Since we're talking about books, here's a passage from the appendix of a text by a well-known, respected mathematician -- the first to correctly identify the author, book, and year of publication wins the prize! (I have no idea what the prize is, but it must be worth winning.)
> Hints to Teachers, and to Teachers of Teachers > > Teachers who wish to make use of this book in their profession should not > neglect the hints addressed to all readers, but they should pay a ttention also > to the following remarks. > As explained in the Preface, this book is designed to give opportunity for > creative work on an appropriate level to prospective high school mathematics > teachers (also to teachers already in service). Such opportunity is desirable, > I think: a teacher who has had no personal experience of some sort of creative > work can scarcely expect to be able to inspire, to lead, to help, or even to > recognize the creative activity of his students. > The averag e teacher cannot be expected to do research on some very advanced > subject. Yet the solution of a nonroutine mathematical problem is genuine > creative work. The problems proposed in this book (which are not marked with a > dagger) do not require much knowledge beyond the high school level, but they > do require some degree, and sometimes a high degree, of concentration and > judgment. The solution of problems of this kind is, in my opinion, the kind of > creative work that ought to be introduced int o the high school mathematics > teachers' curriculum. In fact, in solving this kind of problems, the > prospective teacher has an opportunity to acquire thorough knowledge of high > school mathematics ÃÂ real knowledge, ready to use, not acquired by mere > memorizing but by applying it to interesting problems. Then, which is even > more important, he may acquire some know-how, some skill in handling high > school mathematics, some insight into the essentials of problem-solving. All > this will enable him lo lead, and to judge, his students' work more > efficiently.
=================================== Wm C Bauldry, PhD Professor and Chairperson Department of Mathematical Sciences Appalachian State University Boone, NC 28608-2092 ===================== phone: (828) 262-3050 fax: (828) 265-8617 mailto://BauldryWC@appstate.edu http://math.appstate.edu/~wmcb/ ===================================