Schools should honestly have two parallel tracks of math (which students should take at the same time). There should be the standard "analysis" mathematics of algebra, geometry, trigonometry, calculus. But there should also be a track of (what I will shorthand to) Discrete mathematics, which focuses on proofs, combinatorics/ probability, number theory, graphs, etc. Discrete Mathematics used to very much be a niche mathematical field, who needs to know about number theory!? But computers has really made these other fields incredibly important to modern society. Plus writing proofs is a good exercise for anyone.
I think you need Algebra 1... maybe I'm too stuck in the old ways.. but at some point you need to understand what a variable is and how to "solve for x". How to plot points, read and interpret a graph. Identify patterns in series of numbers, etc.. Call it what you want, but without the content of Algebra 1 you're going to have a hard time communicating ideas in the language of Mathematics. And these kids also have a Physics graduation requirement where they will need to at least solve f=ma.
Geometry is usually the "proofs" class. You're only really learning geometry so you can write proofs. You could plug&play that with a Discrete Math/Sets/Boolean/Logic class. I think Geometry is conceptually easier to understand as a 14/15 year old because you can "see" that the proofs work. Truth tables are kind of visual, but still a little more abstract than triangles and rectangles.
Combinatorics/Probability is already a half year course that's usually combined with the half year course of Statistics. I can see non-AP versions of this class split into two full year classes.
I imagine this would be something like what you're thinking of:
Algebra 1 -> Discrete Math -> Probability -> Statistics
The only thing standing in the way of something like this is politicians (state boards of education) and startup costs. For example, the graduation requirements in Texas are "4 credits of Math including Algebra, Geometry, and Algebra 2" (and the content of those classes are explicitly laid out in the TEKS). And you would also need to buy new textbooks/curriculum... which is money that schools don't really have to spend.
I agree with most of what you wrote, but it’s puzzling to me that you think that proofs are more of a feature of discrete math than continuous (analysis). My first introduction to proof-writing was in geometry, and a majority of proofs that I have read or written have been in analysis. But I was a math major in college.
I also did proofs for the first time in Geometry. But the reason I think of proofs as more in Discrete, is that you usually get proofs immediately in Discrete via number theory, graphs, or things like induction. But you usually don't really get proofs in analysis until you take, what real analysis or complex analysis? So you typically have trig, precalc, calc 1/2/3, differential equation and partial differential equations that is just calculations. That's my thinking anyways.
