The self-contradiction is in your post: the word "basic," upon assumption that all they need to be teaching is calculus or that such constitutes adequacy in a college math department. My point was and is that computational methods are now "basic," or should be but for the inadequacies in k-12 education. They are used throughout many major industries and are becoming increasingly common as a resource management and optimization tool. Having an understanding of how they work, their limitations, and what the resource and personnel requirements might be is intuitively important to twenty-first century leadership in industry, something for which these students and PHC should be aspiring.
That's but one of the reasons why, in my discussion with GOPrincess, I asserted that calculus should be done before entering college or studying physics, biology, and chemistry at the high school level. We have a fundamental problem in teaching continuous mathematics in a world of computational methods: Discrete mathematics aren't at all intuitive; i.e., they don't teach understanding of the relationships among physical principles. Humans need continuous mathematics to viscerally understand the relationship between field strength and gravitational attraction as an inverse square with distance. Computers don't, and there lies a problem.
When a person has spent their entire academic career with continuous mathematics, albeit with infinite series approximations, they are so far along and habituated to seeing the world that way that when somebody finally pops finite difference equations on them as a perfectly sufficient numerical substitute for differential equations (the Fourier transformations are the same), the mental gear grinding is tremendous. It occurs so late in the curriculum that there isn't time for the concepts to settle in. Indeed, many schools don't get to it at all. It's a problem, because the future belongs to people who can handle it.
I can hear it now, "What does this have to do with being a judge?" My response, "How many times do expert witnesses bamboozle judges and congressmen on regulatory issues using computational methods or dimensional analyses?"
It matters.
Here is what I am doing about it. I front-loaded my kids' instruction with mathematics, three to four hours per day. They were both doing high school algebra by eight. We will have calculus done by thirteen. We will do college physics, chemistry, and biology instead of introducing them at the high school level. We have thus eliminated a good many years from the k-16 curriculum. We study history, english, etc. at a college level as well. The expectations are high, the work is focused and protracted. It works. My elder daughter tested "post high school" on the Stanford 9 test in every subject at the age of nine. They do college level work, slbeit at a slower pace than college requires. They're damn proud of it too, and should be. The work is more enjoyable, because they can now study the richness of Western civilization and read all those great works we wished we had time for when we went to school.
I have NO INTEREST in a curriculum for my kids that delivers anything less. In a nation where its educational product that lies at the bottom of the industrialized world, I owe my kids nothing less. "Adequate" sucks.