Conrad Wolfram's 4 steps (not really original with him) highlights the problems with maths education. Understanding the problem, translating the problem into maths, doing the computation, and verifying the result in the real world is a good rubric for what most people needs maths for. Traditional education has been tied up with computation, since that was an obvious 'hard part', and one that has been revolutionized by technology. Using technology has to be done correctly, though, or people just go through a different series of "magic" steps to solve problems, with the related issues of platform (HP calculators vs TI, Mathematica vs MatLab, c vs Python, etc.). There is also the issue of what learners need to be able to do by hand. Traditionalists (e.g. "maths was painful for me, it should be painful for everyone) may see n reason to change, but I think that there are reasonable things that a student should be able to do with some facility -- standard multiplication tables, differentiating and integrating polynomials, etc. This question may best be solved by what maths is going to be used for. Engineers have different needs from economists.
The real problem is that maths has been taught almost entirely divorced from reality. People do not realize that a problem they have in the real world has any relationship to maths at all, or that they are 'doing maths' without realizing it. The insurmountable barrier to making maths relevant is not that the computation bit is (often) presented in a mindless, dull manner. The barrier is step one of Conrad's four steps.
If there is any rational for "two tracks", it is to distinguish between people who are to become professional mathematicians, and those (a vastly larger number) who need to use maths for their work -- physics, biology, finance, engineering, etc. As an example, a lot of people need to be able to solve and use differential equations in their work. For these people, being able to recognize that their problem is amenable to diff Eq, being able to set up the problem in maths, using Mathematica to solve the problem is sufficient. For a mathematician interested in differential equations (for their own sake), then being able to create the algorithms Mathematica uses may be necessary. There are other examples from pure maths that are of use (always a dangerous word) primarily to mathematicians.
Maths education is just the most obvious example of the breakdown of the model for education in general. We as a society do not need the factory model of education anymore. Preparing children for jobs on the assembly line or doing routine office work is obsolete. Technology can help with this by letting students select the mode of learning that suits them best, usually with a lot of guidance and coaching from teachers. This approach has been shown to work, and work effectively, but it is expensive and there are a lot of political and social opposition. In the US, there are a lot of people who do not want students to learn to be critical thinkers because it undermines parental and religious authority. (See recent activity in Texas about standards.) While the teaching of evolution gets a lot of press, the issue involves maths to a surprising degree. The one advantage that drill-and-kill methods have is that they are easy to test for, while learning to think critically is really hard to assess using multiple-guess tests.
The good news is that people can take the initiative on their own. They can reject the notion that there is a special "maths gene" and if you don't have it, you will be hopeless at high school or college maths. They can reject the notion that being good at maths means being able to do sums or long division quickly -- you will always lose to a computer if this is the standard of achievement. You can start with what interests you, and by pursuing those areas, you will learn maths in context. For some people, coding is a good entry point, but not everyone will be able to get hooked into maths in that way. It is entirely likely that for a large percentage of the population, a child's natural curiosity will have been killed to the extent that they are not really interested in anything to the extent that they are willing to keep working if the work becomes hard.
This is not a new problem. It was a problem when I was in school a half century ago. About 5% of students became interested in science and maths through a variety of experiences, and managed to pursue this interest in spite of the educational system.
Stephen Wolfram demoed a tool for creating interactive courseware. I hope to see that in the wild soon. I think there could be a cottage industry of people who a passionate about a particular subject preparing material so that students could learn on their own. Quality would vary, but cream rises.
