Example Of Mathematics Textbook Evaluation Essay

Mathematics is a complex subject that calls for critical thinking skills and not so many students find it interesting (Rathwon, 1999). There has been concerted effort to improve mathematics abilities of American students, and in line with this, so many mathematics books have been published (NCEO, 2010). With excess competition in this niche, many books purport to offer the best instructional guide for learners. For that matter, this book evaluates three mathematics books on the basis of the strengths and weaknesses of their instructional approaches. Mathematics is a very wide subject with different topics. This paper will dwell on books that have studied algebra.
The first book, Contemporary Abstract Algebra, was authored by Joseph Gallian. The seventh edition of this book has been advanced and has made the study of abstract algebra friendly and encouraging. It is essential to recognize the fact that algebra is one of the most challenging topics in mathematics. Most students are discouraged to attempt algebraic sums because of the perception that this topic is hard. However, Gallian has taken the responsibility of making algebra clear and gives the learners the much needed enthusiasm. Unlike other books that dwell on rigor, Gallian’s book has concentrated on making the readability of the concepts easy. His book provides a solid starting point for beginners. The writing of the author is not only inviting, but also comprehensive. He handles every topic gently and provides numerous examples and exercises, as well as a numerous biographies on outstanding mathematicians. Gallian’s book makes a friendly companion for both instructors and students. Additionally, the book gives numerous practical examples where the algebraic concepts can be applied in real life. The author highlights how these concepts can be employed by mathematicians, computer experts, physicists, and chemists. Besides, the book is filled with different figures, charts, examples, tables, photographs, and computer exercises.
Another instrumental merit of this book is that the author provides definitions for difficult questions and theorems, as well as employs diagrams in the description of those definitions or theorems. Besides, the author has made each chapter concise, and for that matter, the readers is not bored. The first 22 chapters address the major concepts that are normally covered in an undergraduate algebra course. In the final nine chapters, the authors addresses other topics that are often ignored by other authors such as finite simple groups, Frieze groups, Galois theory, coding theory, and Sylow theorems. These chapters offer students with resourceful information that would help them in completing their research projects. In each chapter, there are exercises ranging from 20-80, and in others, there are supplemental exercises. Most importantly, the author provides hints and solutions to a number of exercises. This resource is exceptionally vital because it helps students test their understanding at the end of each chapter. The hint encourage students to attempt the exercises provided.
However, the book has some few demerits. The author has not included questions with true or false options. Such questions are vital in testing the students’ comprehension of the concepts. Another major undoing is that the publisher keeps on coming with new editions that lack significant news ideas. Thirdly, there are no CDs or e-copies; students have to use the printed copy.
The second book is Abstract Algebra authored by David Dummit and Richard Foote. This book easily catches the attention of algebraic students because of its conciseness. The authors have provided detailed information on every page. The authors have presented the concepts in an open and relaxed manner, and this strategy effectively introduces learners into the realm of complex algebraic theories and concepts. Another vital aspect of this book is that it successfully narrows the gap between graduate and undergraduate algebraic studies. Additionally, the book has significant succinct proofs and numerous clear examples and exercises. The authors manage to construct the theories of various algebraic structures and provide definitions of complex terms.
The instructional approaches are user friendly. The authors have provided a detailed description of the some of the most difficult concepts such as a clear developing of the group, field, and ring theory, as well as dozens of exercises at the end of every chapter. Besides, the authors highlight different examples in the text. This approach is extremely vital because it helps the reader to connect with the authors. In other words, the reader gets a succinct example of how those concepts can be applied.
However, the instructional approaches used by David Dummit and Richard Foote have a few shortcomings. First, the authors do not provide hints to the numerous exercises in the book. There is no usage of true or false questions; these questions are exceptionally helpful in gauging how well the reader has understood the concepts at hand. Additionally, some of the chapters have not been given much consideration; they have not been simplified as the preceding chapters. At some point, the student might be discouraged when they encounter complex topics with less clarity in the explanations given. On top of that, there is no CD for the book, and for that matter, students must use the printed copy.
The third and final book is Practical Algebra: A Self-Teaching Guide, Second Edition authored Peter Selby and Steve Slavin. This book has some if the best instructional approaches in algebra. The authors champion the use of “learn-by-doing approach”. This book can be used either at the elementary or intermediate level. The format of the book is significantly user friendly, and it can be used during individual study outside the classroom. The “learn-by-doing” approach encourages the learners to take the charge of the learning process. Unlike other approaches, this approach encourages the practical part; it has less theory but more of practical activities and exercises. The authors also use the pre-test approach that helps the readers to identify problematic areas as early as possible, as well as skip areas that they feel have been well understood. This approach helps make the learning process enjoyable; less cumbersome.
Additionally, the authors have also used post-tests. The post-tests are used for self-evaluation. The approach employed by Peter Selby and Steve Slavin champions the practical aspects of the learner by providing the techniques that learners can use in problem-solving in different disciplines. The approach provides step-by-steps techniques in solving algebraic equations. Students can do it practically and at their own pace. Most importantly, self-tests at the end of every chapter help the learners to gauge their mastery of the concepts they have learned. This book has a few demerits. Firstly, it is not as detailed as the other two books. It requires a learner who has some basic information on algebra. Secondly, it has fewer chapters than the other two books meaning that the reader has to find additional information from other sources.
The study of mathematics requires the deployment of easy to use instructional materials. The materials ought to provide a detailed description of the key concepts and theorems, provide sufficient examples, and numerous exercises. They should also provide the learners with hints and alternative resources that will help in solving those exercises. Contemporary Abstract Algebra, authored by Joseph Gallian fits into this description.

References

Dummit, D., and Foote, R. (2003). Abstract Algebra authored. New York: John Wiley and Sons.
Gallian, J. (2009). Contemporary Abstract Algebra. Boston: Cengage Learning.
National Center of Educational Outcomes (NCEO). (2010). Glossary of Math Teaching Strategies. Retrieved from http://www.cehd.umn.edu/nceo/presentations/nctmlepiepstrategiesmathglossaryhandout.p df
Rathwon, N. (1999). Effective School Interventions: Strategies for Enhancing Academic Achievement and Social Competence. New York: The Guilford Press NYC.
Selby, P., and Slavin, S. (1991). Practical Algebra: A Self-Teaching Guide, Second Edition.
New York: John Wiley and Sons.