
Re: Serra's _Discovering Geometry_
Posted:
Apr 6, 1995 4:39 PM


Several years back we adopted the Serra thinking it the best thing "since sliced bread"...to quote a previous posting but we, too, saw the difficulty with too few problems in the problem sets. Also, when a brand new teacher came on board, it was difficult for him to teach from the book. So, I would say Serra is a fantastic teacher resource and I think the discoveries are well worth doing but the overall book gets a C+/B from me.
Do we really need a full year of geometry, anyway?
In a previous article, mcdougal@cs.uchicago.edu (Tom McDougal) says:
>In article <Pine.3.89.9503161947.A54450100000@belnet.bellevue.k12.wa.us> >Art Mabbott, mabbotta@belnet.bellevue.k12.wa.us 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 afterschool tutoring program for innercity >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 loosygoosey approach does not >seem to be effective. The book asks students to make arguments supporting >various conclusions (just like any proofbased 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, proofbased >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. > > >Tom McDougal University of Chicago Artificial Intelligence > mailto:mcdougal@cs.uchicago.edu > http://cswww.uchicago.edu/~mcdougal > PPRH >
 Linda Dodge Math Consultant Frontier Regional High School South Deerfield, MA

