Most of school mathematics can be represented visually. Abstraction serves its purpose in making the mathematical language more efficient, but it is futile to jump straight there until you have played with concepts in their visual form (for an extreme example of this, see New Math).

A Harvard math major once told me they didn’t realise that the quadratic formula was simply the generalised form of completing the square. Here we have a supposedly educated, high-flying mathematician who abstracted away, solving all manner of equations, without taking pause to understand the underlying procedures. Visualisation would have helped!