I suppose it depends on which hood you want to look under. :)
I see CS as basically dual-grounded: everything is ultimately just syntactic sugar on machine code, and everything is ultimately just syntactic sugar on lambda calculus. Which reduction makes more sense depends on what you care about; the bare-metal view comes into play more when you're talking about low-level performance, while the mathematical view comes into play more when you're talking about algorithms and correctness. I guess it can get into some philosophical debate about which reduction is more "real"...
I'm not entirely sure which way is easier to start from. The argument you make here, that students have trouble going from mathematical abstraction to bare-metal implementation, is probably true; but I think students who first learn on asm and C also have trouble going the other way, from thinking about executing a series of instructions to thinking about enacting computations. That's one reason there's been some experimentation at places like MIT and UT-Austin with not starting with an imperative language, which they feel is very hard to get people off of once they've started with it.
I see CS as basically dual-grounded: everything is ultimately just syntactic sugar on machine code, and everything is ultimately just syntactic sugar on lambda calculus. Which reduction makes more sense depends on what you care about; the bare-metal view comes into play more when you're talking about low-level performance, while the mathematical view comes into play more when you're talking about algorithms and correctness. I guess it can get into some philosophical debate about which reduction is more "real"...
I'm not entirely sure which way is easier to start from. The argument you make here, that students have trouble going from mathematical abstraction to bare-metal implementation, is probably true; but I think students who first learn on asm and C also have trouble going the other way, from thinking about executing a series of instructions to thinking about enacting computations. That's one reason there's been some experimentation at places like MIT and UT-Austin with not starting with an imperative language, which they feel is very hard to get people off of once they've started with it.