> Further my post of Oct 16, 2010 11:52 AM: > <SNIP> > > > The main idea in this > > > document is that not only does proportional > > > reasoning develop without > > > formal education, formal education may actually > > > significantly hinder that > > > development in many students. > > > On this point, I'd like to go somewhat further than > in my earlier response. I'd like to claim: > > ... it's not just "proportional reasoning" that > develops without formal education, it's ALL > reasoning. Formal education is a useful aid to > effective reasoning - but it's NOT the only way. > > And yes, formal education (if it insists on 'by-rote > learning') definitely does significantly hinder the > development of reasoning all round. > > GSC
Though the document I had mentioned focuses on proportional reasoning, I too would not doubt that these findings carry over to any form of mathematical and everyday, common sense reasoning. I see nothing special about proportional reasoning that allows this phenomenon to happen other than possibly being that this reasoning that had developed in these people intuitively without formal schooling--the people that have been observed by various researchers over the years--because those people had been exposed to proportional reasoning frequently outside of school.