Regarding Asian cultures and memorization, there is a recent change that has to be pointed out. The role of memorization classically was to aid manana/contemplation after shravana/hearing-the-teaching. The stage of manana is a kind of inquiry where you raise questions and clarify them or see how the teaching applies to various situations in your life(Like learning a principle in physics and solving problems based on the principle). In the case of poetic works the inner-feeling/bhaava sinks into you allowing one to access blissful states.

However, in the modern context, this has been transformed into memorizing arcane lists/tables, on which one is graded without any further manana.