Here’s what I said in a discussion about it elsewhere.

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These things are all about (1) experience piling on experience, through deliberate practice, and (2) having the right mindset to approach learning and problem solving. Every “I’m just bad at math” student I tried to tutor in high school algebra was entirely capable of understanding the concepts, when forced to focus by 1-on-1 help and when provided with some slight bits of guidance. Most of their inability to do the work was psychological blocks, reinforced over time by a destructive self-vision and -message. I.e. repeat enough times “some people just can’t do math, and I’m one of them”, and, little surprise, the prophecy fulfills itself.

In my firm opinion, the best to approach complex abstract systems is by building a thorough and cohesive mental model of how they work. To add a new concept or abstraction into the existing model requires testing the new part against all the existing parts in many combinations to see how they fit together, to think about how they might be used with each-other, to find out where the mismatches are or where prior understandings were faulty... But the learner must start with a thorough and cohesive model before it’s possible to fit anything new into it. So this is a process which takes years, and can’t be magic-wanded later.

Unfortunately, it is extremely hard to convince a classroom of students to adopt the right mindset and then focus serious amounts of attention for long periods of time on learning, if they haven’t figured it out already. And it’s easy for external factors – stress, sleep deprivation, distractions – to throw things off. So instead, many teachers try to teach atomized and easier-to-test chunks of “plug-and-chug” type material. This is in the long term entirely destructive, because without something to attach it to, students forget what they learned last time, and must start from scratch on each new formula or method. Instead of understanding the meanings of what they’re doing, or having any clear motivation (other than “if you fail the test you’ll spend your life serving fast food”), students are left with only a mechanical process to copy. I think of the relationship between this and real mathematics as something like the relationship between candyland and chess, or between filling in a color-by-numbers picture and learning to paint.

The ones who for whatever reason are slightly better at copying the mechanical processes (in whatever subject) are praised, feel bits of accomplishment, and are willing to devote a bit more time. Some of them even start to piece together more comprehensive models on their own, or play with the parts a bit for fun, and are promoted through this work into the ranks of the mathematically literate. The ones who start out really stuck, who have difficulties performing the mechanical processes, don’t see the point, and don’t receive any further help, just start to adopt a defeatist view of the whole thing. They aren’t willing to spend time on something so unrewarding and painful. They start to doubt their basic competence. Avoidance becomes a more and more attractive alternative to effort.

The idea that there are a sizable proportion of people just innately incapable of abstract thought is complete nonsense. Some people have obvious severe mental handicaps (down syndrome or similar), but everyone else is plenty capable of learning high school algebra.