If mathematics class only ever asked you to do things you already knew how to do, it would be a photocopying service. The learning happens in the stretch — standing at a whiteboard with your random group, holding a Ferris wheel problem none of you can model yet. But not all struggle is equal. Stuck-and-thinking means you still have a next move to try: test a number, sketch the graph, shrink the problem to one period. Spinning means repeating the last move harder and hoping. The first builds mathematicians; the second just builds frustration — and telling them apart from the inside is a skill this course teaches on purpose, with Getting Unstuck as its field guide.
Questions worth arguing about:
- Recall a problem that finally gave in after real struggle. What did the moment of giving-in feel like — and would being handed the answer have produced anything like it?
- What are your personal tells that you have slipped from stuck-and-thinking into spinning? Who should notice first: you, your group, or your teacher?
- Why does this class put you in random groups at vertical whiteboards? What do standing up and a shared marker do to struggle that a worksheet at a desk does not?
- The group beside yours is stuck on a problem you have cracked. When does helping them actually take something from them — and what does good help look like instead?
- Where is the line between productive struggle and genuinely being out of your depth? Is admitting the second a failure, or a move?
This is why every practice set here folds its answers away and why nothing is ever timed: the callouts protect your struggle from your own curiosity. Attempt first, peek second — the order is the whole point.