Wayfinder GED — Learning Framework

All four subjects with tier breakdowns, prerequisites, common misconceptions, diagnostic probes.

GED LEARNING FRAMEWORK

Four Subjects, Pure Learning Architecture, Progress Measurement

Status: Core framework artifact for GED module
Date: June 2026
Scope: Mathematical Reasoning, Reasoning Through Language Arts, Science, Social Studies
Design principle: Focus on what needs to be learned and how we know if it worked. No pedagogical bias.

PART 1: FOUR SUBJECTS — MAIN SECTIONS & PREREQUISITES

SUBJECT 1: MATHEMATICAL REASONING

Section 1.1: Number & Operations - Place value (whole numbers, decimals, fractions) - Integer operations (addition, subtraction, multiplication, division) - Order of operations (PEMDAS) - Factors, multiples, prime numbers - Fractions: equivalent, compare, operations (add, subtract, multiply, divide) - Decimals: place value, compare, operations - Percents: convert, calculate percent of, percent change, simple interest - Ratios & proportions: identify, set up, solve - Exponents & roots: square roots, cube roots, scientific notation

Prerequisite for next: Must be fluent (automatic) in basic operations before moving to algebra. Fluency = accurate + fast (< 5 seconds per simple problem).

Section 1.2: Algebra & Functions - Variables & expressions: write, evaluate, simplify - Linear equations (one variable): solve, applications - Systems of linear equations: solve by substitution, elimination, graphing - Linear inequalities: solve, graph, applications - Exponent rules: product, quotient, power, zero, negative - Polynomials: add, subtract, multiply, divide, factor - Quadratic equations: solve by factoring, quadratic formula, completing square - Rational expressions: simplify, operations - Exponential & logarithmic basics - Functions: definition, domain/range, operations, inverse, composition

Prerequisite for next: Must understand linear equations before systems. Must understand polynomials before quadratics.

Section 1.3: Geometry & Measurement - Basic angle relationships: supplementary, complementary, vertical, adjacent - Parallel lines & transversals - Triangle properties: angles, congruence, similarity, Pythagorean theorem - Area & perimeter: triangles, rectangles, circles, polygons, composite shapes - Volume & surface area: prisms, cylinders, pyramids, cones, spheres - Coordinate geometry: distance formula, midpoint, slope, equations of lines - Transformations: reflections, rotations, translations, dilations - Trigonometry basics: sin, cos, tan, inverse functions - Circles: central angles, arcs, sectors, inscribed angles

Prerequisite for next: Must understand angles and basic shapes before area/perimeter. Must understand Pythagorean theorem before trigonometry.

Section 1.4: Data & Statistics - Measures of center: mean, median, mode - Measures of spread: range, interquartile range, standard deviation - Data displays: dot plots, histograms, box plots, scatter plots - Probability basics: simple events, compound events, independent vs. dependent - Normal distribution: z-scores, percentiles - Experimental design: bias, random sampling, control groups - Correlation vs. causation - Two-way tables: marginal & conditional frequency

Prerequisite for next: Must understand mean/median before measures of spread. Must understand basic probability before normal distribution.

SUBJECT 2: REASONING THROUGH LANGUAGE ARTS (RLA)

Section 2.1: Reading Comprehension & Analysis - Main idea vs. topic vs. theme - Supporting details vs. main idea - Explicit vs. implicit information (stated vs. inferred) - Inference: reasonable conclusions based on evidence - Author’s purpose: inform, persuade, entertain, explain - Text structure: cause-effect, compare-contrast, chronological, order of importance - Point of view & perspective: first, second, third person; objective vs. subjective - Fact vs. opinion vs. interpretation - Tone vs. mood vs. voice

Prerequisite for next: Must understand main idea before moving to more complex inference and analysis.

Section 2.2: Argument & Evidence - Claim vs. evidence vs. reasoning - Types of evidence: factual, logical, expert opinion, personal experience - Strength of evidence: relevant, sufficient, credible, recent - Logical fallacies: ad hominem, straw man, appeal to authority, hasty generalization, false dilemma, slippery slope - Counterargument & rebuttal - Bias in sources: detection, acknowledgment, integration - Rhetorical strategies: parallelism, repetition, allusion, metaphor

Prerequisite for next: Must understand claim and evidence before evaluating counterarguments.

