Learning Science Standard
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The 11 Invariants

Non-negotiable principles that must be met for learning to occur. These aren't best practices or nice-to-haves — they're constraints derived from cognitive science that determine whether an app actually teaches.

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1

Target skill = only path to success

The Principle

The learner cannot bypass the intended cognitive process. The skill being taught must be the only way to succeed at the task.

Why It Matters

If students can guess answers from pictures, context clues, or pattern matching without engaging the target skill, no learning occurs. The app becomes a game of clever workarounds rather than genuine skill acquisition. Research on Direct Instruction shows that faultless communication requires the target skill to be the sole path to correct responses.

What Violation Looks Like

  • ✗Multiple choice where images give away the answer
  • ✗Matching exercises where elimination strategy works
  • ✗Fill-in-the-blank where sentence context makes the answer obvious
  • ✗Reading exercises where pictures tell the whole story

What Compliance Looks Like

  • ✓Decodable text where phonics knowledge is required
  • ✓Math problems that require calculation, not estimation
  • ✓Vocabulary exercises where context alone is insufficient
  • ✓Assessments that isolate the specific skill being tested

Detection Method

We attempt to answer questions using only visual cues, context, or elimination. If success is possible without using the target skill, the app fails.

2

One new knowledge component per lesson

The Principle

Each lesson introduces only one new concept or skill component. Everything else in the lesson should be previously mastered material.

Why It Matters

Working memory has severe capacity limits. Cognitive Load Theory demonstrates that introducing multiple new elements simultaneously causes interference and prevents transfer to long-term memory. The KLI Framework's research on Knowledge Components shows that atomizing instruction into single components dramatically improves learning outcomes.

What Violation Looks Like

  • ✗Teaching multiple new letter sounds in one lesson
  • ✗Introducing a new math operation with new number types
  • ✗Combining new vocabulary with new grammar structures
  • ✗Multi-step problems where multiple steps are unfamiliar

What Compliance Looks Like

  • ✓One new phoneme per lesson, practiced with known phonemes
  • ✓New operation practiced with familiar numbers first
  • ✓New vocabulary used in familiar sentence structures
  • ✓Scaffolded complexity that adds one element at a time

Detection Method

We analyze lesson content to count novel elements. More than one new knowledge component per lesson fails this invariant.

3

All content uses taught patterns only

The Principle

Every element the learner encounters in practice should use patterns they've been explicitly taught. No untaught exceptions appear without explicit flagging.

Why It Matters

Encountering untaught patterns during practice creates confusion and undermines the systematic nature of instruction. Engelmann's Direct Instruction research shows that 'teaching to the test' in the best sense means ensuring practice material perfectly matches taught content.

What Violation Looks Like

  • ✗Irregular words appearing before being taught
  • ✗Math problems using operations not yet covered
  • ✗Sentences with grammar structures not yet introduced
  • ✗Vocabulary used in contexts beyond taught meanings

What Compliance Looks Like

  • ✓Strictly controlled vocabulary lists matching instruction
  • ✓Practice problems that only use taught operations
  • ✓Reading passages with 100% decodable words at that level
  • ✓Clear flagging when exceptions must appear ('tricky word')

Detection Method

We inventory all elements in practice content and verify each has been explicitly taught. Any untaught element fails unless explicitly marked as exception.

4

Vocalization required

The Principle

Learning requires active production, not passive recognition. For reading instruction specifically, the app must require vocalization—silent recognition is not reading.

Why It Matters

Recognition and production use different cognitive processes. The testing effect research shows that retrieval practice (active recall) produces dramatically better retention than recognition tasks. For reading, subvocalization is essential to developing fluent decoding.

What Violation Looks Like

  • ✗Tap-the-correct-answer without saying it
  • ✗Silent matching exercises
  • ✗Multiple choice without verbal response
  • ✗Reading comprehension without reading aloud

What Compliance Looks Like

  • ✓Speech recognition for reading responses
  • ✓Mandatory verbal responses before proceeding
  • ✓Recording features that capture vocalization
  • ✓Teacher/parent verification of verbal production

Detection Method

We check whether the app requires active production or accepts passive selection. Apps that allow silent completion of reading tasks fail.

5

Binary diagnostic mastery checks

The Principle

Mastery checks must be pass/fail (binary), not percentage-based. They must also be diagnostic—identifying specific gaps, not just overall performance.

Why It Matters

Percentage scores hide specific weaknesses behind averages. A student scoring 70% might have mastered 70% of concepts perfectly or might have partial knowledge of all concepts. Diagnostic mastery checks identify exactly which knowledge components need remediation.

What Violation Looks Like

  • ✗'You got 7/10 correct!'
  • ✗Star ratings (3 out of 5 stars)
  • ✗Percentage scores without breakdown
  • ✗Advancing based on average performance

What Compliance Looks Like

  • ✓Pass/fail on each specific skill component
  • ✓Clear identification of which items were missed
  • ✓No advancement until specific gaps are addressed
  • ✓Detailed reporting of exact error patterns

Detection Method

We examine how mastery is measured and reported. Percentage-based advancement without diagnostic specificity fails.

