Algebra I - Performance vs Learning Matrix

Example of Algebra I: Performance vs Learning Matrix

Core Mathematical Operations

Task/Activity Primary Goal AI Role Rationale & Recommendations
Basic Arithmetic Operations Learning Prohibited Students must develop mental math and estimation skills as foundational building blocks for algebraic thinking. These skills support number sense and pattern recognition.
Fraction Operations Learning Prohibited Understanding fraction relationships and operations is fundamental to algebraic concepts like rational expressions.
Integer Operations Learning Prohibited Mastery of positive and negative number operations is essential for equation solving and graphing.
Decimal Operations Learning Prohibited Decimal computation skills support understanding of real numbers and approximation.
Complex Calculations Performance Allowed as Calculator Once foundational skills are established, AI can be used like a calculator for complex computations that might otherwise slow down higher-level problem-solving.
Order of Operations Learning Prohibited Understanding PEMDAS is fundamental and requires hands-on practice. Students need to internalize these rules through direct experience.
Estimation & Reasonableness Learning Prohibited Students must develop the ability to estimate answers and judge reasonableness without technological assistance.
Scientific Notation Learning → Performance Phased Approach Initially learn conversions manually, then allow AI for complex calculations involving very large/small numbers.

Variables and Expressions

Task/Activity Primary Goal AI Role Rationale & Recommendations
Variable Recognition Learning Prohibited Students must learn to identify and understand variables in various contexts independently.
Expression Writing Learning Prohibited Converting words to algebraic expressions must be mastered without assistance.
Expression Evaluation Learning → Performance Staged Implementation Begin without AI for simple substitution, allow AI for complex substitutions after mastery.
Combining Like Terms Learning Prohibited Essential skill that requires understanding of algebraic structure.
Distribution Property Learning Prohibited Fundamental concept that requires manual practice for mastery.
Factoring Expressions Learning Prohibited Core algebraic skill requiring pattern recognition and number sense.
Expression Simplification Learning → Performance Phased Approach Master basic simplification manually, then allow AI for complex expressions.

Equation Solving

Task/Activity Primary Goal AI Role Rationale & Recommendations
One-Step Equations Learning Prohibited Fundamental skill requiring complete mastery without assistance.
Two-Step Equations Learning Prohibited Building block for more complex equation solving.
Multi-Step Equations Learning → Performance Phased Approach Master basic steps manually, allow AI verification for complex equations.
Equations with Fractions Learning Initially Prohibited Must understand fraction operations in algebraic context before using AI.
Linear Equations Learning Initially Prohibited Core skill requiring mastery of inverse operations and algebraic properties.
Literal Equations Learning → Performance Staged Implementation Learn rearrangement manually, then allow AI for complex formula manipulation.
Absolute Value Equations Learning Initially Prohibited Understand concept and solution process before using AI for verification.
Systems of Equations - Substitution Learning Prohibited Must master the substitution method manually.
Systems of Equations - Elimination Learning Prohibited Must master the elimination method manually.
Systems of Equations - Graphing Learning → Performance Phased Approach Learn graphing manually, then allow AI for complex systems and verification.

Inequalities

Task/Activity Primary Goal AI Role Rationale & Recommendations
Basic Inequalities Learning Prohibited Must understand inequality symbols and basic solving without assistance.
Multi-Step Inequalities Learning Initially Prohibited Core skill requiring understanding of inequality properties.
Compound Inequalities Learning → Performance Staged Implementation Master basic concepts manually, then allow AI for complex problems.
Absolute Value Inequalities Learning Initially Prohibited Understand concept and solution process before using AI.
Graphing Inequalities Learning → Performance Phased Approach Learn manual graphing first, then allow AI for complex situations.
Systems of Inequalities Learning → Performance Staged Implementation Master basic systems manually, allow AI for complex systems and verification.

Functions and Relations

Task/Activity Primary Goal AI Role Rationale & Recommendations
Function Definition Learning Prohibited Must understand the concept of functions without technological assistance.
Domain and Range Learning Prohibited Essential skill requiring understanding of input/output relationships.
Function Notation Learning Prohibited Core concept requiring manual practice and understanding.
Input/Output Tables Learning Prohibited Must be able to create and interpret tables manually.
Function Recognition Learning Prohibited Ability to identify functions vs. relations must be mastered independently.
Composition of Functions Learning → Performance Phased Approach Learn composition manually, then allow AI for complex compositions.
Inverse Functions Learning → Performance Staged Implementation Master concept manually, then allow AI for verification and complex problems.

