I would only teach applied math in high school, not the Applied Math curricula from most universities, but a vertical that covers things that can be made sense without depth, just breadth. I'd leave most abstractions and numeric solving for later in life or STEM students. I just feel I did so much equation solving for nothing in my student life! I remember too many times the teacher would assign the equation solving exercises 1 - 10 as homework, and only problems 11 and 12, leaving problems 13 to 20 out. Why? Well, problems are hard to teach, to grasp and to solve!
Most math is actually very easy if kept easy, even integrals only have a few rules. Don't make a student do 700 variations of integral solving. Find a practical use for it (ie find the satellite velocity and position), introduce the subject with the problem "Today we're going to find a velocity of a satellite, there's a thing called integral that helps us do that, this is why and how..." and do that problem 20 times over and over. A variety of real-world problems have very simple math to solve, like stress and strain in materials engineering, center of gravity in physics, etc. Problem-solving is the worst of all math for most kids - so do repetitive problems and teach kids to extract information from problems into formulas and equations. And, yes, do plenty of statistics which is rich in real-world use too. Having a problem-solving, math applying mind and probabilistic view of the world are the skills to have at any field!
Most math is actually very easy if kept easy, even integrals only have a few rules. Don't make a student do 700 variations of integral solving. Find a practical use for it (ie find the satellite velocity and position), introduce the subject with the problem "Today we're going to find a velocity of a satellite, there's a thing called integral that helps us do that, this is why and how..." and do that problem 20 times over and over. A variety of real-world problems have very simple math to solve, like stress and strain in materials engineering, center of gravity in physics, etc. Problem-solving is the worst of all math for most kids - so do repetitive problems and teach kids to extract information from problems into formulas and equations. And, yes, do plenty of statistics which is rich in real-world use too. Having a problem-solving, math applying mind and probabilistic view of the world are the skills to have at any field!