Date: Apr 6, 1995 4:39 PM Author: Linda Dodge Subject: Re: Serra's _Discovering Geometry_

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.A5445-0100000@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 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.

>

>--

>Tom McDougal University of Chicago Artificial Intelligence

> mailto:mcdougal@cs.uchicago.edu

> http://cs-www.uchicago.edu/~mcdougal

> PP-RH

>

--

Linda Dodge

Math Consultant

Frontier Regional High School

South Deerfield, MA