Knowing and teaching elementary mathematics

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…gh Professor Richard Askey's review of that book. http://www.aft.org/publications/american_educator/fall99/ame... Askey's review is actually a review of Ma Liping's book Knowing and Teaching Elementary Mathematics that quotes a passage of Gelfand's book in a sidebar. I later saw a glowing description of Gelfand's books in the same series in a bibliography by a U of Chicago mathematics student. http://www.ocf.berkeley.edu/~abhishek/chicmath.htm I use the Gelfand textbook to teach supplemental math lessons for gifted elementary-age students. They LOVE the Gelfand problems. They haven't even gotten to the really funny parts of the book yet, which such sections as "How to Confuse Students on an Exam." Gelfand's book(s) exemplify what you are looking for in math textbooks. Of course they are not used in very many public schools in the United S…

… of the system in the United States. In many other countries, teachers specialize by subject in the elementary grades, the better to teach their subject effectively. See Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic... for a detailed discussion of elementary math teaching, or The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom http://www.amazon.com/Teaching-Gap-Improving-Education-Class... for a broader perspective on other ways to organize schools.

…ery influential on my thinking about math education. A link that furthered my process of pondering how to teach mathematics better was Richard Askey's review of the book Knowing and Teaching Elementary Mathematics by Liping Ma. http://www.aft.org/pubs-reports/american_educator/fall99/ame... Another review of that excellent book http://www.ams.org/notices/199908/rev-howe.pdf is also food for thought. Professor John Stillwell writes, in the preface to his book Numbers and Geometry (New York: Springer-Verlag, 1998): "What should every aspiring mathematician know? The answer for most of the 20th century has been: calculus. . . . Mathematics today is . . . much more than calculus; and the calculus now taught is, sadly, much less than it used to be. Little by little, calculus has been deprived of the algebra, geometry, and logic it needs to sus…

…tes entering tough college programs have more catching up to do than the (much more stringently selected) international undergraduates at American colleges. See the book Knowing and Teaching Elementary Mathematics http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic... (or its review by mathematician Richard Askey) http://www.aft.org/pubs-reports/american_educator/fall99/ame... for example of ways American primary education could do better.