I think we are in violent agreement. Your use of language comes from a theoretical perspective (what word problem should mean), and mine from a practical perspe

I think we are in violent agreement. Your use of language comes from a theoretical perspective (what word problem should mean), and mine from a practical perspective (the things that were called "word problems" throughout my schooling, and throughout all the curriculum-based teaching materials I've read). In my experience, the first step to solving a "word problem" is always to reverse the find-and-replace performed by the question setter, to yield the original algebra (e.g. the first part of the Hannah's sweets question). This is what we're taught to do in schools. You're right to object from a pedagogical perspective, because this is a horrible thing to make children do, and completely defeats the purpose of word problems. The trouble comes when schools teach people how to pass exams. But, given how hard exams are, and how little they reward understanding beyond that stage of the curriculum, the optimal strategy is to learn no more than your current stage (plus exam technique), then learn no more than the next stage (plus exam technique), and never get around to actually learning maths.