Date: Apr 2, 1995 7:04 PM Author: Tom McDougal Subject: Serra's _Discovering Geometry_ 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