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We have reached a point of mutual understanding and considerable agreement, but I feel we have circled around to the original problem. In your last paragraph,

We have reached a point of mutual understanding and considerable agreement, but I feel we have circled around to the original problem. In your last paragraph, you consider the case of calculator vs. slide rule, but one can, I think, make a more apposite case with calculator vs. learning arithmetic (and even if you don't agree that it is more apposite, the point can still be made!) By your logic, we should not be assigning any arithmetic problems that can be solved with a calculator. But why stop there? Even current calculators can do much more than basic arithmetic, and their capabilities pale in comparison to those of general-purpose computers. I do not believe you can teach mathematics in a way that begins at a point beyond what has been automated, and before long that may be true for computing as well. This has not led to the demise of mathematics education, and neither will it for computing, for the same reason in both cases: anyone who needs to use these tools to get through the introductory classes will wash out later - which brings us right back to spcebar's original comment about only hurting themselves in the long run.

Kamq 4y ago
> I think, make a more apposite case with calculator vs. learning arithmetic (and even if you don't agree that it is more apposite, the point can still be made!) By your logic, we should not be assigning any arithmetic problems that can be solved with a calculator. I think that's an excellent point, and one whose nuances shouldn't be un-examined. I guess the difference to me is that arithmetic feels more fundamental. I may be using fundamental in a weird way here, but I don't mean it in the sense of something that you build on. I mean it in the sense that arithmetic itself is the idea that's trying to be taught. Whereas a sorting algorithm has both a explanation as a semi-platonic ideal and as an implementation and they're very different things. You can fairly effectively wield the implementation only using the idea in your head, mostly regardless of your understanding of the implementation. In fact, it's generally considered good practice to hide an implementation from your eventual users. I'm not so convinced that you could do the same with arithmetic, although I'm open to arguments to the contrary. Now that I'm thinking about it, I think this is the dividing line between math and computing in my head. The ability to separate out the real world part from the ideal and operate the former using only the latter. Perhaps I'm mistaken, but I would be very surprised if a mathematician could operate without understanding arithmetic, but I've seen quite competent programmers construct APIs just fine without having been taught sorting algorithms.

Kamq 4y ago

> I think, make a more apposite case with calculator vs. learning arithmetic (and even if you don't agree that it is more apposite, the point can still be made!) By your logic, we should not be assigning any arithmetic problems that can be solved with a calculator. I think that's an excellent point, and one whose nuances shouldn't be un-examined. I guess the difference to me is that arithmetic feels more fundamental. I may be using fundamental in a weird way here, but I don't mean it in the sense of something that you build on. I mean it in the sense that arithmetic itself is the idea that's trying to be taught. Whereas a sorting algorithm has both a explanation as a semi-platonic ideal and as an implementation and they're very different things. You can fairly effectively wield the implementation only using the idea in your head, mostly regardless of your understanding of the implementation. In fact, it's generally considered good practice to hide an implementation from your eventual users. I'm not so convinced that you could do the same with arithmetic, although I'm open to arguments to the contrary. Now that I'm thinking about it, I think this is the dividing line between math and computing in my head. The ability to separate out the real world part from the ideal and operate the former using only the latter. Perhaps I'm mistaken, but I would be very surprised if a mathematician could operate without understanding arithmetic, but I've seen quite competent programmers construct APIs just fine without having been taught sorting algorithms.