The point he's making is against unnecessary rigorization of introductory calculus and I think you are getting a bit too hung up on the "function-based approach". I repeat - introductory calculus. There's lot of time and space to make things more rigorous in a class like Analysis.
When I help students with calculus most of them have no trouble with the ideas but the implementation that they are required to perform. I spend a lot of time getting them to understand the simple particulars. There are ways of teaching calculus that would dispense with some of the more rigorous aspects and make it a much more bearable experience for most.
When I help students with calculus most of them have no trouble with the ideas but the implementation that they are required to perform. I spend a lot of time getting them to understand the simple particulars. There are ways of teaching calculus that would dispense with some of the more rigorous aspects and make it a much more bearable experience for most.