The key to mastering any complex skill is to learn it in layers - only progressing to the next layer when the previous has become muscle memory.

Have you ever driven from one place to another on "autopilot"? Have you ever caught a ball without thinking? Have you ever completely forgotten if you did something routine like brush your teeth or lock the door but find you did when you checked? If I ask you what 2 + 2 is, does the answer appear in your mind instantly?

All of these are examples of doing something almost without thinking - not always using muscles, but still a kind of muscle memory. When we do the same thing enough times, we get so good at it that it no longer requires conscious effort to do.

The key to learning a new skill is to break it down into layers, learn the bottom layer, and only progress to the next layer when the previous has become muscle memory. Learning is like lasagne.

Think about learning elementary maths. First, you learn how to count, then you learn addition and subtraction, then you learn multiplication and division, and so on. These are the first few layers.

It's obvious that you can't learn how to add or subtract before you learn how to count. It's less obvious that you can't quickly and accurately add and subtract until you have memorised adding and subtracting all the pairs of numbers less than 10. For example, instinctively knowing 5 + 7 = 12, or that 2 + 4 = 6. As people become better at mental arithmetic they often develop muscle memory for this on their own, however, because it often isn't taught explicitly like multiplication tables, you'll find some children still adding on their fingers years after they were introduced to addition

Learning systems for most skills have evolved to build layers of muscle memory through repetition. We learn the alphabet off by heart, we memorise multiplication tables, and in almost every sport we drill foundational movements thousands of times until we can do them subconsciously. Trying to move to the next layer before mastering the previous, is inevitably met with slower learning and lower success.

What I've said so far might sound obvious. Everyone already knows that you need to master the basics of a field before progressing to more complex tasks. What's less obvious is that the sign of mastering a layer is when it becomes muscle memory - not when you can adequately perform tasks. Something even less obvious is the mechanism that forces us to learn this way.

It's well known that humans cannot multi-task. The caveat that's often missed is that our conscious mind can't multi-task, but we can multi-task on things that we have muscle memory for. We can have a conversation while driving, or solve 3 Rubik's cubes while juggling them. Being able to complete a lower-layer task without consciously thinking about it frees up your conscious mind to process the next layer. For example, when learning a new language, adults will initially translate foreign words to their native language while constructing sentences. This is their conscious mind attempting to both manage vocabulary and sentence construction at once which is slow and error-prone. However, over time vocabulary becomes muscle memory, meaning they understand the meaning of foreign words immediately, and the conscious mind is free to focus on constructing the right sentence.

Next time you're learning (or teaching) something, try to see the lasagne. Ask yourself what the layers are, and if you've truly mastered the previous layers. Identifying gaps in muscle memory is a high leverage way to improve your overall proficiency in the skill because it affects every layer above it.

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Here's one article which shows a different view on this:

FWIW, my experience is that I learn better going up and down the different layers, rather than exhausting and completely "automating" the lower layers before attempting to go to the advanced material on the upper layers.

Plus, some experience with something what you're learning is useful for is a great motivator and can help focus.

I guess the failure to avoid is the conclusion "I have already done this successfully once, no need to pay attention to this ever again, because I am already good at it".

Practicing it is one option, doing something related and then revisiting it later seems like even better option, because it can give you a different perspective.

By the way, in the linked article, I can confirm that this little known thing is true for most teachers. It may sound weird if you had good math education, but that is an exception, not the rule:

the people who teach in elementary schools are not mathematicians. Most of them are math-phobic, just like most people in the larger culture.

I wish that instead of giving up on math, we could find a way to teach the teachers. Technically it should not be difficult (we only need to teach them the elementary school math, but in a way they will understand), the main problem would probably be admitting that "teachning elementary school math to elementary school math teachers" is a thing that needs to be done (to avoid the situation where the teachers are ashamed to participate, because that would mean admitting that they actually suck at their jobs). Perhaps redesigning the math curriculum, and then teaching math to math teachers under the pretense that we are "preparing them for the new curriculum" could be a solution.

I can confirm that my maths teachers at primary school were terrible: if you stepped a little bit outside what's in the book, they were absolutely lost.

They were a lot better in secondary school, possibly because they had a much stronger mathematical education (secondary school teachers usually have a university degree in the subject they teach or in a closely related field, at least in my country).

I also absolutely agree with what you say about overconfidence and the need to revisit a subject / layer instead of thinking "it's over for good".