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Topic: Serra's Discovering Geometry, Rhoad's Geometry for Enjoyment
Replies: 17   Last Post: Jul 10, 2013 10:45 AM

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Linda Dodge

Posts: 1
Registered: 12/6/04
Re: Serra's _Discovering Geometry_
Posted: Apr 6, 1995 4:39 PM
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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
>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
>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,
>(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

Linda Dodge
Math Consultant
Frontier Regional High School
South Deerfield, MA

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