math-intuition-builder

# Math Intuition Builder ## When to Use Trigger on phrases like: - "help me understand" - "build intuition for" - "what does this mean geometrically" - "why does this work" - "visualize this concept" - "concrete example of" - "what's the intuition behind" Use before computation to establish understanding (Polya's "understand the problem" phase). ## Process Guide through Mason's specializing-generalizing cycle: ### 1. Restate in own words **Ask:** "Can you state the problem in your own words?" - Forces re-processing - Catches misunderstandings early - Verifies shared understanding ### 2. Try concrete examples **Ask:** "What would a concrete example look like?" - Specialize: try N=3, x=2, simple case - Ground abstract concepts in specifics - Use computation tools to verify examples ### 3. Anticipate the answer **Ask:** "What form should the answer take?" - Work backwards from expected result - Constrain solution space - Check dimensional consistency ### 4. Visualize **Ask:** "Can you draw a picture or diagram?" - Multiple representations matter - Algebraic <-> geometric <-> numeric - ASCII diagrams for quick sketches ### 5. Simplify **Ask:** "What's a simpler version of this problem?" - Reduce dimension - Remove terms - Special cases reveal structure ### 6. Find analogies **Ask:** "Does this remind you of anything you've solved before?" - Pattern matching across domains - Transfer solution strategies ## Key Quest...