1. Read (Passive Exposure)

Reading alone produces the illusion of learning. You can finish a chapter and remember nothing. To turn reading into active studying, you have to pause and be intentional throughout your time reading. At every section header, pause and write a short summary in the margin or on a brace { } alongside the paragraph. Write one to three sentences that capture what changed between the headings. Those tiny pauses convert reading into real encoding.

2. Highlight (Vocabulary Only)

Highlighting is almost never worth the time. It feels productive but rarely is. The only legitimate use is for vocabulary. You highlight terms that can later be defined in your own words. Once highlighted, go back and create a micro-glossary: for each term, write a one-sentence personal definition or analogy. If you can’t restate it, you don’t know it.

3. Rewrite (Transformative Output)

Rewriting is where studying turns kinetic. Translating information into your own language activates selection, organization, and synthesis. These are the three engines of cognition. The key is to rewrite differently each time:

• Calligraphy notes: Turn rewriting into art. Beautiful notes slow you down just enough to process meaning and design structure.
• Brace summaries: Use the { } margin method to condense long explanations into quick recaps.
• Write a letter to an expert: Imagine emailing a mathematician or scientist. How would you summarize what you’ve learned and what you’re still unsure about?
• ChatGPT dialogue: Treat an AI as a study partner. Ask, “Here’s what I think about quadratic transformations—what might I be missing?” Then correct and expand together.
• KWL reflection: Write what you Know, what you Want to know, and what you Learned—then walk through it conversationally with an AI or classmate.

4. Summarize (Compress Information for Clarity)

Summarizing forces you to decide what matters. Unlike rewriting, which is expressive, summarizing is reductive. It’s the intellectual act of compression. Try these strategies:

• One-minute papers: Write a 60-second summary after every topic explaining what changed in your understanding.
• Concept maps: Visualize connections between definitions and examples—especially effective in math and sciences.
• Analogy method: Finish this sentence: “This topic is like ___ because ___.” The analogy reveals whether the core concept clicked.
• Teach-back slides: Create 3-5 simple slides explaining the idea to an imaginary audience or a parent. If you can create a script for the slides, you understand the logic chain.

5. Apply (From Knowing to Doing)

Application is where learning proves itself. In math, this usually means working problems, but it can extend to definition-building, proofs, or even digital simulations. Application bridges theory to usage.

With today’s tools, you can scaffold application across levels:

• Low-level application: Prompt an AI to role-play an expert. Ask it to explain your topic back to you, or debate your explanation. This builds diagnostic awareness.
• Mid-level application: Have an AI generate custom concept questions or word problems, then answer and justify your reasoning.
• High-level application: Design your own practice set or mini-lesson for peers. When you can build assessment, you’ve crossed into mastery.

6. Explain (The Final Transformation)

Explaining is the summit of learning. It demands retrieval, sequencing, and contextual awareness. When you can teach it, accurately and simply, you’ve achieved integration. Here’s how to refine that skill:

• Verbal rehearsal: Explain a topic out loud while recording yourself. Listen back and note weak spots or skipped logic.
• Whiteboard teaching: Physically stand and walk through examples as if presenting to a class. Movement solidifies sequence.
• Peer or AI interviews: Have someone (or ChatGPT) quiz you unpredictably. True understanding is flexible under pressure.
• Two-minute challenge: Set a timer and explain the entire topic in under 120 seconds, using zero notes. Brevity exposes gaps and forces synthesis.