Mary O’Malley

Math G - Dr. Ian Walton

December 9, 2002

 

Textbook Review

(A ≤ B)

 

 

            I went into the library wondering if it was possible to make an unbiased comparison of a book I used all semester to a book I would review for a few short hours.  It seemed like an overwhelming task to me until I had an idea.  Why not apply some of the problem solving techniques we learned in class to this assignment?  

More specifically, why not use Polya’s four-step process.

1.     Understand the problem

2.     Devise a plan

3.     Carry out the plan

4.     Look back and check

I could break this assignment up into the same four steps to make it more manageable.

            The first step was easy.  I understood the problem (or more appropriately - the assignment).  Pick a math textbook from the list of books provided and compare it to our textbook entitled “Mathematical Ideas” by Miller, Heeren and Hornsby.  I labeled my textbook “Text A.”  After looking at several of the books on the list, I decided on the textbook entitled “Math in Life, Society & the World” by Parks and Musser.  I labeled this “Text B.”  My assignment was to determine which sign to place between A and B (=, ≥ or ≤).

            Next I needed to devise a plan to help me organize, categorize and analyze the information in both books in a manner that was easy to compare.  I set up two columns, labeling the first column “Text A” and the second column “Text B” and I began to compare the contents of each of the textbooks.   First I compared the obvious things; the size of the books, their table of contents, and the aesthetic presentation of the materials. Then I moved on to a more in-depth comparison.  I picked several mathematical concepts that were covered in class and looked for those sections in each of the books.  Finally, since I had not yet reviewed the material in our textbook on Euler’s theory (and, as with all new math concepts, this one was not particularly clear to me) I decided to take an in-depth look at that material in both books and to try some of the problems as well.

            The textbooks were similar in size. Text A contained approximately 900 pages and Text B contained approximately 740 pages.  Text A contained 15 chapters and Text B contained 12 chapters plus a chapter at the end on review topics.  The review chapter contained some good basic refresher information that would probably have come in handy during the semester.   Text A was definitely flashier in appearance, containing a variety of colors, advanced graphics and a more sophisticated appearance.  All information in Text B was in black ink with the exception of the examples which were in blue ink.

            It was difficult to compare the topics in each textbook using the Table of Contents alone because they were organized in completely different ways.  Text A was organized like a traditional math book, with each chapter dedicated to a clearly identified mathematical concept.  Text B was organized in a more social manner, with each chapter focusing on different types of real life problems and the associated math required to solve them.  Even the language used to describe the mathematics was different.

            For example, when discussing geometry and Euler’s theory, Text A talked about “Networks,” which it described as “a modern branch of geometry using graph theory…..to show points between vertices or nodes (a more Silicon Valley high tech type of approach), while Text B described the same information as “routing problems” and used a map of the United States to illustrate the problem of getting from point A to point B on a road trip.

            To illustrate further, if you looked up Venn Diagrams and Sets in Text A, you would find a well organized, comprehensive explanation in Chapter 2.  If you looked specifically for Venn Diagrams or Sets in Text B, you would find a short section on Sets on pages 626-632.  However, this was misleading because although not specifically called Venn Diagrams in the other chapters of Text B, the concept of Venn Diagrams is used in several of the chapters (for example the section on critical thinking in Chapter 1).  To make a good comparison of these two textbooks, it is necessary to look beyond the Table of Contents.

            Once inside the books it becomes increasingly obvious that although the mathematical concepts contained in each book are similar, the approach is not.  Text A, although very well organized, takes a more technical approach.  The focus is on the numbers and the problems.  It is geared to teach math.  Text B on the other hand is much more “chatty.”  The English is easier (less technical sounding) and I found myself enjoying the textbook much like I would enjoy any other type of book.  I read Text A to get through the problems.  I was reading Text B because I found it interesting.

            I particularly enjoyed the “Human Side of Mathematics” presented at the beginning of each chapter in Text B.  Each of these segments introduced two mathematicians who contributed to the mathematical concept discussed in the chapter.  They ranged from Hypatia, the first female mathematician to be mentioned in the history of mathematics to Marilyn vos Savant, the modern day Ann Landers of mathematics with a wide variety of mathematicians in-between.  There were a total of 21 mini biographies, each of them equally fascinating.  While Text A does introduce some mathematicians, the excerpts are short and dry and they do not contain any of the interesting tidbits that made me want to read more.

            I also liked the format of the chapters in Text B.  They started with the “Human Side of Mathematics,” then presented an initial problem based on some real life scenario you could imagine yourself in.  Discussion and explanations of the math necessary to solve the problem are followed by easy to understand explanations and examples.  Text B also does a very good job of defining key words.  Text A was not particularly good at that.  At the end of each chapter (before the problem section), the solution to the initial problem is presented and discussed.  I felt that Text B gave more thorough explanations and spent more time applying the math to real-life scenarios.  In general, Text B was easier for me to understand.

            Finally, in comparing the material on Euler’s theory in Text A to that of Text B, I found Text B to be a more thorough presentation with easier to understand explanations.  In fact, that particular section was so helpful that I copied it to use as reference material for our second take-home exercise.

            However, I do not want to give the impression that Text A is completely lacking.  There are several areas where Text A is superior.  For instance, Text A gives comprehensive, easy to understand explanations of Permutations and Combinations.  These were not even discussed in Text B (at least not as far as I could tell).  Text A also has a very nice Index of Applications which allows you to look up and locate any of the many types of problems presented in the textbook by name (such as the Birthday problem on page 682). The problems and keywords were further broken down into easy to identify categories such as Consumer Information and Engineering.  Text B does not have this type of index.  In fact, the regular index in Text B is substantially smaller and less comprehensive than the one in Text A. 

 

Summary

            It is difficult to say which of these textbooks is better. In fact, I don’t think one is better than the other.  They are just very different.  Text B is geared for the class made up primarily of students who do not plan to go on to a higher level of mathematics.  It is geared toward the student (who much like myself) is not particularly good at math but is interested in the general principals and the historical aspects of math.  Text B takes a less intimidating, more “entertaining” approach to math.

            Text A on the other hand, is geared toward the more mathematically inclined student.  It’s primary focus is the math.  It is better organized, more comprehensive, and takes a technical, in-depth approach to mathematical concepts.

            So for me, A ≤ B but that is just a theory based on my review and bias’.  It may or may not be true for others. Perhaps you have already received a counter-example from one of my classmates.