Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

 Messages: [ Previous | Next ]
 Michael Keyton Posts: 138 Registered: 12/3/04
Re: Serra's _Discovering Geometry_
Posted: Apr 2, 1995 7:04 PM

Is this book referred to by Rhoad, Milauskas, ... written by teachers at
a school called NewTrier(?) near Chicago. If so, I agree that the
problems are superb but the organization and the development of the book
is by far one of the worst ever presented on American education. They
confuse theorem/proof, axiomatic development, and definition to the point
of hopelessness.
For example, in one of the sections there is presented the "Isosceles
Triangle Theorem" without proof, with an indication that it will follow
in the exercises. In the exercises, the following problem is presented:
Given: AB = AC in Triangle ABC; Prove: <A = <B (I have used equals for
congruent here.)
Following is the "Proof"
1. AB = AC 1. Given
2. <A = <B 2. Isoscles Triangle Theorem

To me, any author who believes this even begins to resemble a proof needs
to investigate mathematics.

Throughout, in the middle of a proof, suddenly a new "property",
"theorem", or "postulate" is referenced without any foundation. My
inquiry is if this is permissable then why not reference the "theorem" in
question as a known (or obvious) idea.

Rarely, did I find a definition written with any degree of semblance of
meaning. Within mnay there is little distinction between properties and
objects, there is confusion between the object defined and the property
defining the object.

As far as the problems, I can not remember any problem contained therein

What I found to be a strength of the book was the constant use of
algebra, though in many cases the problems were forced and artificial.
For example, one base angle of an isosceles triangle is 3 more than twice
some number, the other angle is 5 less than three times the number, what
is the number. (As thought "the number" had any meaning at all.)

Michael Keyton
St. Mark's School of Texas

On 2 Apr 1995, Tom McDougal wrote:

> 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

>
> 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 &
> 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
>

Date Subject Author
4/2/95 Tom McDougal
4/2/95 Michael Keyton
4/3/95 Tom McDougal
4/3/95 Lynn Stallings
4/3/95 Lois B. Burke
4/4/95 John A Benson
5/27/10 Todd Miller
12/20/12 Achla
7/10/13 Debbie Hunt
4/5/95 Lee Rudolph
4/5/95 Dennis Wallace
4/5/95 Lois B. Burke
4/6/95 Linda Dodge
4/11/95 Michael Keyton
4/6/95 Top Hat Salmon
4/7/95 F. Alexander Norman
4/11/95 Mike de Villiers
4/29/08 Raja Singh