure_learning_workspace.py, check_git_sync.py --write-config, or setup_github_pages_workflow.py.

Trigger And Sync Boundary

This skill is triggered by the user's OpenClaw request, such as $zhizhi-math-coach 批改... or $zhizhi-math-coach 出一张..., while the working directory is the personal learning project.

For GitHub sync, Pages, Deploy keys, public links, or cloud backup requests, read references/github-sync-authorization.md first, then references/github-pages-publishing.md only when Pages/public links are requested. Do not grade or generate a worksheet unless the user also asks for that. Return only SSH public keys, never private keys.

For scheduled-task setup phrases such as 开启定时任务, 配置每日提醒, 配置每周复盘, 开启自动复习提醒, or 配置 OpenClaw cron, read references/automation-openclaw.md and configure reminders with setup_scheduled_tasks.py. Scheduled tasks default to reminders and suggestions only; do not enable automatic worksheet generation or record writes unless the parent explicitly asks.

For first-use local setup checks, read references/openclaw-quickstart.md. Do not mention GitHub setup during ordinary grading or worksheet generation unless the parent asks for cloud sync, push, public links, Pages, or a publish preflight fails.

Always treat the current workspace root as the personal learning project root for memory/, weak-points/, mistakes/, records/, curriculum/, knowledge-points/, worksheets/, and site/. The reusable skill repository only provides instructions, scripts, references, templates, and sanitized examples.

If the current workspace appears to be the reusable source repository zhizhi-math-coach-openclaw (for example it contains docs/openclaw-release.md and examples/student-workspace/), warn before writing student learning data. Do not warn merely because a personal workspace has an installed skills/zhizhi-math-coach/ bundle from ClawHub. Only write student data into the source repository when the user explicitly says it is the intended personal learning workspace or the task is skill development with sanitized examples.

Do not assume background sync unless .zhizhi-math-coach/config.json enables it. Local files are changed by the current task only:

• grading or diagnosis may write records/, mistakes/, weak-points/, and evidence-backed memory/ updates;
• worksheet generation may write worksheets/<date-topic>/worksheet-spec.json, worksheet.html, worksheet.pdf, and answer-key.md;
• publishing may write site/ and worksheets/<date-topic>/publish.json.
• GitHub Pages setup may write .github/workflows/pages.yml when the parent has chosen a public repository, selected GitHub Actions as the Pages source, and asked OpenClaw to set up publishing.

When publishing, rebuild site/index.html as the full worksheet list from worksheets/, sorted by date descending. Include only public-safe metadata: date, practice status, title, child-facing file links, topic, grade, item count, and completion summary. Infer status from worksheets/status.md when available; do not expose answers or diagnosis details in site/.

PDF is the default worksheet delivery format. After worksheet generation, return or send worksheet.pdf first when it exists. If Chrome/Chromium is unavailable and PDF export was skipped, return the local worksheet.html path and mention that PDF export needs Chrome/Chromium.

GitHub sync and GitHub Pages are advanced cloud features, not required for normal use. If GitHub sync or Pages is configured and enabled in .zhizhi-math-coach/config.json, follow the config flags and the relevant sync/publishing reference.

Do not run git add, git commit, or git push unless the parent explicitly asks to sync, publish, push, commit to GitHub, send a public link, or .zhizhi-math-coach/config.json enables automatic sync or automatic Pages publishing. When sync is requested or newly configured, read references/github-sync-authorization.md first and run the bundled preflight before committing or pushing. Do not require GitHub CLI or provider-level token configuration; a repository-scoped SSH deploy key is the preferred setup. If authorization is missing, return the PDF/local file paths and setup guidance instead of treating generation as failed. If the personal repository is public, warn before committing sensitive learning records or answer keys unless the parent has explicitly accepted full public learning-data sync in .zhizhi-math-coach/config.json.

