A test score is just one data point. True mathematical understanding is deeper. Here's how to assess it.

1. The Power of Explanation: Can the student explain a concept in their own words, simply and clearly?

2. The Ability to Create: Can they create their own example problem for a given concept? This is a high-level skill.

3. The Flexibility of Method: Can they solve the same problem in multiple different ways (e.g., graphing and substitution)?

4. The Art of Error Analysis: When they make a mistake, can they find it, identify the flawed thinking, and explain why it was wrong?

5. The Skill of Connection: Can they explain how the current topic connects to previous topics?

6. The Resilience to Struggle: Do they give up immediately when faced with a novel problem, or do they have the persistence to try different strategies?

7. The Confidence to Question: Do they ask deep, probing 'why' questions, or just 'how do I get the answer?' questions?

These indicators are far more telling than a multiple-choice test score.

True understanding is not about having a memorized set of procedures; it's about having a flexible, interconnected web of knowledge.