On Tue, May 5, 2009 at 5:03 AM, Albert Cahalan <[email protected]> wrote: > > To benefit from a given lesson, one must master any prerequisites.
The good news is that as time goes on, people (slowly) develop ways to help kids acquire prerequisites within learning new topics. For example, you can build lessons about proportionality on multiplication, which you can build on addition, which you can build on counting. Alternatively, you can work with unfair sharing, growth/shadows/perspective and other similarity, or intensive unit (e.g. speed) metaphors directly, incorporating development of multiplicative reasoning and its coordination with additive reasoning into this work. As the culture progresses, math gets more and more "packed," prerequisites and all. I found Bill's non-universals summary to be quite useful in thinking about these issues, especially the "similarities over differences" part http://learningevolves.wikispaces.com/nonUniversals As we figure out to help kids work with similarities in deeper ways, and as we uncover better metaphors for similarities, prerequisites get subsumed into other topics. -- Cheers, MariaD Make math your own, to make your own math. http://www.naturalmath.com social math site http://groups.google.com/group/naturalmath our email group http://www.phenixsolutions.com empowering our innovations _______________________________________________ IAEP -- It's An Education Project (not a laptop project!) [email protected] http://lists.sugarlabs.org/listinfo/iaep
