There are many steps to acquiring any new skill. Not only do you have to learn how and why to do it, but then you have to practice to actually gain proficiency. Let’s look at these steps through the lenses of school, self-studied math, and tennis since I know each fairly well and it’s helpful to have a few different angles of attack in these kinds of demonstrations.
The first step I’ll call “learning”. This is what happens during a lecture, or while reading a book. It’s a direct transfer of knowledge from one party to another. In school, it’s the teacher providing instruction. In math this is reading through the definitions in a chapter, and learning what new terms mean. In tennis, it’s understanding what a volley is, or what shape the stroke takes to generate more topspin.
After learning is practice, which everybody has a pretty good feel for. You’re working on something, often repetitively, and filtering out mistakes. In school this is homework with a variety of problems on the same subject. In math, it’s doing the exercises or maybe coming up with a few interesting proofs of the theorems you’ve learned. In tennis, it’s changing your serve technique slightly every point and trying to find what works best for you.
There’s a level beyond these two which I think is relatively overlooked. Call it “training”. This happens once you know what a skill is, you’ve filtered out most major mistakes, and now you want to increase efficiency or effectiveness in some way. In school, this could be looking over your previous homework and notes to find connections between subjects that make them stick better in your mind. In math, training looks like not just discovering proofs in the first place, but finding ways to improve them and set them all into a broader framework. In tennis, it’s the most intuitive of all, where you’re hitting shots you know how to hit, or putting yourself in scenarios you know how to handle, and making sure you handle them as best you can.
If learning is creating a scratch in your previous mental models, then practice is adjusting the position of the scratch so it lines up correctly, and training is deepening it into a nice groove where your related knowledge is applied automatically. I may have chosen my terms confusingly, because “deliberate practice” is really a form of training, whereas usual practice is about figuring out the extent of the boundaries to a skill in the first place.
The learning step can be almost superficial if the practice is performed well. For example, reading a mathematical definition provides almost no value for long-term memory unless you’re practicing with it. You can practice by imitating others, seeing how they solve various examples. It’s a little striking that we tend to reserve the term “training” for physical activities though, since true learning comes from deep understanding. The deeper you can train the grooves in your mind to be, the easier it is to recall and correctly perform a skill in the future.
Training might come in the form of finding another perspective that tackles the same subject. If there are three textbooks about a subject, two of which agree strongly, you’ll likely get the most value from selecting one of the agreeing books and the disagreeing book, versus selecting both agreeing books.
It might be true that learning by repetition is the only sort of true learning that exists. Repeated exposure may be a prerequisite for deep understanding. If so, it makes sense not just to practice until you start getting things right, but to train until you’re surprised when you get things wrong.