alt Hacker NewsWe 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.
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> We teach math this way. Addition and subtraction. Then multiplication. Then division
The first graders in my neighbourhood school are currently leaning about probability. While they did cover addition earlier in the year, they have not yet delved into topics like multiplication, fractions, or anything of that sort. What you suggest is how things were back in my day, to be fair, but it is no longer the case.
We teach math starting with basic arithmetic, starting from the middle. We don't go explaining what numbers are in terms of sets, we don't teach Peano arithmetic or other theories that can give logical definitions of arithmetic from the ground up.
Plus, it is literally impossible to do any kind of math without knowing arithmetic. It is very possible to build a modestly advanced career knowing no assembly language.