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Math Curriculum Engine

This app now has a standards-anchored Grade 1 through Grade 4 math curriculum data source in curriculum/math-curriculum.js.

The design goal is acceleration without skipping foundations:

  • start with a first-grade refresher
  • place by skill, not just grade label
  • advance only on repeated evidence across days
  • protect confidence with hints, worked examples, and calmer review

Files

  • curriculum/math-curriculum.js
    • complete math skill graph
    • onboarding assessment bank
    • daily session loop rules
    • mastery and advancement rules
    • reward hooks for the light companion
    • parent summary model
    • UX recommendations
    • seeded Grade 1 to Grade 4 lesson bank
  • app.js
    • now loads the external math curriculum runtime and placement summary
  • index.html
    • loads the curriculum file before the app runtime
  • sw.js
    • caches the curriculum asset for offline PWA use

Curriculum Shape

The math roadmap is a skill graph, not a chapter list. Skills are connected by prerequisites so the app can slow down and repair gaps before pushing ahead.

Current graph coverage:

  • Grade 1
    • counting and number sequence to 120
    • skip counting by tens
    • comparing numbers
    • addition and subtraction within 20
    • make ten and missing addends
    • tens and ones
    • story problems
    • time to hour and half hour
    • length comparison
    • shapes and simple data
  • Grade 2
    • skip counting by 5s, 10s, 100s
    • place value to 1000
    • addition and subtraction within 1000
    • money, time to 5 minutes, measurement
    • data, geometry, equal groups foundations
  • Grade 3
    • multiplication and division meaning
    • fact families and fluency foundations
    • fractions as numbers
    • area and perimeter
    • multi-digit problem solving
  • Grade 4
    • place value through large numbers
    • multi-digit operations
    • factors, multiples, and patterns
    • equivalent fractions and fraction operations foundations
    • decimals
    • measurement, lines, angles, symmetry, and geometry

Onboarding / Placement

The onboarding bank has 24 seeded questions with read-aloud text and low-reading prompts.

Structure:

  1. Questions 1-6: confidence-building Grade 1 foundation checks
  2. Questions 7-17: first-grade mastery and early Grade 2 readiness
  3. Questions 18-24: stretch items for children who may be ahead

Placement output model:

  • estimatedStartingLevel
  • masteredSkills
  • shakySkills
  • blockedSkills
  • recommendedFirst7Days
  • parentFacingSummary

Adaptive intent:

  • stop early into Grade 1 refresher if the first foundation band is shaky
  • continue into stretch items only when the child shows stable readiness
  • place by weakest meaningful skill, not by one lucky score

The current prototype app still shows a simple linear check UI, but it now records skill-level math evidence and uses the curriculum placement function to choose the starting lesson and store a parent-readable summary in localStorage.mathPlacementSummary.

Daily Session Loop

Target length: 10-20 minutes.

  1. Warmup review: 2-3 minutes
  2. Main lesson/practice: 5-8 minutes
  3. Checkpoint: 3-5 minutes
  4. Reward moment: 1-2 minutes

Daily rules:

  • normal daily total: 10-16 questions
  • shorter day if hint use is heavy or frustration appears
  • hint 1 after first miss or clear hesitation
  • hint 2 after second miss or repeated help tap
  • lower difficulty after 2 misses on the same pattern
  • increase difficulty only after calm success across multiple items or days
  • stop early before frustration spirals
  • screen time counts as unlocked once the planned loop is completed or the app intentionally stops to protect the child from overload

Mastery Model

Skill states:

  • introduced
  • practicing
  • almost_mastered
  • mastered
  • needs_review
  • blocked

Advancement principles:

  • accuracy matters most
  • across-day consistency matters more than one short quiz
  • hint usage softens mastery evidence
  • repeated misconception misses trigger review
  • spaced review is required for true mastery
  • response time is a light signal only

Reward Hooks

The light companion reward system is deterministic and effort-based.

Reward events included in the data:

  • first_try_correct
  • fixed_after_hint
  • mastered_skill
  • review_streak
  • brave_retry
  • daily_complete
  • checkpoint_complete

Rewards map to:

  • gems
  • brightness growth
  • accessory or outfit progress
  • gentle recovery messaging after mistakes

No random loot design is used.

Parent Reporting

The parent summary model includes:

  • today completed or not
  • time spent
  • skills practiced
  • accuracy
  • hints used
  • new mastery
  • frustration signals
  • recommended next session
  • screen-time unlocked

UX Recommendations

Keep child mode simpler than the current prototype:

  • one question at a time
  • larger answer buttons
  • read-aloud always visible
  • no subject picking in child mode
  • progress shown as distance to unlock, not a busy dashboard
  • companion feedback short and supportive
  • no clutter during questions
  • all detailed reporting hidden behind parent mode

Standards Anchor

The sequence is aligned to Common Core-style elementary math progression using official sources:

How To Use

In the browser:

  • run the app as before
  • the app now loads the external math curriculum automatically
  • onboarding math placement uses the seeded assessment bank
  • the chosen math start chapter comes from the curriculum placement summary

For future engine work:

  • use window.DragonMathCurriculum.skillGraph for mastery and dependency logic
  • use window.DragonMathCurriculum.lessons for richer lesson sequencing
  • use window.DragonMathCurriculum.onboarding.inferPlacementFromSkillResults(...) for parent summaries and lesson assignment