Graphing & Visualization

Task/Activity Primary Goal AI Role Rationale & Recommendations
Coordinate Plane Plotting Learning Prohibited Essential skill requiring manual practice.
Number Line Graphing Learning Prohibited Fundamental skill for understanding real numbers and inequalities.
Linear Functions Learning → Performance Staged Implementation Master slope-intercept form manually, then allow AI for complex analysis.
Slope Calculations Learning Prohibited Must master manually for understanding rate of change.
Point-Slope Form Learning Prohibited Essential skill for understanding linear relationships.
Standard Form Learning → Performance Phased Approach Learn conversion manually, allow AI for complex problems.
Parallel/Perpendicular Lines Learning → Performance Staged Implementation Understand relationships manually, use AI for verification.
Quadratic Functions Learning → Performance Phased Approach Master basic parabola concepts manually, then use AI for analysis.
Transformations of Functions Learning → Performance Staged Implementation Learn basic transformations manually, use AI for complex cases.
Scatter Plots Performance Allowed with Guidelines AI can help create visualizations after data collection and initial analysis.
Line of Best Fit Learning → Performance Phased Approach Understand concept manually, then use AI for precise calculations.

Word Problems and Applications

Task/Activity Primary Goal AI Role Rationale & Recommendations
Problem Translation Learning Prohibited Must master converting word problems to algebraic expressions.
Age Problems Learning Prohibited Classic application requiring independent problem-solving skills.
Money Problems Learning Prohibited Real-world applications requiring careful analysis.
Distance/Rate/Time Learning Initially Prohibited Must understand relationship before using AI for complex calculations.
Mixture Problems Learning → Performance Phased Approach Master concept manually, allow AI for complex calculations.
Percent Problems Learning Prohibited Essential real-world application requiring thorough understanding.
Geometry Applications Learning → Performance Staged Implementation Learn basic applications manually, use AI for complex problems.

Practice & Assessment

Task/Activity Primary Goal AI Role Rationale & Recommendations
Homework Problems Learning Verification Only Complete work independently, use AI only for answer checking.
Practice Problem Generation Performance Encouraged AI can create differentiated practice problems for specific skills.
Quiz Preparation Learning Limited Use Generate practice problems but solve independently.
Test Review Performance Guided Use AI can identify areas needing review and generate targeted practice.
Error Analysis Learning Initially Prohibited Find errors manually first, then use AI for verification.
Worked Examples Learning Limited Use Create own worked examples before using AI for verification.
Self-Assessment Performance Allowed with Guidelines Use AI to identify knowledge gaps and create study plans.

Study Skills & Support

Task/Activity Primary Goal AI Role Rationale & Recommendations
Note Organization Performance Allowed AI can help structure notes after manual creation.
Concept Mapping Learning Initially Prohibited Create concept connections independently before AI enhancement.
Formula Sheet Creation Learning Prohibited Manual creation ensures deeper understanding of formulas.
Study Guide Development Learning → Performance Phased Approach Create initial content manually, use AI for organization and enhancement.
Vocabulary Review Performance Allowed AI can help create flashcards and practice exercises.
Peer Tutoring Support Learning Limited Use Use AI to generate examples but explain concepts personally.

Implementation Guidelines

  1. Mastery Verification

    • Establish clear criteria for demonstrating mastery before allowing AI use
    • Create checkpoints for transitioning from prohibited to allowed AI use
    • Document student progress in mastering fundamental skills

  2. AI Usage Progression

    • Start with no AI for fundamental concept learning
    • Introduce AI for verification after basic mastery
    • Allow AI for complex problems only after strong foundational understanding
    • Use AI for performance enhancement only after learning goals are met

  3. Documentation Requirements

    • Students must show manual work even when using AI
    • Clear notation of when and how AI was used
    • Maintain learning logs to track progress and AI usage

  4. Ethical Considerations

    • Clear policies on appropriate AI use
    • Guidelines for citing AI assistance
    • Consequences for misuse clearly stated
    • Regular discussions about responsible AI use

  5. Assessment Strategy

    • Different AI policies for learning vs. testing situations
    • Clear communication about when AI is/isn't allowed
    • Regular assessment of both AI-assisted and non-AI skills

  6. Differentiation Approach

    • Adjust AI permissions based on individual student mastery
    • Create personalized progression plans
    • Monitor impact of AI use on learning outcomes

Remember: The goal is to use AI to enhance learning without replacing essential skill development. Regular review and adjustment of these guidelines may be necessary as both AI technology and our understanding of its educational impact evolve.