Section 2.3: Grammar & Usage - Sentence structure: simple, compound, complex, compound-complex - Subject-verb agreement: number, person - Verb tense: simple, progressive, perfect (all tenses) - Pronoun-antecedent agreement: number, person, gender - Pronoun case: nominative, objective, possessive - Modifiers: placement, dangling, misplaced, agreement - Parallel structure in lists & paired items - Comma rules: coordinating conjunctions, introductory phrases, nonrestrictive clauses, items in series - Other punctuation: semicolons, colons, dashes, hyphens, apostrophes

Prerequisite for next: Must understand sentence structure before verb tense. Must understand subject-verb agreement before pronoun agreement.

Section 2.4: Writing - Thesis development: clear, specific, arguable, not too broad - Organization: introduction, body paragraphs, conclusion - Paragraph structure: topic sentence, supporting sentences, conclusion - Evidence integration: direct quotes, paraphrases, summaries with citations - Transitions: within paragraphs, between paragraphs, between ideas - Revision: content, organization, word choice, tone, mechanics - Extended Response essay structure: analyze two sources, develop thesis, support with evidence, acknowledge counterargument - Tone & audience awareness: formal academic, professional, persuasive

Prerequisite for next: Must understand thesis before organizing body paragraphs. Must understand paragraph structure before integrating evidence.

SUBJECT 3: SCIENCE

Section 3.1: Life Science - Cell structure & function: prokaryotic vs. eukaryotic, organelles, transport (diffusion, osmosis, active) - Genetics: DNA, genes, alleles, dominant/recessive, inheritance patterns, Punnett squares - Evolution: natural selection, adaptation, fossil evidence, speciation - Ecology: ecosystems, biomes, food chains/webs, energy flow, population dynamics, community interactions - Human body systems: skeletal, muscular, circulatory, respiratory, digestive, nervous, endocrine, immune, reproductive

Prerequisite for next: Must understand cell structure before genetics. Must understand evolution before ecology.

Section 3.2: Physical Science - Motion & forces: distance, speed, velocity, acceleration, Newton’s laws - Energy: kinetic, potential, mechanical, thermal, electrical, conservation of energy - Waves: mechanical vs. electromagnetic, wavelength, frequency, speed, sound, light - Atoms & matter: atomic structure, elements, periodic table, compounds, chemical bonds, states of matter - Chemical reactions: reactants, products, exothermic vs. endothermic, combustion, oxidation - Acids & bases: pH, neutralization, strong vs. weak

Prerequisite for next: Must understand force before energy. Must understand atoms before chemical reactions.

Section 3.3: Earth & Space Science - Geology: minerals, rocks, rock cycle, plate tectonics, earthquakes, volcanoes, weathering, erosion - Weather & climate: atmosphere composition, weather patterns, climate zones, climate change, water cycle - Astronomy: solar system, planets, moons, stars, galaxies, Big Bang, light-years - Earth systems: interactions between atmosphere, hydrosphere, lithosphere, biosphere - Natural resources: renewable vs. nonrenewable, sustainability, conservation

Prerequisite for next: Must understand minerals & rocks before plate tectonics. Must understand atmosphere before weather patterns.

Section 3.4: Science Practices - Scientific method: observation, hypothesis, experiment, analysis, conclusion - Variables: independent, dependent, control - Data collection: precision, accuracy, measurement tools - Data representation: tables, graphs, charts - Experimental design: controls, variables, replicability, bias minimization - Hypothesis testing: null hypothesis, alternative hypothesis, significance - Sources of error: systematic vs. random, minimization - Data interpretation: patterns, outliers, limitations, conclusions

Prerequisite for next: Must understand variables before designing experiments. Must understand data representation before interpretation.

SUBJECT 4: SOCIAL STUDIES

Section 4.1: U.S. History - Colonial period through founding: European exploration, colonial development, causes of revolution, Declaration of Independence - Constitution & early republic: Constitution ratification, Federalism, political parties, Westward expansion - 1800s to Civil War: Manifest Destiny, slavery & abolition, causes & consequences of Civil War - Reconstruction through Progressivism: Reconstruction, Gilded Age, Industrial Revolution, Progressive Era reforms - 20th century: World War I, Roaring Twenties, Great Depression, New Deal, World War II - Cold War era: containment policy, Korean War, Cuban Missile Crisis, Vietnam War, space race - 1970s-2000s: Watergate, civil rights movements, end of Cold War, September 11, Iraq/Afghanistan wars

Prerequisite for next: Must understand colonial period before revolution. Must understand Civil War before Reconstruction.