6

Accuracy before speed

The Principle

Speed is introduced only after accuracy is established. Fluency follows accuracy, not the reverse.

Why It Matters

Premature speed pressure creates errors that become habituated. Cognitive science shows that practicing errors strengthens incorrect neural pathways. Accuracy must be automatic before speed is introduced, or speed training reinforces mistakes.

What Violation Looks Like

  • ✗Timed exercises for new learners
  • ✗Speed bonuses from the start
  • ✗Leaderboards based on completion time
  • ✗Countdown timers during skill acquisition

What Compliance Looks Like

  • ✓Untimed practice until accuracy threshold met
  • ✓Speed elements introduced only after demonstrated mastery
  • ✓Clear separation of accuracy and fluency phases
  • ✓No penalties for taking time during learning

Detection Method

We check when timing elements are introduced. Timing before demonstrated accuracy fails this invariant.

7

Irregular items mapped, not memorized

The Principle

Exceptions and irregular items are taught systematically through patterns, not presented as arbitrary items to memorize.

Why It Matters

Pure memorization has severe capacity limits and doesn't transfer. Research shows that even 'irregular' items often follow sub-patterns. Teaching these patterns reduces cognitive load and enables generalization to new irregular items.

What Violation Looks Like

  • ✗'Sight words—just memorize these!'
  • ✗Irregular verbs as a list to memorize
  • ✗Exceptions presented without explanation
  • ✗No connection to regular patterns shown

What Compliance Looks Like

  • ✓Grouping irregular words by shared patterns
  • ✓Explaining why irregulars are pronounced as they are
  • ✓Connecting exceptions to historical/linguistic patterns
  • ✓Building mental models, not just memory banks

Detection Method

We examine how irregular items are introduced. Pure memorization approaches without pattern explanation fail.

8

No mastery bypass

The Principle

The learner cannot skip ahead or self-assess as mastered. The system determines mastery through assessment, not learner self-report.

Why It Matters

Learners are poor judges of their own competence (Dunning-Kruger effect). Allowing self-pacing or 'I already know this' buttons lets gaps persist. Research on desirable difficulties shows that perceived ease often indicates shallow learning.

What Violation Looks Like

  • ✗'I already know this' skip button
  • ✗Unlocked levels from the start
  • ✗User-controlled difficulty settings
  • ✗Self-assessment determining advancement

What Compliance Looks Like

  • ✓Locked progression based on demonstrated mastery
  • ✓No skip functionality for core content
  • ✓System-determined, not user-determined pacing
  • ✓Assessment gates between levels

Detection Method

We check for ways to bypass content. Any mechanism allowing progression without demonstrated mastery fails.

9

Errors interpreted, not averaged

The Principle

Each error is diagnostic information identifying specific knowledge gaps. Errors are not just counted and averaged but analyzed for what they reveal.

Why It Matters

An error pattern tells you exactly what's wrong. 'You got 70%' tells you nothing actionable. The same score can result from completely different underlying problems requiring completely different interventions.

What Violation Looks Like

  • ✗Generic 'try again' feedback
  • ✗Scores without error analysis
  • ✗Moving on after errors without addressing them
  • ✗Same feedback regardless of error type

What Compliance Looks Like

  • ✓Specific feedback addressing the exact error
  • ✓Different interventions for different error types
  • ✓Pattern recognition across errors
  • ✓Targeted remediation based on error analysis

Detection Method

We make deliberate errors and examine the response. Generic or averaged feedback fails; diagnostic interpretation passes.

10

External validation priority

The Principle

The app trusts external assessments over internal metrics. Real-world performance matters more than in-app scores.

Why It Matters

In-app metrics can be gamed or inflated. Transfer to real-world performance is the actual goal. An app claiming mastery while students struggle on external assessments is providing false confidence.

What Violation Looks Like

  • ✗No connection to external benchmarks
  • ✗Internal metrics presented as definitive
  • ✗No mention of real-world application
  • ✗Closed ecosystem with no external validation

What Compliance Looks Like

  • ✓Correlation with standardized assessment performance
  • ✓Recommendations for external verification
  • ✓Honest representation of what in-app scores mean
  • ✓Support for teacher/parent external assessment

Detection Method

We examine how the app positions its metrics relative to external validation. Closed-loop confidence without external anchoring fails.

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Every error triggers a fixed corrective loop

The Principle

Wrong response triggers: interrupt → model correct response → guided replay → required retry. The sequence is non-negotiable.

Why It Matters

Errors that go uncorrected become encoded. The specific sequence matters: immediate interruption prevents error reinforcement, modeling provides the correct pattern, guided replay builds the correct motor/cognitive sequence, and required retry confirms the correction took hold.

What Violation Looks Like

  • ✗"Oops! Try again" with no correction shown
  • ✗Correct answer shown but no retry required
  • ✗Moving on after showing the right answer
  • ✗Letting student attempt again without modeling

What Compliance Looks Like

  • ✓Immediate stop on error (no delayed feedback)
  • ✓Correct response modeled explicitly
  • ✓Guided practice through the correct sequence
  • ✓Required successful retry before proceeding

Detection Method

We make deliberate errors and verify the full corrective sequence executes. Any missing step fails this invariant.

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