When we learn some new subject, I believe, there are always some common properties of learning, regardless the field of the subject. Here I'll try to consider some of them to summarize the process of learning itself, using some notions from system thinking as it is greatly unites knoweldge about systems and their interactions, and of course the subject to learn is also a system. And I'll be very abstract.
So, if we want to learn the subject we may want to be aware of the following:
- The definition of the subject. It is required not only to recognize the subject, but also to recognize something, which is not a subject, to know its 'borders' and distinctive properties and features. It is also useful to know the conditions for the subject to exist (if approriate).
- Which parts constitute the subject? Sure enough every part can be quite complex, i.e. a standalone subject to learn.
- How these parts interact and relate to each other?
- How the subject interacts with other subjects, which primarily are out of scope of the study?
- What are inputs and outputs for the subject and all of its parts?
- What kind of information and materials are transferred through those inputs and outputs?
Why these are important? Because if we are really serious about learning, we can not learn only one part and ignore the others (like learning speaking without learning grammar). It is not only incomplete, but can also leads to incorrect understanding of the subject, because the subject is a system, and by throwing away some part, we are modifying this system (keep in mind system emergence feature). Sometimes it makes us unable to communicate with other people (without knowing some 'auxiliary' definitions from other fields it is generally impossible to write a proper mathematical statement).
Some examples:
1. Language learning.
Definition: usually there is no definition, but it is good to understand how the language relates to other languages, what are differences and similarities. This is usually given in most textbooks and is intuitively learned during the process.
Parts: grammar, phonetics, vocabulary, morphology, speaking, listening, writing.
Interactions: quite straightforward and common for most languages.
Other subjects (possible variant): history of language, history & geography & culture of a country. Of course it is not required to know all of these to the full extend, but at least knowing some key events and ideas is useful (and not only from the language learning point of view!).
Inputs and outputs (just a few): ears, mouth, books, video, songs, radio, talks.
Information and materials: meanings, sounds, sound waves.
2. Learning some mathematical subject (like probability or functional analysis).
Definition: should give a general picture on what kind of problems are considered by the field and by what means.
Parts: definitions, properties, theorems, proofs, rules, algorithms, exercises, open problems, applications.
Interactions: logical connections between different parts. Very crucial to understand the subject.
Other subjects: history of the subject, main contributors and their results, prerequisites, subjects that can be learned using knowledge from learning the current subject.
Inputs and outputs (just a few): timetable, locations, Internet, eyes, ears.
Information and materials: ideas, properties, specific skills (like integration), books, videos, publications, lecture notes.
3. Learning musical theory.
Definition: to know what for musical theory gives and what happens if we don't study it?
Parts: notes, intervals, chords, harmony, styles.
Interactions: straightforward.
Other subjects: history of musical theory, playing a particular instrument, musical software.
Inputs and outputs (just a few): books, Internet, ears.
Information and materials: sounds, compositions, songs.
How can we use the information like this? If we want to learn something we should attack the subject from all the possible directions, because the parts of the subject are not independent, they overlap significantly. Thus we can generate synergistic effect, but to do this we first should know the options, otherwise it will be random and less effective. The other important thing is that learning requires memorizing and by looking at different things from various angles (like reading, listening, writing, practising) we intrinsincally repeat them.
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