Paraphrasing is particularly useful for finding out whether you understood the other person correctly. For example, if a person says "I'm a cellular biologist.", you could paraphrase that as "You currently work in cellular biology. Right?"
Exercise:
Paraphrasing is useful because it forces you to check the parts of the concept (elements and their relations) you are about to explain. While just giving something back word-by-word could hide the lack of understanding, if you understand the concept, you should be able to give back the details in a different order/point of view. If you understood the main parts, and how they are connected, you can give a different explanation (changing the order/showing different sides, replace parts etc), while also retaining the meaning of the content. While trying to do this, you have to make sure all details are connected properly (and are actually observed, as a lot of them may be be assumed to be known implicitly), otherwise you will not be able to follow through with the exercise.
A good analogy could be building a lego object: if I show you how to do it, and then you have to assemble it again from scratch, you should be able to succeed in this while starting at a different part and adding the blocks in a different order than I did. This requires a much better understanding than just copying the very moves I made in the same order.
Example: I explain to you, how to make an omelette (heat up pan, put on oil to avoid the eggs sticking to it, pour scrambled eggs into the pan, use the spatula to optimize form/density, add grated cheese then fold the sides on top). To paraphrase the process back to me, you should understand how the steps are connected, so even if your circumstances are different, you can replace/move around object to fulfill the meaning: the point is to scramble and fry eggs on an open surface without burning them.* If you do not have a pan, a pot may suffice, you can use butter instead of oil, and so on.
*a valid point could be made that omelette is more than that, please excuse the simplification I made for demonstration.
Paraphrasing is good because you can express the same thought in multiple ways in natural language. Repeating the words is something a tape recorder can do, paraphrasing means going WORDS -> MEANING -> WORDS, so, if the last step is correct, the middle one is likely to be correct too. For example F = ma -> reality of motion -> so you say ohh like when you slide a lot on ice on rollers because there is so little friction (force)
Architects. Teachers. Teachers of teachers, but the art of teaching teaching is much the same as the art of teaching. Three levels is enough. Though the levels have to mix. The teacher who trains the next architect must be a master both of teaching and of architecture.
Paraphrased for my own purposes:
Tutors. Tutees. Tutors tutor tutees, but the art of being taught is much the same as the art of teaching. The levels have to mix. The tutor who tutors the tutee must be a master both of teaching and of learning.
Much has been written about the Feynman Technique as a method of learning that involves teaching. The main problem with the Feynman technique is that it takes too much time to ever actually execute in practice. Instead, I will describe two TAPs that are my 80/20 for both learning and teaching.
Trigger: Notice you made a claim with some amount of vagueness.
Action: Start saying "For example, ..."
For example (see what I'm doing), I might say "regular exercise is good for you" and notice that "regular" and "good" are words with multiple possible interpretations, so I would follow it up with "For example, walking for 10 minutes a day makes you happier". Another example: I might say "functions map inputs to outputs, for example, the square function takes numbers and maps them to the square of that number, e.g. it would take 2 to 4, 3 to 9, etc." Notice that sometimes your example itself can have some vagueness, so the TAP fires recursively. This is the key TAP for teaching.
There is also a dual TAP for learning; trigger: notice someone else made a claim with some amount of vagueness, action: say "for example?". For example, someone might tell me that they "dislike mundane activities", to which I would say "for example?" They then might tell me that "scheduling Facebook events" is a mundane activity, giving me a much better understanding of what they had in mind when they said "mundane". This TAP is especially helpful because your interlocutor is likely to give you a particularly representative example. For example (this TAP is strong), if I asked for an example of a bird, the person I'm asking is much more likely to say "robin" than "penguin".
Asking for examples is extremely powerful because it encourages specificity. It is much easier to reason about The Feynman Lectures on Physics than the abstract concept of a textbook/book/information. The first sample gives the most information, so be sure to ask for it.
