We teach math this way. Addition and subtraction. Then multiplication. Then division. Fractions. Once those are understood we start diversifying and teaching different techniques where these make up the building blocks, statistics, finance, algebra, etc.

It may put people off a programming career, but perhaps that is good. There are a lot of people who work in programming who don't understand the machines they use, who don't understand algorithms and data structures, they have no idea of the impact of latency, of memory use, etc. They're entire career is predicated on being able to never have to solve a problem that hasn't been solved in general terms already.