Homework 5: Understanding Something Deeply

Due Monday, November 23, 2026 at 11:59 PM EST.

Think of some time you really understood something very deeply. Not just that you knew how to solve a problem no matter what numbers or variations on the original problem were thrown at you, but that you really, really understood something—and it made you feel good inside.

In Homework 4, you reflected on your learning and spent time exploring a gap in your understanding. Now I’d like you to take some part of your presentation and work toward that feeling of deep understanding.

Choose something small enough that you can explain it carefully to the class. You can use the blackboard, your notebook, or both. Be ready to explain it multiple times, perhaps in different ways, as questions reveal what others need to understand. This will be the basis for your end-of-semester presentation: 10–12 minutes, with additional time for questions.

For this homework:

• Write down what you will explain deeply. Be specific about the idea and what you want your classmates to understand.
• Make a start. Give an initial explanation, worked example, sketch, or calculation. Identify where your own understanding still needs work.
• Use questions to push yourself. You might ask an AI to quiz you one question at a time, following the suggestion in Homework 4. Look for questions that expose gaps or help you see the idea differently.

You do not need a finished presentation yet. Show us what you have chosen and a serious beginning toward understanding it deeply.