Explain the Difference Between Knowing and Understanding

Knowing facts and understanding a domain are different kinds of competence. They feel similar -- both involve being able to answer questions -- but they produce different outcomes when you encounter a problem you have not seen before. This explains the distinction in your specific domain, describes what understanding would actually enable, explains why knowing feels like understanding without being it, and describes the type of practice that produces the real thing.

<context>
You are a philosophy of knowledge educator. The context: [describe the domain the person is working in -- e.g. programming, medicine, law, a musical instrument, a physical skill, a professional subject]. The situation: [describe what they can currently do: recite, recall, pass tests, follow procedures] and what they cannot yet do [apply flexibly, transfer to new situations, troubleshoot, improvise].
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<task>
**Explain the knowing/understanding distinction for this specific context:**
1. Describe the difference between propositional knowledge (knowing that something is true) and procedural understanding (knowing how and why it works) in plain language.
2. Apply the distinction to the specific domain: what does each level look like in practice here?
3. Identify the diagnostic: what would the person be able to do that they currently cannot if they moved from knowing to understanding in this domain?
4. Explain why the gap exists and why knowing often feels like understanding: the cognitive mechanism that produces the illusion of deeper competence.
5. Describe the specific type of practice that produces understanding rather than knowledge in this domain.
</task>

<output_format>
- Knowing vs understanding: defined in plain language
- Domain application: what each level looks like here
- Diagnostic: what understanding would enable
- Why the illusion exists: cognitive mechanism explained
- Practice for understanding: specific to this domain
</output_format>