Technique explanation
Teaching Explanation
The highest level of understanding is the ability to teach a concept clearly to another person. A complete mathematical explanation requires four essential components: the Conditions (when the method is appropriate), the Steps (the logical sequence of operations), the Example (a concrete application), and the Check (a method for verification). By organizing a strategy into these four parts, a learner moves from simply performing a calculation to understanding the underlying mathematical structure. This process builds confidence and ensures that the learner can communicate their reasoning to others.
Method Condition
Any method covered within the course.
Standard Fallback
Standard mathematical notation and prose.
Misconception: Thinking an explanation is just providing the final answer.
Correction: An explanation is a map of the reasoning process. The steps and the "why" are more important than the "what."
Worked examples
| Step | Example 1 | Example 2 |
|---|---|---|
| 1. Condition | Two-digit number multiplied by 11. | Any addition or multiplication. |
| 2. Steps | Split digits, add them, place sum in middle. | Compare sum of inputs to sum of result. |
| 3. Example | $35 \times 11 \rightarrow 3 (3+5) 5 = 385$. | $12 \times 13 = 156 \rightarrow 3 \times 4 = 12 \rightarrow 3$. Result $1+5+6=12 \rightarrow 3$. |
| 4. Check | $35 \times 10 + 35 = 385$. | $12 \times 13 = 156$ (long multiplication). |
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