Beth in SW WA Posted March 12, 2012 Share Posted March 12, 2012 http://networkedblogs.com/v48bg. The original study from CMU is linked in the post. 'Cognitive' pathways were activated whether a problem was hard or easy; 'metacognitive' pathways were activated especially when challenging problems were presented, and they were activated for a much longer time after problems were already solved. Regular problems involved small positive number values and a single unknown, whereas exception problems used fractions, negative numbers, or repeated variables. Dd8 is doing the 'exception' problems daily so I guess we're ok on that front. It's good to know that hours and hours of challenging word problems have a residual effect. Thoughts? Quote Link to comment Share on other sites More sharing options...
snowbeltmom Posted March 12, 2012 Share Posted March 12, 2012 Another excerpt from the study: "If our students are up to the challenge, it's important we give them a chance to work on very hard problems. If they aren't getting anything wrong, then they're probably not getting any workouts to their metacognitive network. It's not just students, of course. If you're not making and analyzing you're mistakes, then maybe you're coasting too much on cognitive auto-pilot." I remember an AoPS instructor once telling ds's class that if the students could solve every problem, that the instructor was not doing a good enough job of challenging them. Quote Link to comment Share on other sites More sharing options...
regentrude Posted March 12, 2012 Share Posted March 12, 2012 I am not surprised by the results. A student who gets everything correct has work that is too easy. Quote Link to comment Share on other sites More sharing options...
wapiti Posted March 12, 2012 Share Posted March 12, 2012 Speaking of RR, he has an article about hard problems. We ask hard questions because so many of the problems worth solving in life are hard. If they were easy, someone else would have solved them before you got to them. This is why college classes at top-tier universities have tests on which nearly no one clears 70%, much less gets a perfect score. They’re training future researchers, and the whole point of research is to find and answer questions that have never been solved. You can't learn how to do that without fighting with problems you can't solve. If you are consistently getting every problem in a class correct, you shouldn't be too happy -- it means you aren't learning efficiently enough. You need to find a harder class. The problem with not being challenged sufficiently goes well beyond not learning math (or whatever) as quickly as you can. I think a lot of what we do at AoPS is preparing students for challenges well outside mathematics. The same sort of strategies that go into solving very difficult math problems can be used to tackle a great many problems. I believe we’re teaching students how to think, how to approach difficult problems, and that math happens to be the best way to do so for many people. Quote Link to comment Share on other sites More sharing options...
8filltheheart Posted March 12, 2012 Share Posted March 12, 2012 THe results are not really surprising. Our brains keep processing info even when we aren't consciously thinking about them. How many times does an answer to a problem suddenly pop into our minds when we are thinking about something else completely? Or how often do we dream about something that we haven't been able to solve? I don't think the "data" is restricted to math. I would suspect that similar results would be found from stories which evoke strong-lasting images or language w/multiple layers of meaning, brain teasers, strategy games, construction problems, etc. (or dare I suggest......imaginative play ;) ) I think it is just more affirmation that cognitive development is at its highest when there critical thinking/problem-solving issues involved (and why knowlegde-based learning is so lacking.) Quote Link to comment Share on other sites More sharing options...
Guest amandadun Posted March 12, 2012 Share Posted March 12, 2012 Speaking of RR, he has an article about hard problems. Interesting read, although it seems common sense. Cheers - Amanda Quote Link to comment Share on other sites More sharing options...
Crimson Wife Posted March 12, 2012 Share Posted March 12, 2012 I needed to hear this today after the sturm und drang out of DD this morning resulting from some Singapore IP problems. Quote Link to comment Share on other sites More sharing options...
beaners Posted March 13, 2012 Share Posted March 13, 2012 I think it's also important for those challenging problems to remain challenging. Looking back at my own education, I'm frustrated by the times "enrichment" was a sheet of problems where the first two required hard work to figure out, but the rest of the problems were the same exact type of question. In hindsight, it is so easy to spot all those missed opportunities. I hope I'll be able to use those mistakes to craft better experiences for my children. Quote Link to comment Share on other sites More sharing options...
stripe Posted March 13, 2012 Share Posted March 13, 2012 I think it's also important for those challenging problems to remain challenging. Looking back at my own education, I'm frustrated by the times "enrichment" was a sheet of problems where the first two required hard work to figure out, but the rest of the problems were the same exact type of question. When I was in elem school, harder math problems consisted of more and longer numbers to add up. I have these awful memories, and I wondered if they were real. My mom recently gave some papers from school, and they really were that boring. Quote Link to comment Share on other sites More sharing options...
Spy Car Posted March 14, 2012 Share Posted March 14, 2012 http://networkedblogs.com/v48bg. The original study from CMU is linked in the post. 'Cognitive' pathways were activated whether a problem was hard or easy; 'metacognitive' pathways were activated especially when challenging problems were presented, and they were activated for a much longer time after problems were already solved. Regular problems involved small positive number values and a single unknown, whereas exception problems used fractions, negative numbers, or repeated variables. Dd8 is doing the 'exception' problems daily so I guess we're ok on that front. It's good to know that hours and hours of challenging word problems have a residual effect. Thoughts? Weird. I was just wondering (out loud) about how brain imaging example might compare between children working on "challenging" problems vs procedural math in a Beast Academy thread. I have not yet read the study, but it does not surprise be that there is a measurable difference. Bill Quote Link to comment Share on other sites More sharing options...
TeaTotaler Posted March 15, 2012 Share Posted March 15, 2012 I needed to hear this today after the sturm und drang out of DD this morning resulting from some Singapore IP problems. This brings back one of my favorite homeschooling memories. Ds was in 2nd grade and working through one of the Sing IP books when he turns around and says to me: "Mom, this problem is just odious.":lol: I didn't know that word was part of his vocab!! Quote Link to comment Share on other sites More sharing options...
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