Memorize or derive?
What is the best way to learn mathematics? Is it to memorize formulas and algorithms, and remember when to apply what rule? Or maybe it is better to get to the point of each concept, make a visual aid, and let a kid derive a rule or a formula themselves? When I studied at the mathematics lyceum, we were taught not to memorize trigonometric formulas, but to understand the idea of formula derivation, so we were able to do it on the tests without any extra help. What I notice often, is that kids at secondary and high schools nowadays are given tons of rules, and formulas, but when 2-3 weeks pass after the test, they simply forget these algorithms, and their minds are already packed with new very intensive packs of mathematical information. As a result, the student gets credit, but the essence of the topic is lost. When I tutor a student, we spend some time making drawings and creating charts to understand the concept itself, then I ask them to explain it to me or imagine that they expla