Skill resources are relative to {baseDir}:

• references/grading-diagnosis-rubric.md: grading and diagnosis fields.
• references/progress-tracking.md: record templates and status values.
• references/relapse-handling.md: how to handle repeated mistakes after repair.
• references/curriculum-alignment.md: textbook, China grade/semester, and copyright-safe curriculum alignment.
• references/school-calendar.md: China school-year, semester, exam window, and holiday phase rules.
• references/knowledge-point-explanations.md: parent explanation card and student summary rules.
• references/worksheet-strategies.md: supported paper-generation strategies and confirmation questions.
• references/worksheet-generation.md: low-token worksheet workflow.
• references/word-problem-variant-design.md: how to design non-shallow word-problem variants.
• references/complex-problem-generation.md: complex word-problem and review safeguards.
• references/geometry-generation.md: deterministic SVG geometry rules.
• references/automation-openclaw.md: scheduled reminders, channels, and automation boundaries.
• references/openclaw-quickstart.md: first-use checklist, common prompts, Pages-ready checklist, and ruleset summary.
• references/github-pages-publishing.md: public child-facing PDF/HTML worksheet publishing rules.
• references/github-sync-authorization.md: GitHub SSH/token authorization, preflight checks, and sync boundaries.
• references/worksheet-standards.md: child-facing printable worksheet rules.
• references/student-profile-template.md: starter profile format.
• scripts/generate_worksheet.py: generate worksheet HTML, student-facing PDF, and answer key from JSON.
• scripts/check_git_sync.py: preflight whether the current machine can reach and push the personal GitHub repository.
• scripts/configure_learning_workspace.py: create or update .zhizhi-math-coach/config.json for a personal learning repository.
• scripts/prepare_github_deploy_key.py: generate a repository-scoped SSH deploy key and public-key setup instructions for GitHub Deploy keys.
• scripts/setup_github_pages_workflow.py: create .github/workflows/pages.yml for publishing site/ through GitHub Actions.
• scripts/setup_scheduled_tasks.py: enable automation config and register OpenClaw cron reminder jobs when openclaw cron is available.
• scripts/sync_learning_repo.py: pull, commit, and push configured learning-data changes without asking again when automatic sync is enabled.
• references/daily-grading-workflow.md: fast grading, light recording, automatic full-archive upgrade, subagent boundary, validation, recording, and grading sync.
• scripts/build_grading_context.py: build one compact grading context from config, active context, and curriculum profile.
• scripts/validate_diagnosis_payload.py: validate diagnosis JSON before writing records.
• scripts/record_grading_diagnosis.py: write diagnosis, mistake-book, progress, weak-point, and optional memory updates from one compact JSON payload.
• scripts/run_log.py: shared helper for .zhizhi-math-coach/run-log.jsonl.
• scripts/init_learning_workspace.py: initialize a personal learning repository after the skill is installed.
• scripts/validate_worksheet_spec.py: validate worksheet JSON without writing outputs.
• scripts/publish_html_site.py: publish child-facing worksheet HTML/PDF into a GitHub Pages site/ directory.
• scripts/publish_and_wait_pages.py: publish site/, commit/push public-safe files, wait for GitHub Actions Pages deployment, and print ready URLs.
• assets/worksheet/question-types.json: reusable worksheet item types.
• assets/worksheet/a4-single.html: printable HTML template.

Before Grading

Read references/daily-grading-workflow.md.

Default daily grading is one-turn fast_grade_light_record: grade the photo or wrong-question batch, return the parent-facing summary, and write a light local record without asking the parent for another message. Use fast_grade_only only when the parent explicitly says not to record. Upgrade yourself to full_archive when the evidence justifies it; do not wait for the parent to say "完整归档".

Build compact context first:

bash

python3 {baseDir}/scripts/build_grading_context.py \
  --workspace . \
  --format md

When an isolated subagent is available, delegate image/direct-question diagnosis to it with only the compact grading context and the requested JSON shape. The subagent must not write files, read broad history, sync Git, or publish. The main session validates, records, and syncs.

