Hi Paul,
I think that two tracks are appropriate, but it is important not to separate them too soon. I remember my mother telling me about my 5th grade teacher who told her, "David will have to find something to do in life that does not involve mathematics." It turns out my final choice was physics, with a degree in math as well. I suspect I was tired of doing page after page of long division.
In my life, I experienced what was for the time a typical math education: various forms of "number theory" and arithmetic, until about the 9th grade, and then algebra, algebra 2, geometry, college algebra, analytic geometry, trig and a year of calculus all crammed together. And all taught by "math teachers."
Eventually, at college level, I wound up in physics classes where physics professors considered math to be too important to be left to the math teachers.
I think the most fundamental problem with early math education is that, with math taught as a stand-alone topic, for many it lacks motivation. That is not to say that students should not be expected to take on some learning as merely required, but where a connection to interesting activities can be made, it is well to do so. Who wants to spend a year sawing boards in half -- it's so much more interesting if you're building a soap box derby race car. And it matters to you if the cuts are square.
So, early on I would look for every opportunity to connect math with applications. Theory and mechanics are still important -- learning the algorithm for long division teaches you the meaning behind a base system representation for a number. But sending a 5th grader home with 10 pages of long division problems is excessive. Once the point is made, a calculator works very well. I would connect math with other academic work closely, all the way through high school, coordinating the "pure math" classes with other academics to the extent that new math learning was introduced as needed in non-math classes, where it has a purpose, and reinforced in a synergistic manner in the math classes.
This would remain one-track into early high school, and not separated until the student knew how to think quantitatively. Not just by making a budget, balancing a checkbook (if anyone still does that), calculating take-home pay, or making change -- but by solving the "dreaded story problems." Learning math at this level is more than learning math; it is learning how to think.
At this point, separating tracks makes sense to me. Being a confirmed nerd, I do think that a brief intro to calculus is beneficial to those who will never use it, merely because it introduces the concept there are things which depend on the rate of change of other things, as all of the laws of nature, or the accumulation of other things as the inverse. But I see no need to expect those who will not pursue quantitative work in science and technology to master calculus or differential equations. (Or perhaps even college algebra, trig, . . . ) But using algebra to solve story problems is a great learning experience.
There is however the the cultural need for discipline and learning in the early years. To a great extent, many of the activities we force on the young are those which they would not choose for themselves, but are none the less essential to a good life. We humans have a long childhood because we have a rich and complicated social structure. There are animal species wherein the young still learn by instinct-driven play, but we have evolved so much more culturally that physically that we must make our children learn things the genetic programming does not require of them. (And refrain from doing quite a bit which it does.) So I think this will remain an issue, and there is only so much we can do to sweeten the pills which we must force down their throats at an early age.
Kind regards,
David