How does instruction utilizing problem-solving differ from rote memorization of math concepts and formulas?
Using an analogy for reading: one first learns to read, then reads to learn. Begin by learning the alphabet, then words, then sentence structure, then composition, then creative writing. Each aspect is built on foundations learned in previous lessons. “Rote memorization” is required in the beginning, but at some point, understanding of concepts is the mechanism by which ideas are made into printed word. Similarly, in mathematics one learns the concept of numbers, then arithmetic, then algebra, then geometry, then trigonometry, then calculus, then differential equations. Each aspect is built on foundations learned in previous lessons. Rote memorization tends to result in someone being able to solve a problem in only one way. There is often more than one way to solve a problem, or there may be more than one correct answer. Fundamentals should be “learned” rather than “memorized.” Understanding of concepts allows one to derive an equation/formula rather than recalling something stored in
