It's all about building higher and higher abstractions. Arithmetic - > Algebra -> higher order algebraic algorithms. For example, when I taught differential eq

It's all about building higher and higher abstractions. Arithmetic - > Algebra -> higher order algebraic algorithms. For example, when I taught differential equations, my non-scientific observation was that otherwise smart students struggled more with getting the algorithms down, if they struggled with algebra. Having to constantly jump down to a lower level of abstraction while performing the algorithmic steps is what caused confusion to mistakes.