Practice Explanation vs Derivation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The distinction between explaining WHY a result is true (conceptual insight) and showing HOW it can be derived step by step (procedural derivation).
Derivation: here are the steps. Explanation: here's why it makes sense.
Example 1
easyDerive the quadratic formula from ax^2+bx+c=0, then give an explanation of what the formula tells us conceptually.
Example 2
mediumThe sum formula \sum_{k=1}^{n}k = \frac{n(n+1)}{2} can be derived by induction or explained by Gauss's pairing argument. Give both.
Example 3
easyYou know that (a+b)^2 = a^2+2ab+b^2. Give an explanation (not just algebraic expansion) of why the cross-term 2ab appears.
Example 4
mediumState the difference between a derivation and an explanation in mathematics, then give one example of each for the statement e^{i\pi}+1=0.