Mary O’Malley

Math G - Dr. Ian Walton

December 9, 2002

Textbook Review

(A ≤ B)

            Iwent into the library wondering if it was possible to make an unbiasedcomparison of a book I used all semester to a book I would review for a fewshort hours.  It seemed like an overwhelmingtask to me until I had an idea. Why not apply some of the problem solving techniques we learned in classto this assignment?  

More specifically, why not use Polya’sfour-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 upinto the same four steps to make it more manageable.

            Thefirst step was easy.  I understoodthe problem (or more appropriately - the assignment).  Pick a math textbook from the list of books provided andcompare it to our textbook entitled “Mathematical Ideas” by Miller,Heeren and Hornsby.  I labeled mytextbook “Text A.”  Afterlooking 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 whichsign to place between A and B (=, ≥ or ≤).

            NextI needed to devise a plan to help me organize, categorize and analyze theinformation in both books in a manner that was easy to compare.  I set up two columns, labeling the firstcolumn “Text A” and the second column “Text B” and Ibegan to compare the contents of each of the textbooks.   First I compared the obviousthings; the size of the books, their table of contents, and the aestheticpresentation of the materials. Then I moved on to a more in-depth comparison.  I picked several mathematical conceptsthat were covered in class and looked for those sections in each of thebooks.  Finally, since I had not yetreviewed the material in our textbook on Euler’s theory (and, as with allnew math concepts, this one was not particularly clear to me) I decided to takean in-depth look at that material in both books and to try some of the problemsas well.

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

            Itwas difficult to compare the topics in each textbook using the Table ofContents alone because they were organized in completely different ways.  Text A was organized like a traditionalmath book, with each chapter dedicated to a clearly identified mathematicalconcept.  Text B was organized in amore social manner, with each chapter focusing on different types of real life problemsand the associated math required to solve them.  Even the language used to describe the mathematics wasdifferent.

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

            Toillustrate further, if you looked up Venn Diagrams and Sets in Text A, you wouldfind a well organized, comprehensive explanation in Chapter 2.  If you looked specifically for VennDiagrams or Sets in Text B, you would find a short section on Sets on pages626-632.  However, this was misleadingbecause although not specifically called Venn Diagrams in the other chapters ofText B, the concept of Venn Diagrams is used in several of the chapters (forexample the section on critical thinking in Chapter 1).  To make a good comparison of these twotextbooks, it is necessary to look beyond the Table of Contents.

            Onceinside the books it becomes increasingly obvious that although the mathematicalconcepts 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 technicalsounding) and I found myself enjoying the textbook much like I would enjoy anyother type of book.  I read Text Ato get through the problems.  I wasreading Text B because I found it interesting.

            Iparticularly enjoyed the “Human Side of Mathematics” presented atthe beginning of each chapter in Text B. Each of these segments introduced two mathematicians who contributed tothe mathematical concept discussed in the chapter.  They ranged from Hypatia, the first female mathematician tobe mentioned in the history of mathematics to Marilyn vos Savant, the modernday Ann Landers of mathematics with a wide variety of mathematicians in-between.  There were a total of 21 minibiographies, each of them equally fascinating.  While Text A does introduce some mathematicians, the excerptsare short and dry and they do not contain any of the interesting tidbits thatmade me want to read more.

            Ialso 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 couldimagine yourself in.  Discussionand explanations of the math necessary to solve the problem are followed byeasy to understand explanations and examples.  Text B also does a very good job of defining key words.  Text A was not particularly good atthat.  At the end of each chapter(before the problem section), the solution to the initial problem is presentedand discussed.  I felt that Text B gavemore thorough explanations and spent more time applying the math to real-lifescenarios.  In general, Text B waseasier 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 understandexplanations.  In fact, thatparticular section was so helpful that I copied it to use as reference materialfor 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 issuperior.  For instance, Text A givescomprehensive, easy to understand explanations of Permutations andCombinations.  These were not evendiscussed in Text B (at least not as far as I could tell).  Text A also has a very nice Index ofApplications which allows you to look up and locate any of the many types ofproblems presented in the textbook by name (such as the Birthday problem onpage 682). The problems and keywords were further broken down into easy toidentify categories such as Consumer Information and Engineering.  Text B does not have this type ofindex.  In fact, the regular indexin Text B is substantially smaller and less comprehensive than the one in TextA. 

Summary

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

            TextA on the other hand, is geared toward the more mathematically inclined student.  It’s primary focus is themath.  It is better organized, morecomprehensive, and takes a technical, in-depth approach to mathematicalconcepts.

            Sofor me, A ≤ B but that is just a theory based on my review andbias’.  It may or may not betrue for others. Perhaps you have already received a counter-example from oneof my classmates.