Imagine trying to drive across town and you hit every single red light. That is what algebra feels like when multiplication facts are not automatic. I mean, you will eventually reach your destination, technically, but every stop slows you down and makes you wait. And it is so frustrating. You know, the student is supposed to be solving equations, right? Simplifying expressions, isolating the variable. And instead they get stuck on factoring. What are all the factors of 48? And they're sitting there waiting at this red light before they can get back to driving through the problem again. See, that's the problem. The student is not just doing algebra. They're doing algebra while constantly having to stop to multiply numbers. And every time they do that, it takes up extra time, it divides their attention. They kind of forget what they're doing, where they're even going. And it increases the chance that they make an arithmetic mistake. That's why multiplication needs to be automatic first, so that the student can then focus their attention on the algebra road ahead. Further reading:

Cognitive/intellectual workouts are just like physical workouts. You can't expect your body or even your attitude towards exercise to transform in a single day. And it's not just about time. You gotta spend that time doing well-calibrated exercises. -- If you spend months repeatedly trying and failing to lift the heaviest weight in the gym... you don't get better. -- If you spend months repeatedly lifting the lightest weight in the gym... you don't get better. You gotta 1) start at your level and 2) incrementally layer on more difficulty as your level increases.

The joy of math is similar to the joy of exercise. You gotta earn it. Exercise gets way more fun once you notice a body transformation getting underway. It's the same way with math. But nobody feels the transformation on day one. Or day two, or even day three. You gotta stick with it for months before you really notice a difference.

If you just consume information and don’t practice retrieving it, then you forget almost entirely. This is really obvious if you think about how your brain works in daily life. Have you ever had the experience of being unable to remember something despite repeated exposures, because you keep automatically looking it up from a reference instead of trying to retrieve it from memory? That’s happened to me an embarrassing number of times with addresses, phone numbers, directions, etc. And any books you read, movies you watch – the only ones you remember in proper detail are the ones you periodically think about and replay in your head.

Often the biggest motivational hurdle is just starting the (physical or intellectual) workout. When you're not looking forward to it, you might think that negative feeling is going to intensify during your workout, but often it just dissipates and you feel great 5 minutes in. Procrastinating builds up the dread but just getting started often makes it dissipate.

Learning is a positive change in long-term memory, and long-term memory doesn’t change much when you just “follow along,” even if you understand perfectly. It’s the act of retrieving information from memory that really slows its decay. If you don’t practice retrieval, then the information quickly dissipates. It stays with you only briefly in short-term memory – just long enough to trick you into thinking it’ll stick with you for the long term, when it’s really on the way out the door. But, of course, if you don’t check that it’s there, you won’t notice that it’s gone.

The key to learning fast is reducing friction in the learning process. One of the biggest sources of friction: Not knowing the prerequisites for the thing you're trying to learn. Knowing the prereqs can make the difference between feeling like new content is being presented overwhelmingly fast vs at a comfortable pace. Another big source of friction: Not periodically reviewing things you've previously learned. If you don't review, then you forget, and if you forget prereqs, then there you are back at the first source of friction.

Retrieval practice is always vastly more effective than re-consuming information (re-reading, re-watching, transcribing, etc.). The way you make it easier to pull information out of your head is, well, by practicing pulling it out of your head.

If you want a new skill to stick: 1. Blocked retrieval practice initially, refining consecutive attempts until you can consistently execute correctly. 2. Interleaved spaced retrieval practice afterwards, ideally obtained by layering more advanced skills on top.

The #1# misconception about retrieval practice is that some people mistakenly think it slows down their learning. They experience a comfortable sense of fluency while following along with a stream of information, whereas pausing to pull that information out of their head breaks the flow, and occasionally failing the retrieval makes them feel like they’re not learning as much. But really, all that’s happening is that retrieval practice is bringing their perception of learning more in line with their actual learning. It speeds up their actual learning, slows down their perception of learning, and exposes that “following along” is not the same as learning.