Part of the problem is that the entire point of textbook problems is to not be representative. Failing all else, even all the also-excellent points described by

Part of the problem is that the entire point of textbook problems is to not be representative. Failing all else, even all the also-excellent points described by other people in other comments, they have to be pedagogical. The vast bulk of almost all jobs, tasks, problems, etc. are highly stereotyped, and trying to give some sort of "uniformly random" sample of some task set would produce problems that are simultaneously 1. too boring to be worth using to teach with and 2. too complicated to be useful. If that seems paradoxical, the resolution is that it would be generally the same complication, over and over and over, from whatever problem set you're drawing from. We have to present simplified problems, and in order to get a sampling across many possible complications that our students could be going out into the world and seeing (because while all of them are likely to end up solving stereotyped problems in some domain, we don't have any idea which ones they are yet!), we need to sample things in an unrealistic manner. It is an unsolvable problem. I still have my opinions about how education is done; I think one of the most fundamental errors it makes that is not talked about is that it is virtually impossible to provide a solution to someone who doesn't have the problem in the first place, and our entire system is top-to-bottom structured around providing solutions. This, I think, is an even more fundamental view of the disconnect underlying the issue of textbook problems not being representative... "textbook problems" are a misnomer, really, because they aren't problems. I don't care if Sally does or does not get her 1/7th of an apple, and the technique of connecting a grade to whether or not I answer correctly is really quite clumsy and of dubious effectiveness. But it would take a top-to-bottom rethink of the curriculum of the sort I've never really seen anyone try. I've seen people peck around the edges and I've seen people throw the baby out with the bathwater but a problem-first-centric education would be such a radical departure that I don't think people can even think it.