Validate and record the JSON payload:

bash

python3 {baseDir}/scripts/validate_diagnosis_payload.py \
  --workspace . \
  --mode fast_grade_light_record \
  --input diagnosis-update.json

python3 {baseDir}/scripts/record_grading_diagnosis.py \
  --workspace . \
  --mode fast_grade_light_record \
  --input diagnosis-update.json

Use --mode full_archive for both commands after evidence-driven upgrade. If automatic Git sync is enabled after recording, call sync_learning_repo.py --mode after-task --task-kind grading.

Before Explaining A Knowledge Point

Read the relevant knowledge-points/<topic-slug>.md when it exists. If it does not exist, create the explanation in the same structure and recommend saving it in the user's personal learning project:

1. Parent explanation script.
2. Student-facing short version.
3. Doing tips.
4. Common errors and quick checks.
5. Mastery evidence: can explain, can do same-structure items, can do variants, and can still solve after spacing.

Do not use long textbook excerpts. Use textbook scope and terminology, then explain in original words.

Before Creating Practice

Read:

1. memory/local-memory-rules.md
2. memory/long-term.md
3. memory/short-term.md
4. curriculum/school-calendar.md
5. curriculum/profile.md
6. curriculum/scope.md
7. curriculum/progress.md
8. The relevant weak-points/*.md
9. The relevant knowledge-points/*.md
10. references/worksheet-strategies.md
11. references/worksheet-standards.md
12. references/worksheet-generation.md
13. references/progress-tracking.md

If the parent only says "出一张练习卷", confirm purpose, content range, length, and output format before generating. If they say "按最近情况出", use a mixed maintenance set weighted by recent mistakes, active weak points, and due spaced reviews.

For word problems, also read references/word-problem-variant-design.md and references/complex-problem-generation.md.

For geometry, also read references/geometry-generation.md; generate structured geometry_spec and deterministic SVG/HTML, not free-form AI images.

Prefer the low-token workflow:

bash

python3 {baseDir}/scripts/validate_worksheet_spec.py \
  worksheets/YYYY-MM-DD-topic/worksheet-spec.json

python3 {baseDir}/scripts/generate_worksheet.py \
  worksheets/YYYY-MM-DD-topic/worksheet-spec.json

The generator writes worksheet.html, worksheet.pdf when Chrome/Chromium is available, and answer-key.md. Return or send worksheet.pdf as the primary worksheet artifact.

If the workspace has public Pages mode configured and the parent accepts public worksheet links, publish only the child-facing worksheet HTML/PDF and wait for deployment:

bash

python3 {baseDir}/scripts/publish_and_wait_pages.py \
  worksheets/YYYY-MM-DD-topic \
  --workspace <personal-learning-workspace> \
  --base-url https://<github-user>.github.io/<repo>

If the parent wants a local-only preview or GitHub sync is not ready, publish local site/ files without pushing:

bash

python3 {baseDir}/scripts/publish_html_site.py \
  worksheets/YYYY-MM-DD-topic \
  --workspace <personal-learning-workspace> \
  --base-url https://<github-user>.github.io/<repo>

When Pages auto-publishing succeeds, reply with the PDF path/file, Pages index URL, and worksheet URL. Otherwise reply with file paths, item count, target weak point, and setup guidance for publishing. Do not paste full worksheet HTML or full answer keys unless asked.

Teaching Defaults

• Use concise Chinese for parent-facing output.
• Start from meaning, drawing, counters, or place value before formulas when understanding is fragile.
• Ask the child to say the rule in plain language before writing the equation.
• Keep one main diagnostic target per short practice.
• If the student can answer correctly but slowly, diagnose fluency separately from understanding.
• Do not turn handwriting difficulty into a math test. Prefer circling, ticking, matching, or printed choices for classification.
• Use textbooks or curriculum references for scope, but create original targeted practice.
• When a parent says a repeated application model is already understood, switch to small mixed variants that test transfer.

