Learning from multiple sources
Learning from multiple sources refers to using multiple source materials while learning a subject. For instance, a student may attend lecture and later watch a YouTube video that explains the same concept at home.
- An autodidact reads from multiple textbooks
- A student reads a textbook and a blog post explaining the same concept
- A student encounters a concept in the classroom, then later asks their tutor to explain the same concept
- A college student attends lecture and later watches a YouTube video that explains the same concept
In math, learning from multiple sources can give attention to certain contingencies in the subject (e.g. notation, specific constructions, specific encodings of structures) which may have seemed like necessities. This can make the concepts themselves more robust.
Since in general two people will learn the same subject from different sources, being familiar with other notation/terminology will help with communication.
Different sources place emphasis on different parts, and overlap may not be exact (see e.g. discursiveness), so one may in general learn new things by trying multiple sources.
Some sources will suit one's background knowledge and thinking styles more than others. Finding sources that one "clicks with" will make learning easier.
Importance of struggling in learning discusses one possible downside to finding explanations that are "too easy".
Varying the format
It is possible to learn from multiple sources by sticking with one format (e.g. reading multiple textbooks), but it is also possible to vary the format (e.g. read a section in a textbook and then watch a video about the topic).
Varying the format can address certain blind-spots of any given format. For example, many textbooks have a huge amount of material, not all of which can be covered in a single-semester course. In such a case, the textbook may not give enough information to prioritize which sections/chapters to cover. Watching video lectures or looking at a course outline/syllabus can give information on which parts of the textbook are actually essential to cover.
Compared to written material, video lectures give a more realistic pacing of the material (e.g. a textbook might just skip a long calculation and then say "as the reader can verify", with no indication of how long the verification should take, whereas a lecturer would have a more difficult time skipping the long calculation without explanation).
Lectures can also give a better indication of what one is expected to know (e.g. if a lecturer says "you don't need to know this" or "I always have to look this up", that gives an indication of something one does not need to memorize/understand as deeply). Theoretically a textbook can also do this, but it seems much less common for some reason.
On the other hand, a textbook is usually written in a much more organized way/with more of the formalities included, which helps if one wants to deeply understand something.
For subjects that have been around for a long time and are learned by many people, there will be many different explanations available (e.g. many books on calculus).
For less popular subjects, there will sometimes be one or two dominant/obvious choices.
For new or obscure topics, there may only be a single explanation (e.g. the original paper announcing the discovery).
From Peter Smith's Teach Yourself Logic guide: "I very strongly recommend tackling an area of logic by reading a series of books which overlap in level (with the next one covering some of the same ground and then pushing on from the previous one), rather than trying to proceed by big leaps."