In article <Pine.3.89.9503161947.A5445email@example.com> Art Mabbott, firstname.lastname@example.org writes: >I cannot more strongly >recommend Michael Serra's Discovering Geometry - An Inductive Approach. >It is an incredible text. In my opinion, it is the best thing since >sliced bread.
Since other posters seem to agree with this view, I want to provide a different opinion.
Working as a volunteer at an after-school tutoring program for inner-city kids, I have had a very negative experience with the Serra book. I have three complaints with it.
My first complaint is with the problems. The selection is very small and the problems get hard very quickly. There is also very little variety, and little connection between problem sets.
My second complaint is with the lack of examples. Students are expected to go out and use new relationships and new facts with almost no problem- solving examples to guide them.
Related to this, the book does not pay attention to the difficulty students often have in (visually) recognizing certain patterns. For example, it does not help students learn to identify overlapping triangles.
Third, it is very difficult to go back and look stuff up. The kids often forget the various theorems/concepts. When we flip back several pages, all we find are uncompleted conjectures.
Finally, when it comes to proof, the loosy-goosey approach does not seem to be effective. The book asks students to make arguments supporting various conclusions (just like any proof-based book) but provides no help to the students in learning *how* to make such arguments. Imagine what a student would do if she were home sick for an extended period?
Now, many of the complaints listed above are true of other, proof-based books as well. But they are not true of _Geometry for Enjoyment & Challenge_, by Rhoad, Whipple, & Milauskas, published by McDougal, Littell.
(Truth in advertising: I used to work for McDougal, Littell, but only since then, in my tutoring experience, have I come to appreciate the merits of that book. Furthermore, although my father started McDougal, Littell, the company is now owned by Houghton Mifflin. So I have no current connection with the company or this book.)
This book was written by three teachers, two of whom have won the Presidential award for teaching. Their teaching skill and their understanding of students is evident in the book.
The problem sets in the Rhoad book are large & diverse and build slowly in difficulty. Each problem has its own diagram, so kids don't get confused about what is given. The problems build on similar problems in earlier lessons.
The Rhoad book provides lots of sample problems showing how each new idea can fit into a proof or be used to solve a problem.
The Rhoad book helps students learn to recognize visual patterns. When the three main triangle congruence theorems are introduced, the book devotes considerable space -- in the sample problems and in the problem set -- to showing diagrams and asking students merely to identify which theorem (if any) applies. It devotes an entire lesson to overlapping triangles. It shows students the "N", "Z", and "F" patterns associated with parallel lines cut by a transversal and also shows students how alternate interior angles can occur in more complicated figures, esp. parallelograms with diagonals drawn in.
The bottom line is, it all seems to work. The kids I have worked with who use the McDougal, Littell book perform head and shoulders above all the others in terms of their understanding of geometry concepts and their ability to write mathematical arguments.
I agree with the goal that students should discover geometry relations for themselves. One can pursue this goal no matter what text one uses. In fact, I conjecture that the success people have had with the Serra book is due more to a change in their teaching than to the contents of the book. However, as a source of problems, as a source of examples, and as a reference for the student to use while working at home, the Serra book is a disaster.