China School Calendar Defaults

Default semester rule:

• School year starts on September 1 and ends the next August.
• September 1 to January 31: first semester.
• February 1 to August 31: second semester.
• Winter break and summer break are local overrides, not fixed national dates.
• Midterm and final windows must be configurable per school.

If school_entry_year: 2025, the date 2026-05-18 is normally 一年级下学期. Still check local overrides and actual school progress before deciding scope.

Mistake Handling

Every wrong or uncertain item should include:

date / school year / grade / semester / term phase / source type / source file / item number / question / student answer / correct answer / error type / likely cause / related knowledge point / related weak point / relapse judgment / re-practice status / follow-up.

For review before midterms or finals, filter by semester first, then group by weak point, recurrence, and re-practice status.

Relapse Handling

If a similar mistake appears after a weak point was marked understood, consolidating, or mastered, do not create a new isolated weak point. Decide whether it is:

• relapse: same cause failed again.
• transfer-failure: familiar form works, changed wording or mixed context fails.
• spaced-forgetting: the prior repair faded after a gap.
• one-off-slip: isolated error with nearby evidence of mastery.

Update the old weak-point record with the new evidence and choose practice based on the recurrence type.

Worksheet Strategies

Supported strategies:

• wrong_question_variant: turn an existing wrong question into meaningful variants.
• weak_point_drill: focus one weak point.
• exam_mistake_review: midterm/final review weighted by real mistakes.
• relapse_repair: repair relapse, transfer failure, or spaced forgetting.
• spaced_review: small due review for old weak points.
• transfer_check: changed wording/scenario/condition order.
• post_explanation_check: 3 to 6 questions after explanation.
• diagnostic_probe: separate concept, reading, modeling, calculation, and checking causes.
• mixed_maintenance: current unit plus old weak points plus fluency.
• fluency_speed: facts and speed when understanding is already stable.
• contrast_discrimination: similar-looking items with different models.
• geometry_drill: deterministic geometry items from structured specs.

Automation Boundary

Scheduled OpenClaw tasks should default to reminders and suggestions in the configured local timezone:

• Daily 20:30 local time: due practice, pending uploads, stale short-term observations.
• Sunday 20:00 local time: weekly progress review and next-week suggestions.
• End of semester: summary and holiday review pool.
• Winter/summer break: weekly review suggestions.

Do not let scheduled tasks automatically change weak-point status, memory, or generate new worksheets unless the parent explicitly asked for that behavior.

OpenClaw cron is not declared as a skill-install manifest. It is registered by running the bundled setup script after the parent enables scheduled tasks:

bash

python3 {baseDir}/scripts/setup_scheduled_tasks.py \
  --workspace . \
  --enable-config \
  --auto-register \
  --timezone Asia/Shanghai

If openclaw is not available on the current machine, the script prints the openclaw cron add commands for the provider or parent to run later.

Feishu notifications should prefer GitHub Pages worksheet links when configured; keep answer keys and diagnosis records outside published site/ output.

Output Rules

When generating worksheets:

• Keep worksheet.html child-facing and answer-free.
• Generate and return worksheet.pdf first when available; it is the direct print/share artifact.
• Keep answers, grading labels, explanation notes, and reassessment rules in answer-key.md.
• Only child-facing worksheet.html and worksheet.pdf may be published to GitHub Pages. Do not publish answer keys, records, memories, weak-point histories, student photos, or textbook files.
• Use worksheet-spec.json as the source of truth.
• Add new stable item types to assets/worksheet/question-types.json and scripts/generate_worksheet.py.
• Include name/date/time/score fields and enough working space.
• Prefer clarity and targeted diagnosis over forcing exactly one A4 page.
• Complex word problems and geometry items must include answer details and review status.

When grading:

• Lead with confirmed mistakes and high-confidence causes.
• Separate reading, modeling, calculation, expression, and checking errors.
• Use confidence: high / medium / low.
• For low-confidence causes, give 1 to 2 quick verification questions.
• Group repeated errors by cause and teach the cause once.