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> "word problems" are just algebra obfuscated with a prefabricated template. This is absolutely not true. It's worth throwing some "trick questions" at kids fr

> "word problems" are just algebra obfuscated with a prefabricated template. This is absolutely not true. It's worth throwing some "trick questions" at kids from time to time to make sure they read carefully, but the best word problems, while non-obvious to solve, are not obfuscated in their setup. Young children should not be taught to solve word problems using algebra, but should be helped to try a wide variety of their own methods (guessing and checking, making a table, drawing a picture, breaking the problem down into several steps, solving a simpler problem, working backwards, using physical props, etc. A rush to turn everything into algebra is harmful to children's mathematical development, and many if not most types of word problems can be more profitably attacked with a variety of other tools/ideas. Word problems are infinitely varied, and can get as difficult as you like, from 1st grade arithmetic up through unsolved professional math research problems. > cutting that down to something you can fit into a mark scheme This has nothing to do with the fundamental purposes of word problems. We're talking here about learning mathematics per se, not busywork or arbitrary ranking systems done for some bureaucratic purpose.

wizzwizz4 2y ago
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.
- jacobolus 2y ago
  This is why I say that most US primary/secondary education to first approximation doesn’t have any nontrivial word problems. The single-step formulaic problems called “word problems” are not remotely the same thing, and miss the point.

wizzwizz4 2y ago

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.

jacobolus 2y ago
This is why I say that most US primary/secondary education to first approximation doesn’t have any nontrivial word problems. The single-step formulaic problems called “word problems” are not remotely the same thing, and miss the point.