N. Silver wrote, in reply to my question opening the thread:
>>I wonder what you would suggest as a best textbook for a first >>high-school-level geometry course for talented students? I'm trying to >>gather information to make a suggestion to a local mathematics program. > >>I am aware of one program that formerly used Gene Murrow and Serge >>Lang's textbook Geometry (Springer-Verlag) and > > Lang has written "upteen" texts. This is one I have not read, > but the reviews warn me off this one for gifted students.
I have the book at hand, and it looks not too bad to me, maybe because Murrow (the co-author) moderates Lang's touch in how the content is expressed. It is a fact, however, that one program I know of has DROPPED this book after formerly using it. A good review of Murrow and Lang I have seen is by Professor Hung-hsi Wu of UC Berkeley,
who describes that textbook as the "rock bottom minimum" of what a high school geometry teacher should know about geometry. But of course that review implies that the book is suited for a teacher-training course at a university, and doesn't endorse it for gifted preteens and teenagers who later might be scientists or mathematicians.
>>in recent years has used Michael Serra's textbook Discovering Geometry >>(Key Curriculum Press). > > In my opinion, this text is inappropriate. It's designed for struggling > students.
Yeah, that is my dismaying impression too. I am by no means opposed to a "discovery" approach in presenting mathematics, but the content of Serra's textbook seems too easy for a course of the kind I am asking about, certainly not enough geometry for a last look at secondary geometry before a strong calculus sequence. I am told, by program participants, that most of the students in the program where the Serra text is now used think that the textbook talks down to them. Maybe the Serra text has to be used at a VERY young age, if at all, among stronger students--it looks all right to me as a middle-school-geometry book, although it definitely presupposes study of algebra.
>>What do you think? If you were recommending a textbook for a class of >>students selected for high math ability taking a first secondary-level >>geometry course, what would you recommend? What do you like >>about your preferred textbook? > > Look at: Elementary Geometry from an Advanced Standpoint, Third Edition > [FACSIMILE] by Edwin Moise. It's the one I would use. Read the reviews > on Amazon.com.
I have that book at hand too, and like it. I think I bought it originally because of the Amazon reviews that were posted as of early 2001. It's approach is quite different, because it starts out looking a lot like Landau's Grundlagen der Analysis, and gets into geometry proper (mostly from an analytical point of view rather than synthetic) only after laying a foundation of the ordered field properties of the real numbers. I would love to have anyone I know take a course in geometry based on that textbook: I wonder if the program I know of would dare to try it out?
Thanks for the interesting suggestion.
P.S. As you read this thread, do you see a second post, apparently in my name, that has garbage content? Either my newsreader is SERIOUSLY buggy, or somone on Usenet is hijacking threads. I thought this k12.ed.math newsgroup was moderated, and spam messages wouldn't get posted. I sent out a cancel message on the message "I" supposedly posted, but Google's archive still shows the junk message. My apologies to you and to the moderator for something that I didn't intend to do and didn't knowingly do. If this happens again, I will probably switch to a different newsreader.
[moderator responds to PS: Karl, the nonsense post posted under your email address is not through any action of your own. I have just posted your cancel mssg (you do not have the ability to do so, but I received the cancel message and have posted it now). That may or may not remove the nonsense message, due to a variety of issues with how Usenet works.
If you have further questions about this, please contact me privately. Although the newsgroup is moderated, there are ways to get around the moderation procedure, and the forgers of this nonsense message have done exactly that.]