I find the idea of replacing "mathematics" in the curriculum with "computer programming" rather baffling. As important as programming is in our world, only a small fraction of high school graduates are going to need to do what we currently think of as "programming", while everyone will need to interact with technology and understand the world quantitatively. That calls for a much broader view of math and technology education than just "programming", even including machine learning and statistics.
Also, expecting anyone to have any kind of understanding of machine learning and statistics without a real grasp of what is currently considered "mathematics" doesn't make any sense to me. You're going to need algebra and linear algebra at minimum, and probably calculus as well, to have a chance at meaningful use of ML models.
Why do people need to know the under the hood stuff. As I mentioned in my other comment, we have the concept of division of labour.
Also, programming and machine learning will increasingly be most of what people's job description. In fact, in my extremest viewpoint, I think even programming is on it's way out and machine learning will the majority of people's work. Or put more simply, giving computers a few examples.
Already, with things like the Baxter robot from Rethink Robotics, and mechanical turk from amazon, we're seeing what the future of work will be like. The computers will just figure out things extrapolating from the choices we make.
I actually agree with you that programming may be on its way out for the majority of people. I can't agree with sweeping away all of mathematics, including arithmetic and algebra, as "under the hood stuff" for K-12 students.
Algebra (the art of rearranging equations) is not necessary anymore (you just need to know how to realize how things can be quantified - the naming of variables of computer programming). Arithmetic beyond use of calculator is useless.
Maths as traditionally taught is the leading cause of high school dropouts rates and probably a lot more damage than tahat (people who might have been scientists turning to arts instead).
> Algebra (the art of rearranging equations) is not necessary anymore ...
False, and false.
* As to the first, in common use, algebra is the abstraction of mathematical values and operations. If we can abstract a value to a symbol, we then can operate on the symbol rather than the value, greatly increasing the generality of mathematical ideas. Which operation is more useful: sqrt(2) or sqrt(x)? Another example -- which is more useful: D(7^n) = 7^n * log(7) or D(x^n) = n * x^(n-1)? (The first can only be applied to 7, the second can be applied to any values of x and/or n.)
* As to the second, algebra is much more useful now than it was 100 years ago. Those who don't learn algebra are inviting politicians to lie to them, which they will certainly do if given a chance.
> Maths as traditionally taught is the leading cause of high school dropouts rates ...
This confuses cause and effect. If we drop math education to prevent dropouts, we will have implicit dropouts (people who drop out but without physically leaving) instead of explicit ones.
> ... people who might have been scientists turning to arts instead ...
One's preference for art over science has deeper roots than a lack of comprehension of mathematics. And again, it confuses cause and effect.
I'll just have to disagree with you there. Your definition of algebra (beyond the naming of symbols, or variables in programming parlance) is not useful to most people. Where are they going to apply log or sqrt in everday life or even equations as you outlined (in my viewpoint, machine learning will automagically figure out equations or they will be apps on your smartphone).
I think people would be much better served implicitly dropping out than explicitly. People's identity has more to do with performance than innate ability.
Many people are mistakenly led to believe science is about symbolic equation rearrangement on paper (high school maths) + rote memorization and so choose arts instead. For many people, but not all, this is the reason why they don't pursue science careers. If they understood it was much more about teamwork and physical setting up and running equipment/software and thinking creatively, I'm certain we'd see different choices made.
But you aren't disagreeing, you're trying to redefine algebra based on personal preferences, in other words, you're arguing for the ascendancy of postmodernism (the idea that there are no shared truths, that everything is a matter of opinion and outlook). The problem with arguing from a postmodern perspective is that the argument instantly self-destructs (it applies first to itself, which means if you're right, then I have the right to ignore you).
The essential foundation of dialogue is consensus, shared ideas, and shared word definitions. Without those, there's no possibility for dialogue.
> Your definition of algebra (beyond the naming of symbols, or variables in programming parlance) is not useful to most people.
Utility is not the basis on which words are defined. Words mean what they mean, how we feel about those meanings is irrelevant.
> I think people would be much better served implicitly dropping out than explicitly.
So those who are qualified to be in school can be surrounded by those who aren't?
> If they understood it [science] was much more about teamwork and physical setting up and running equipment/software and thinking creatively ...
That's not what science is about, unless plumbing is about wrenches. You're confusing the practice of science with the idea of science.
I'm not doing some post-modernism or whatever sneaky jab you're throwing in.
You're implying that you have some definition of algebra that is truer than mine. But that is all meaningless arguments over words anyway.
The real issue is that I'm arguing that the vast, vast majority of people only need to know that concepts can be "quantified" - "variabilized" or "symbolized". This is mostly so that they can interact with computers for the purposes of computer programming, or for creating tables of data to be fed into machine learning black boxes.
You've also think you know a truer definition of science than me. I think science today is about collecting data and having computers make predictions, increasingly use black box machine learning. I'm inferring that you think it's about theorizing from data and writing out simple equations. I have disagree with you on that (though you'll probably turn around with your post-modernist jabs).
> I'm not doing some post-modernism or whatever sneaky jab you're throwing in.
Corespondent insists that there are definitions on which different people can agree.
> You're implying that you have some definition of algebra that is truer than mine. But that is all meaningless arguments over words anyway.
Correspondent insists that there aren't definitions on which different people can agree.
When you sort out which position you're taking, post again. :)
> You've also think you know a truer definition of science than me.
There is only one definition of science. Postmodernists, of course, disagree. For a postmodernist, there are as many definitions as there are people to have them.
> I think science today is about collecting data and having computers make predictions, increasingly use black box machine learning.
That is not how science is defined. You've just described how people collect data for the purposes of science, but science is defined by the uses to which data are put, not the data itself.
> I'm inferring that you think it's about theorizing from data and writing out simple equations. I have disagree with you on that ...
Feel free. But you need to realize that there are ideas on which people agree,and science is one of them. Indeed, without agreement about what science means, there can be no science -- science requires consensus about its own meaning, even while inviting disagreement about specific scientific theories.
reply to lutusp below because reply link takes too long:
You're just saying my definitions of things are wrong etc. etc. You just want to disagree with anything I say. My views are laid out clearly on the comments in this thread. I don't see what your views are (except to disagree with anything I say).
edit: replying to lutusp
You keep arguing that I'm just personal opinionating and that I'm wrong. I can't figure out what your views are - maybe I'm really dumb and you're really smart. You win.
> You're just saying my definitions of things are wrong ...
Locate where I said that.
> You just want to disagree with anything I say.
No, I want you to grasp some sense of reality -- not virtual reality, the other reality.
> My views are laid out clearly on the comments in this thread.
Yes, but your views are not compelling on what science is, as just one example. You expressed the belief that science's definition depends on personal opinion, which is false.
> I don't see what your views are ...
Then read. I explained what's wrong with defining science any way we please. All you need to do is read the words.
Also, expecting anyone to have any kind of understanding of machine learning and statistics without a real grasp of what is currently considered "mathematics" doesn't make any sense to me. You're going to need algebra and linear algebra at minimum, and probably calculus as well, to have a chance at meaningful use of ML models.