I think analog31's answer gets to the gist of it for me. Lots of kids have a very hard time understanding how math is relevant to them beyond basic arithmetic and a little algebra. However, it's important enough that we dedicate all of k-12 to teaching it.
Yet, computation is basically what runs the world and there's immediate and gratifying application for even very simple and low levels of it. Students learning about computation...and what's computable...can relate to it much more readily and can start looking for applications of this knowledge much more readily than what they learn in mathematics.
But the two subjects are married at the hip (like literature and history) and one can readily lead into another if they're both present.
Just as important, the tools that exist for exploring computation are really quite good these days and students can do some really cool stuff if the environment is well structured. Imagine sitting down in a class and the assignment is to use Python to build a simple sentiment analyzer. Classroom materials are a list of scored sentiment words and a few dozen excerpts from literature or news.
Or reinforce mathematics lectures on probability by building a bloom filter.
K-12 education on computation, if done well, could help tie together many of the other subjects that students are taught and provide immediate application.
(imagine if the assignment for a 10th grade art class was to produce a demoscene demo!)
Perhaps one reason is that outside of school math, computation is actually how most people do math, and to a considerable extent, science.
Don't get me wrong, I was a math & physics major in college, and love doing derivations and proofs by hand. But in my present job, if I have to solve a math problem, or perform an experiment, I reach for my computer.
As it stands, school math is limited to problems that can be solved by hand in "closed form," creating a stilted view of what can be done with math.
I realize that programming is not CS, but an introduction to computation, within the math and science curriculum, might be a way to make those subjects more interesting and relevant, while also providing some preparation for kids who might develop an interest in CS later on.
I think what you are overlooking is that kids CANNOT really do math. 67% or 8th graders are rated as "not proficient" in math, and that is compared to the government standard (which I would bet money is incredibly low). How will they do algebra in a program when they can't do algebra on paper?
Yet, computation is basically what runs the world and there's immediate and gratifying application for even very simple and low levels of it. Students learning about computation...and what's computable...can relate to it much more readily and can start looking for applications of this knowledge much more readily than what they learn in mathematics.
But the two subjects are married at the hip (like literature and history) and one can readily lead into another if they're both present.
Just as important, the tools that exist for exploring computation are really quite good these days and students can do some really cool stuff if the environment is well structured. Imagine sitting down in a class and the assignment is to use Python to build a simple sentiment analyzer. Classroom materials are a list of scored sentiment words and a few dozen excerpts from literature or news.
Or reinforce mathematics lectures on probability by building a bloom filter.
K-12 education on computation, if done well, could help tie together many of the other subjects that students are taught and provide immediate application.
(imagine if the assignment for a 10th grade art class was to produce a demoscene demo!)