Memorizing vs. Rote Learning & Drilling
Ideas of Michael Paul Goldenberg
Ann Arbor, MI, United States
I know of no one who opposes memorization (which by the way is NOT the same as rote learning.)
MINDLESS rote learning of things that can be learned effectively, possibly MUCH more effectively, in other ways needs to be stopped.
Mneomonic methods are, however, extremely easy to understand and put into practical use for a wide range of applications. These methods pay off in inverse proportion to the arbitrariness of the material being memorized. It means is that when faced with , say, a random or arbitrary list of items, dates, facts, etc., the more random the list and therefore the less conceptual links or "common knowledge" might be involved, the more a person using mnemonics would gain from using these techniques. Because otherwise the main option would be some variation on pure rote.
However, less time was needed for memorizing information with more structure, because the "inherent logic" or interconnectedness of the information helped one memorize.
Mathematics already is based on logical and conceptual links. Hence, it is often the case that what needs to be "memorized" in the sense mentioned above is minimal.
What sorts of things would need to be memorized in mathematics? Well, things like Order of Operations, which consists of conventions, not something that simply HAS to be. Terminology. Notation. Axioms. Things that do not follow from first precepts.
Even going beyond that, it is undoubtedly true that we need to "memorize" certain fundamental relationships and identities in specific areas of mathematics in order to not have to tediously look them up for every single instance in which they arise. In trigonometry, for example, understanding the definition of sine, cosine, and tangent in right triangle trigonometry is a key "fact" that one does much better to have at one's mental fingertips than not.
The amount that "must" be memorized is often far smaller than one originally believes, because of underlying relationships and concepts that create natural connections among a smaller set of facts. Anyone who is led to believe that entire chapters of a mathematics book and solutions of all problems need to be memorized by drill or rote is being mistaught.
That which is understood conceptually has a better chance of lasting, and can be more readily recreated through the concepts even if the "at one's fingertips" recall has been weakened or extinguished. Most people are well aware of this through personal experience.