Characteristics of Good Explanations in Mathematics

1. The explanation is factually correct, or nearly so, with only minor flaws (for example, a minor mistake in a calculation).

2. The explanation addresses the specific question or problem that was posed. It is focused, detailed, and precise. There are no irrelevant of distracting points.

3. The explanation is clear, convincing, and logical. A clear and convincing explanation is characterized by the following:
1. The explanation could be used to teach another (college) student, possibly even one who is not in the class.
2. The explanation could be used to convince a skeptic.
3. The explanation does not require the reader to make a leap of faith.
4. Key points are emphasized.
5. If applicable, supporting pictures, diagrams, and equations are used appropriately and as needed.
6. The explanation is coherent.
7. Clear, complete sentences are used.