In a recent article published in “The Hill” the author laments about the US performance in math and then comes up with what is now a bromide in math education circles: “Why not look at what other countries do to teach math–countries whose performance is math is in the top tier. Why not look at, say Japan, the article says and then cites Elizabeth Green’s article that was published in the NY Times Sunday Magazine in 2014: “Why Americans Stink at Math”. The big surprise of all this is that Japan’s techniques, according to Green, came from the U.S., and Japan emulates the reform math ideas promoted by organizations such as the National Council or Teachers of Mathematics, and which are subtly (and not-so-subtly) embedded in the Common Core Math Standards.
In Green’s view, reform math is how math should be taught because math is about “understanding”. In the world according to Green, if math is taught poorly it is either because 1) it is taught in the traditional manner or 2) it was reform math executed poorly. This leaves a nice out for both types of teaching. Pointing to reform math as a possible reason for the bad performance of students over the last two decades is responded to by saying “It wasn’t true reform math.” (See No True Scotsman fallacy )
Since, according to Green, reform math in the United States is done poorly, this accounts for the many examples of ridiculous problems and incomprehensible homework assignments attributed to Common Core, although such approaches were around long before Common Core. She agrees that such approaches are bad and not what Common Core is about. Green writes “With the Common Core, teachers are once more being asked to unlearn an old approach and learn an entirely new one, essentially on their own. Training is still weak and infrequent, and principals—who are no more skilled at math than their teachers—remain unprepared to offer support.” She holds in disdain the “I, we, you” model of classroom teaching (and which is one of the few techniques actually supported by research) and argues instead for “You, Y’all, We”/discovery learning. And to bring that off requires teacher training that is “meaningful”—i.e., allowing for properly implemented reform ideas and Common Core.
Green argues that reform math done right does work, pointing to Japan for evidence. She claims Japan is doing U.S.-style reform correctly. Japan’s method of teaching is admittedly different in how teachers collaborate to create “lesson plans” and anticipation of student misunderstandings and questions. But Green fails to acknowledge that Japanese instruction is strongly teacher-led and does not rely on discovery. A paper by Alan Siegel, (see http://www.cs.nyu.edu/faculty/… ) a math professor at New York University, provides valuable insight into myths about Japanese teaching and shows that it is based on whole class and direct instruction techniques—and much practice.
Wayne Bishop, a retired math professor, is familiar with what has been done in Japan and provides evidence that the approach that Green talks about (which she recommends should be done in the US) did not succeed and that they went back to the way math had been taught. His article about this can be found here. I suggest that anyone swayed by Green’s arguments, including the author of The Hill article read it.
traditional math 