The difference between memorizing and understanding: Don't fall into the trap of hoarding!

Let us try to establish a definition f conservation versus understanding:

Preservation means "cloning" individual states and stuffing them into the head, while understanding means "assimilating" the ideas that explain the general characteristics and the orderly relationships of those individual states and all that resemble them. When someone advises you to "learn the basics", that's exactly what they want to say to you.

But learning the basics of any science will not happen before first learning the "terms" used in it.

Although this point is intuitive, it is frighteningly overlooked. It is well known that the same word may mean completely different meanings according to the science in which it is used. Ignorance in the correct sense of the term in the context of the science you are studying means that you will never understand it, which means that you will automatically resort to memorization. It is assumed that the main job of a teacher is to do exactly this, otherwise there is no point in his presence at all.

For example, mathematics. The failure to elaborate on mathematical terms and ideas is the reason why mathematical theories are treated as literary texts for conservation. It is the reason why people view math as the automatic application of boring, meaningless operations. He is the reason for the arrival of the phenomenon of "memorizing solutions to problems by numbers" for the university stage, and perhaps beyond.

If you studied mathematics at the undergraduate level, you most likely encountered terms like Field, Vector Space, Line integral, Linear Transformation, Eigenvalue ... etc.

What do we mean by any of this?

Let alone undergraduate. If you've completed middle school education, you've definitely heard of "mathematical functions". What is meant by the term "function"? Ok, as for "operations of addition and subtraction", what does the word "process" mean?

You can generalize this example to all other sciences. If you find that you can answer questions that "seem" intuitive like the questions above, this means that you have already reached the stage of understanding and mastering the basics, but if you find that all that you carry in your head is a "method of application" that you do automatically, then this means that you have not learned It should also be after.

Fortunately, there is a way that you can learn the answers to questions of this kind.

The matter is very simple: if you encounter any term that you do not know what it means - regardless of the specialty - read about it on Wikipedia, the English version in particular. Of course, for every science you will find specialized sites for this matter (in mathematics, for example), but I always make the starting point Wikipedia.

For me, if I were asked the name of my mentor to whom I owe most of what I learned about anything, my answer would be Wikipedia.