our entire approach is screwed up. We need to teach calculus first, then physics (I’m also not quite happy with all of this algebra based physics) then chemistry and finally biology.
Your approach ignores the cognitive development of the child's brain. Much of the high school biology curriculum is descriptive, so teaching the scientific method and biology first teaches foundational observation and analysis skills that most students in early high school can grasp. Meanwhile, they are completing the foundational algebra skills required for a more quantitative approach to chemistry - including the ideal gas laws etc. Again, the students are simultaneously building math skills. The problem comes with physics. Very few students take calculus in high school and those who do are rarely prepared before their senior year. This means you have two choices - either teach an introductory, algebra - based physics course to a wider audience or teach a calculus based physics course to a few high school seniors who are simultaneously taking calculus. I did the latter, but worked my tail off that year (it was good for me...) and it was a very small class.
I think everyone should be able to do calculus in high school...I took algebra in 8th, geometry in 9th, trig in 10th and calculus in 11th and I don’t think we had the most amazing high school in the world. We also had a lot less free time available than students in most schools.
I am sure this sequence could be pushed even further back if kids were actually encouraged to learn math and not ridicule those who do, unlike what you see on the “Big Bang Theory” TV show. There is certainly a lot of room for ‘optimization’ in the math curriculum. For example, the Singapore 8th grade curriculum even covers trig:
http://www.sgbox.com/singaporemathss2.html
I'm teaching physics and algebra to my grandkids: 5, 9 and 11 - but they don't know it.
It gets mixed in with all the fun stuff that Papaw does in the barn and around the farm!