Section 4.2: Civics & Government - Constitution: structure, amendment process, Bill of Rights, later amendments - Branches of government: legislative (Congress, lawmaking), executive (President, enforcement), judicial (Supreme Court, interpretation) - Separation of powers: checks & balances, examples - Federalism: division of power between federal & state, examples - Citizenship: rights, responsibilities, duties - Voting: requirements, voting rights history, participation methods - Political parties: ideology, platforms, registration - Political processes: lobbying, campaigns, elections, policymaking

Prerequisite for next: Must understand Constitution before branches. Must understand branches before separation of powers.

Section 4.3: Economics - Basic economic concepts: scarcity, opportunity cost, supply & demand, equilibrium - Production: factors of production, comparative advantage, specialization - Markets: perfect competition, monopoly, oligopoly, types of economies - Money & banking: functions of money, Federal Reserve, interest rates, credit - Personal finance: budgeting, saving, investing, debt, credit scores - Macroeconomics: GDP, inflation, unemployment, fiscal policy, monetary policy - Trade: imports, exports, balance of trade, free trade vs. protectionism - Inequality: income distribution, poverty, social mobility

Prerequisite for next: Must understand supply & demand before market structures. Must understand money before banking.

Section 4.4: Geography & Global Context - Map skills: latitude/longitude, map types, scale, projections, cardinal directions - Physical geography: continents, oceans, climate zones, biomes, natural resources - Human geography: population, culture, religion, language, ethnic groups - Political geography: borders, nations, sovereignty, geopolitics - Economic geography: trade patterns, development levels, urbanization - Global systems: international organizations, treaties, global challenges (disease, climate, poverty) - Regional studies: characteristics, cultures, economies, conflicts (Middle East, Africa, Asia, Europe, Americas)

Prerequisite for next: Must understand map skills before studying regions. Must understand physical geography before human geography.

PART 2: WHAT COUNTS AS LEARNING (Mastery Definition)

Learning is demonstrated when a student can:

1. Define & explain the concept in their own words (not memorized)
2. Identify examples & non-examples in context (can spot when it applies and when it doesn’t)
3. Apply to new situations (not just the ones practiced)
4. Explain reasoning when asked (not just right answer, but why)
5. Retain across time (can do it again next week without re-teaching)

For declarative knowledge (facts, definitions, vocabulary): - Recall without prompting (at least 90% accuracy) - Apply in context - Explain when applicable

For procedural knowledge (skills, processes, algorithms): - Execute without error (at least 90% accuracy) - Explain steps when asked - Apply to variant problems (not just practice problems)

For conceptual knowledge (relationships, patterns, principles): - Identify the concept across different contexts - Explain why the concept works that way - Apply to novel situations - Critique incomplete or incorrect applications

Red flags that learning didn’t happen: - Student got it right but can’t explain how - Student can do the practice problem but fails on similar (not identical) problems - Student forgets between sessions without re-teaching - Student’s reasoning shows misconception underneath correct answer

PART 3: DIAGNOSTIC PROBES (Identifying Gaps)

Every concept has diagnostic probes — short questions that reveal if the student actually understands or is guessing.

For Math: - Can do basic version (no new variables) - Can do variant (change one parameter) - Can set up new problem (given story, student sets up equation) - Can explain why method works (not just algorithm)

For RLA: - Can identify concept in new passage (not the one taught) - Can distinguish from similar but different concepts - Can explain why answer is correct - Can generate their own example

For Science: - Can apply to different scenario (not the exact one taught) - Can predict what would happen if you changed something - Can explain the mechanism (not just memorize facts)

For Social Studies: - Can apply concept to different time period or region - Can evaluate different perspectives on the topic - Can explain cause-effect relationships - Can generate supporting evidence

PART 4: COMMON MISCONCEPTIONS BY SECTION

Every section lists the most common errors students make. These are observed patterns, not theoretical predictions.

Examples:

Math — Negative Numbers: - Error: “negative plus negative equals positive” (confuse with multiplication rule) - Indicator: Student gets signs wrong consistently in addition/subtraction - Correction approach: Number line visualization, concrete examples first

Math — Order of Operations: - Error: “work left to right” (ignore PEMDAS) - Indicator: Student adds before multiplying - Correction approach: Re-teach with exaggerated grouping symbols

RLA — Main Idea: - Error: “first sentence is always the main idea” (confuse topic with main idea) - Indicator: Student selects first statement regardless of support - Correction approach: Reframe: “what is the author trying to convince you of?”

Science — Gravity: - Error: “gravity only applies downward, not in other directions” - Indicator: Student thinks gravity doesn’t affect horizontal motion - Correction approach: Projectile motion demos, orbital mechanics

Social Studies — Causation: - Error: “events that happen together caused each other” - Indicator: Student confuses correlation with causation - Correction approach: Explicit examples of false causation, temporal ordering check

PART 5: PREREQUISITE CHAINS (What Must Be Solid First)

Learning is sequential. Gaps compound.

