I think you're referring to two different points. 1) kids need to know their basic math facts. As you said, parents can help facilitate this with the use of flash cards, teachers can "drill and kill", etc. 2) Kids need to become flexible problem solvers, whether within the context of word problems or as preented as "simple" computational problems. The benefit, in my opinion, in spending class time working on and sharing only a couple of problems is that the kids have an opportunity to add problem solving strategies to their "bag og tricks" so to speak. Having only one "way" to get an answer doesn't always serve the child well. Take, for example the problem 100 - 1 = ? Is the standard subtraction algorithm the best way to get the answer? I really this is a very simple example, but I think it speaks to the need for kids to have many ways to get the answer. As for where these "ways" come from, the ones that make sense to the kids are the ones that will ultimately lead to correct answers. Making sense of the mathematics must be grounded in the child's understanding and experiences, and these understandings and experiences may not match those of the text book author, teacher, parent, etc. If we allow kids to build their own understanding, the structure has to be more sound.