Algebra

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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…

…o all artificial means of attracting their attention--much as one buys books for their content and not for their dazzling jacket designs that engage only for the moment. The most important thing a student can get from the study of mathematics is the attainment of a higher intellectual level." The late professor Gelfand was optimistic--based on long experience--that many learners can attain a higher intellectual level in mathematics, perhaps because of his flexibility as a teacher: "Students have no shortcomings, they have only peculiarities. The job of a teacher is to turn these peculiarities into advantages."

… (I even use his photograph as my avatar on the first website where I used the screenname tokenadult.) His book Algebra http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 is an inspirational example of how to make a textbook both humorous and challenging, and is the start of a great series of textbooks on secondary school mathematics from the viewpoint of advanced mathematics. I use that textbook in the supplementary math classes I teach, and the students LOVE the problems. His MacArthur Foundation Fellowship for his work in mathematics education (which I just learned about from the Wikipedia article you kindly shared) was very well deserved.

…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…