Math chain example:

Integers → Fractions → Decimals & Percents → Ratios & Proportions →
Exponent Rules → Polynomials & Factoring → Quadratic Equations →
Systems of Equations → Functions & Graphing

If a student is weak on fractions, they will fail on decimals, percents, proportions, and everything downstream. Do NOT advance. Go back and solidify fractions.

RLA chain example:

Sentence Structure → Pronoun Agreement → Verb Tense → Complex Sentences →
Paragraph Organization → Thesis Development → Evidence Integration →
Extended Response Essays

If a student can’t identify a sentence, they can’t fix pronoun agreement. Do NOT advance.

Science chain example:

Cell Structure → Genetics → Evolution →
Population Dynamics → Ecology → Ecosystems

If a student doesn’t understand cells, genetics will fail. Do NOT advance.

PART 6: MEASURING PROGRESS (What Data We Collect)

Per assignment: - Accuracy: % correct - Time: minutes to completion - Error type: careless, conceptual, computational, reading comprehension - Misconception flagged: yes/no, which one - Prerequisite gap detected: yes/no, which skill

Per concept: - Assignments completed: count - Accuracy trend: [attempt 1, attempt 2, …, attempt n] - Average accuracy: % - Mastery status: not started / developing / proficient / mastered - Prerequisite status: solid / weak / unknown

Per month: - Concepts started: count - Concepts mastered: count - Accuracy by section: % per section - Error patterns: most common misconceptions this month - Prerequisite gaps surfaced: which skills need rework - Engagement: frequency, consistency, time invested

System performance: - Assignment difficulty calibration: were assignments right difficulty? - Prerequisite detection accuracy: when we predicted a gap, was it real? - Misconception inventory accuracy: are our “common errors” actually common for this student? - Progression timing: are students spending right amount of time per concept?

PART 7: WHEN TO ESCALATE (Red Flags)

Stop and investigate if:

1. Same misconception appears 3+ times despite exposure to correct method
2. Accuracy drops after mastery (student “forgot” a concept they had solid)
3. Procedure correct but reasoning wrong (getting answer right but explaining wrong concept)
4. Multiple choice passed but written response failed (can’t produce work, only recognize)
5. Time per problem increasing (student getting slower, not faster)
6. Accuracy plateaus at 60-75% (stuck, not improving with more practice)
7. Prerequisite gap discovered late (should have been caught earlier)
8. Student can explain but not execute (conceptual understanding without procedural fluency)

Response protocol: 1. Return to diagnostic (what’s the actual gap?) 2. Break concept into smaller pieces 3. Check for prerequisite weakness 4. Change assignment format 5. Add concrete/visual examples 6. Slow progression or pause

PART 8: ASSIGNMENT FORMAT OPTIONS

Math: - Multiple choice (4 options, 1 correct, 3 plausible) - Short answer (show work, correct answer, explanation of method) - Multi-part problem (tests multiple skills in sequence) - Word problem (tests reading comprehension + math) - Error analysis (“find and fix the mistake in this solution”) - Open-ended application (“solve a new problem like this”)

RLA Reading: - Passage + multiple choice comprehension - Passage + short answer (“what is the main idea?”) - Passage + inference (“what can we infer about…?”) - Passage + analysis (“explain how the author uses this evidence”) - Comparison (“compare how two passages approach the same topic”)

RLA Writing: - Sentence correction (fix grammar/usage errors) - Paragraph completion (add topic sentence, supporting evidence, conclusion) - Essay outline (given prompt, create thesis + 3 main points) - Draft essay (full extended response) - Revision task (“improve this paragraph”)

Science: - Multiple choice (4 options) - Short answer (“explain why this happens”) - Scenario application (“if X changes, what happens to Y?”) - Diagram labeling & explanation - Experimental design (“how would you test this hypothesis?”) - Data interpretation (“what does this graph show?”)

Social Studies: - Multiple choice (4 options) - Short answer (“what was the cause of…?”) - Document analysis (“interpret this primary source”) - Comparison (“compare perspectives on…”) - Application (“apply this concept to…”) - Evaluation (“was this policy effective? evidence?”)

PART 9: SUCCESS CRITERIA

Student has learned concept when:

End of GED Learning Framework

This is the foundation. It defines what needs to be learned and how we know if it worked. No pedagogy. Just: here’s the content, here’s the mastery definition, here’s how we measure it.