Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life...This sounds very right to me. The article goes on to note the defenders of the traditional system, who argue that the current progression both prepares one for higher learning in mathematics, while providing certain abstract skills everyone needs.
Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now.
The same was once said about Latin, as the article notes. Once upon a time, people thought that teaching Latin would have those spillovers as well. We've largely abandoned that notion in favor of teaching relevant languages in the classroom, but have kept these ideas in math.
But that's absurd. The current math curriculum is really only well geared to the fraction of the population that anticipates learning much more math. It completely turns off virtually everyone else, to the point that you have millions of people who think of themselves as "not math people," or minimally capable of grappling with essential quantitative skills. An alternate method would focus on street learning math style still that focus on a quantitative fluency for the tasks that typically find themselves facing. Understanding concrete examples in any case is the best way to built up an abstract understanding of the underlying rules, so will help the more math focused folks as well.
This is a huge problem in English too. The dominant way of teaching English rests on the belief that having students read works of literature and write literary analysis in a certain stylistic format somehow imparts knowledge of the English language. This is nuts. It ties together three skills -- reading novels, writing literary essays, and writing skills in general -- that are utterly different. What frequently happens is that you end up with students who can't navigate a complex novel or can't be bothered to figure out how to analyze a novel. So they wind up making their essay as complicated as possible to cover their ignorance. It is difficult to imagine a worse way to teach writing -- yet that's what we do despite the importance of verbal skills in the world.
In both fields there is an unnecessary reliance on Collegiate models of learning. High School math took after the sorts of quantitative skills in demand ~1900. High School English was shaped by the fact that College English departments, shaped by the flourishing of the German Research Institute model, specialized in "research" into works of literature. Whatever the merits of the underlying collegiate forms of education -- they are completely unsuited for teaching the mass of students basic quantitative and verbal skills.