It is much easier to notice vagueness in others than vagueness in yourself. For example, it's much easier to realize that "people deserve a right to life" isn't concrete if someone else says it to you. Use this to your advantage by practicing initially by asking other people for examples. For example, I went through a week or so where "for example?" was my favorite thing to say. My friends would tell me things like "I hate it when teachers assume they know you learn" and my immediate response would always be "for example?", to which they would respond "like when they force you to go to lecture". Sometimes they would be unable to come up with an example; this was not always because they didn't know what they were saying (people often have poor memories), but it does suggest that the claim might be a bit too vague. For example, I there are many organelles in a cell, but I cannot come up with any examples because I remember almost nothing from high school biology.
After one has asked for many examples, one starts to develop a sense of when asking for an example is going to be useful. For example, if someone says "fruit is tasty", I'm not going to ask them for an example, but if they say "some fruits are genetically engineered and thus bad for you", I'm probably going to say "for example?" The point of practicing by asking other people for examples is not to get good at noticing vagueness in others, but rather to improve your ability to notice vagueness in general. After a while, you might begin noticing a curious temptation to say "for example" after you say something. For example, when I explain why I think people should buy more things, I feel a compulsion to give examples like a specialized water boiler.
Trigger: someone explains something to you.
Action: Start saying "so what your saying is"
For example, if someone explains to me a model of muscle memory, I might say something like "so what your saying is that when your brain sends signals to your muscles, it doesn't quite say 'move muscle 1 this way and muscle 2 that way', it says something closer to 'do the walking thing', which then gets interpreted into muscle movements based on history and maybe some other stuff. This means that if you've been doing a particular motion wrong your whole life, you're going to continue doing it wrong by default, e.g. like sitting with bad posture. The point of physical therapy is to say to your muscles 'THIS IS HOW YOU DO THE WALKING THING' over and over again, so that the next time your brain sends the 'walk' signal, you do the walking thing correctly." This generally happens in conversation and is extremely useful, but in the limit, this looks like reading What does the universal prior actually look like? and writing The Solomonoff Prior is Malign. This is the key TAP for learning.
The dual TAP for teaching is noticing yourself explaining something to someone and starting to say "another way of looking/thinking at/about this is...". For example, I might be explaining how computer programming works as "writing a set of instructions that can be executed mechanically" and follow with "another way of thinking about this is that you have a large set of personal assistants that have no initiative and take everything you say as literally as possible. Computer programming is the art of getting those assistants to do useful things." This is very similar to providing extended examples.
Paraphrasing is very powerful because it checks understanding. If you understand what someone means when they describe their model of reality, you should be able to paraphrase it back at them in a way that they agree with. For example, if my friend tells me about options, I should be able to describe what options are back at them. Paraphrasing gets especially powerful when combined with the previous TAP, which strengthens your paraphrasing by including examples. Eli Tyre once told me that "the best way to know you've understood something someone is trying to explain to you is if you can give an example that better demonstrates their point than they did." For instance, I was telling my friend about how I think doing distracting things might permanently decrease your ability to focus and they responded with "like if you watch a bunch of Youtube videos, your brain gets cluttered with that content, which means that you are less able to focus and more likely to watch Youtube videos". This was a better example than the one I previously had, which was getting distracted by instant messenger, and so I was grateful.
It is easier to practice paraphrasing on your own explanations than it is to practice on others. When you're trying to explain something, in theory, you already have a pretty good understanding of the thing. Leverage this understanding to paraphrase yourself. For example, if I'm explaining differentiation, I might use my understanding of differentiation to paraphrase differentiation in terms of position and velocity. Since you are the one doing the explaining, it should be much easier to notice that you're speaking with the intent of conveying knowledge and start saying "another way of thinking about this is..."
After one has paraphrased your own understanding many times, you develop better the ability to put understanding into words. For example, often times when I'm writing blog posts, I begin by explaining the concept to one of my friends. After I explain many times, the good parts of the explanation stick around and the bad parts get lost in the shuffle. When the entire process is complete, I am left with a concise and compelling explanation (at least in theory). After you get a better sense of what it feels like to give a good paraphrasing, it becomes much easier to paraphrase something someone else is trying to explain to you.
Pick three things, like fruits, furniture, or sports, and give three examples of those things, like apples, chairs, and baseball
In the comments, paraphrase my explanation of why paraphrasing is useful for improving and checking understanding. Be sure to include examples.