Ah, it seems like I have created a little stir, due to my sloppiness with words! Hopefully this will clarify some things, but maybe not!! > I just wanted to day how saddened I am by the proposed constraints > within which a geometry book should be 'good'. Sorry for the term 'good'! I deliberately put this in quotes to show that this was a subjective opinion. I am looking for a book that stresses formal proof so this is 'good' for me. Another teacher with a different approach would want a different type of book. I am in no way saying that other approaches are bad. In fact, I think that it is a wonderful that they're many approaches to choose from because different teachers teach in different ways. What works for one teacher might not work for another. In no way am I saying that this is a definitive list or the only good books. I am just trying to be helpful to others that are looking for what I seek. I can debate what the right teaching method is but ultimately it is in the results that I get with the students that matters (more on this below). I may find that a textbook has great success in my class, but the same text falls flat in another. The proof is in the pudding! (pun intended)
> Formal proof IS a piece of mathematics - but only a piece. Yes this is quite true. There is some proof in the algebra I teach (the Students explore and derive everything in class themselves) but I wanted to have proof presented in a formal mathematical way and in my opinion geometry is a good place to do this (less abstract than building algebra from the ground up)
> I hate to see a classroom that tastes like a medicine cabinet rather > that the life of mathematics. You should see my class. I am teaching an algebra 1 class for ages 11-13 where we meet once a week for 3 hours and the students are having a great time. One mother told me a story where her son told her about a nightmare he had where in his bad dream my math class had been replaced by soccer! The parents are ecstatic that math can be so much fun. Half of the students are doing extra homework just because they love it (and the regular load of homework is around 160-200 problems a week and we are using a college text). I was skeptical that students between the ages of 11-13 could pay attention for 3 hours, but the energy in the class is fantastic and they are able to stay on top of it. We have a lot of fun. For example, we were discussing Cantors proof of why the rational numbers are the same order of infinity as the positive integers and the students were able to derive a symbolic formula of how to calculate the integer pairing for any square in the table. And they did this in about 30 minuets! Wow I was impressed. And I could go on and on and on, I am so proud of them. (By the way, this is not a special upper track math class, I have a wide range of student's). I am using a dreadfully boring drill and kill college algebra book that works perfectly with my style.
>It is particularly sad when a rich > and important subject like geometry is pushed into a box of > formal proof. Probably means very little transformations > (probably the key part of applications of geometry) and very > little 3-D geometry - at least until the students have been > so saturated in plane games that they have lost touch with > the world they live in. A book is a springboard for a teacher like me. My whole class is taught using the Socratic method so the students are doing a lot of thinking out of the box all the time. We are constantly doing puzzlers and brainteaser that are woven into class. We also do physics experiments, etc. My point is that I start with the book and do a lot of enrichment way beyond the scope of the book which would be 3-D geometry, etc. I could go on about my philosophy of teaching, but what matters to me is what works for me as a teacher and produces results. When I say results, I mean that I am expanding the students minds to think creatively out of the box visa vie math, have a firm understanding of why things work they way they do (so they are not just memorizing rules), they are getting excited about math and be prepared to do problems (lets say problems from a physics textbook). I have found that the exploratory textbooks that for example Key Curriculum Press publishes, don't work for me and therefore don't work in my classroom. But when I use the 'medicine cabinet' books I get results as defined above. Remember what works for me might not work for the next teacher. Teaching is an art, not a science and there is room form many different and divergent approaches to math. And I firmly believe that there is no one right approach. You might ask, why don't you use an exploratory book since your class is in this direction. To answer this question lets take algebra as an example. What I have found out for me is that the old drill and kill approach has merit and I want the students to go home and drill. The exploratory books I have reviewed and used don't do enough drill for me. By the way, I supplement their homework with explorations. Remember, the proof is in the pudding, and if I had a class of bored students or students that were not learning I would change in a heartbeat. The parents are paying me to teach their children and if this was a mediocre or average class they would leave, I assure you!
Diversity of opinion is what makes the world a great place. The same is true of teachers and teaching methods. Take care Alan PS: missed 2 suggested books A Course in Geometry: Plane & Solid" by Weeks and Adkins. Books by Welchons and Krickenberger