Mathematics Textbooks Comparison - Case Study Example

Running head: mathematics textbook comparison 31st July Introduction In their efforts to achieve economic, political and social development, many countries have taken initiatives to improve their curriculum by ensuring that college and university students are provided with strong mathematics abilities. One of the key aspects that have led to developments in countries such as US, Japan and China is improved technology. According to 2012 results by the Program for International Student Assessment, US students performed below average in the field of mathematics among the most developed countries in the world. Key performers in mathematics were noted in countries such as Shanghai, Hong Kong, South Korea, Japan, and Taiwan among others. In its effort to improve the performance of mathematics among the students, the US government has allowed the establishment of various mathematics text book publishers. Some of the notable publishers include Addison Wesley & Benjamin Cummings, American Mathematical Society, Athena Scientific, Chartwell-Yorke, and Copernicus among others. This paper seeks to review three currently available mathematics textbooks that are intended to provide college students with the appropriate mathematical concepts. Strengths and weaknesses of the textbooks Abstract Algebra: Theory and Applications Abstract Algebra: Theory and Applications is a mathematics textbook that was written by Thomas Judson. Having been reviewed by Linda Pedersen who is a professor of Mathematics, the book is useful for community college students. Additionally, the book is useful for science and math major. Some of the notable aspects of Abstract Algebra: Theory and Applications book is that it is well designed, innovative in the approach it emulates, as well as being adaptive. Contrary to the approaches used by other mathematics books, this book employs the approach of introducing examples first followed by proofs and then formal definitions (Benson, 2000). One of the major advantages of Abstract Algebra: Theory and Applications book is that it provides answers to the well chosen exercises that it provides. In order to make the students appropriately understand the concepts covered by the book, each of the chapters provides a section of history as well as the applications of the theory. In this way, the students are able to effectively tackle the exercises provided at the end of each chapter. In terms of accuracy, readability, interface, consistency, reading level, content usefulness, modularity, and clarity the book has a maximum rating of 5. However, the book does not cover aspects of cultural relevance. This makes it different from other books such as Applied Finite Mathematics which has a rating of 4.9 in terms of cultural relevance. A First Course in Linear Algebra A First Course in Linear Algebra is another useful book for mathematics student. The author, Robert Beezer, covers quite a number of areas aimed at improving the mathematical skills of college as well senior level students. One of the key strength of A First Course in Linear Algebra textbook is that it uses friendly and conversational writing style. As a result, the students are in a position to appropriately understand its concepts. Additionally, the book has maximum rating of 5 on the accuracy, consistency, and interface aspects. However, the book, which was reviewed by Ab Kader, has several weaknesses. These include low level of rating on readability, modularity, and cultural relevance. Collaborative Statistics One of the major areas of mathematics that student must be knowledgeable is statistics. With this awareness, Barbara Illowsky and Susan Dean authored the Collaborative Statistics textbook for college students. The book provides excellent concepts of statistics that are easily understood by the students. In order to ensure that the students fully understand the concepts covered by each of the chapters of the Collaborative Statistics, the authors provide the material in a unified and understandable manner. The book, whose focus is more on the applications of statistical knowledge than the theory behind it, provides introductory statistics concepts that make the student to understand complex statistical applications in their future studies and research. Some of the key areas that Collaborative Statistics has acquired high rating include accuracy, interface, cultural relevance, and appropriateness. Major areas of weaknesses include modularity, content usefulness and reading level. In addition, Collaborative Statistics text book provides some chapters that have advanced statistics for novice mathematics students. This entails complex computations that do not indicate clearly how the authors arrived at the answers. A critique of the instructional approach of the textbooks Abstract Algebra: Theory and Applications Abstract Algebra: Theory and Applications instructional approach aims at making the students have the ability to deal with the mathematical problem. By the use of algorithm approach, that entails the procedure of solving the mathematical problem, the book provides effective guidelines to the students. However, the book approach on some areas such as cryptography, an area that deals with data integrity and confidentiality is not standard (Ibrahim, 1992). Additionally, there are some cases where an exercising is asking for a result that is already proven in the book an indication of editing flaws. Even though it is a good book as far as abstract algebra is concerned, the book is hard-comprehensible especially for the group parts (Thomas, 2013). For new students to clearly understand the concepts adopted by Abstract Algebra: Theory and Applications, they need to have preliminary reading for example from Robert Messer book referred to as Linear Algebra-Gateway To Mathematics. A First Course in Linear Algebra As indicated earlier, A First Course in Linear Algebra by Robert Beezer, writing style of style is not only conversational but also friendly. The author emulates the approach of concepts in order to make the math students understand the content of the book. The book introduction parts expose a student to system of liner equations, followed by matrix algebra and then vector spaces (Robert, 2012). However, based on the weakness of low modularity, the concepts covered by A First Course in Linear Algebra are not appropriately understood by the students. Additionally, the problem of lack of adequate readability makes it hard for the students to get accurately the mathematical concepts that the book is offering. Collaborative Statistics Collaborative Statistics text book aims at using statistical knowledge instead of the approach of use of theory like some of the books. One of the major approaches that make this book to be appropriate for new students in the field of statistics is the use of simple introductory mathematical concepts that makes the student to effectively understand the concepts in other chapters. Additionally, the book has expository texts, homework as well as projects that make the student to have practical experience. However, due to some errors, Shane Rollans, one of the senior lecturers at the Thompson Rivers University indicates that virtually all the graphs in the book are done badly (Barbara and Susan, 2012). On the part of clarity, Shane indicates that Collaborative Statistics text book provides clear text in most places but not clear in others. Other important issues that Shane indicates lack is the boot includes lack of section on ethics, lack of coverage of probability plots and generally lack of motivation to study statistics. A rationale for selecting one of the textbooks over the other Based on the need to get the right mathematics book that provides learners with adequate and useful information, there is a need to come up with a strategy of selecting the text books. A rationale for selecting one of the three books which includes Abstract Algebra: Theory and Applications, A First Course in Linear Algebra and Collaborative Statistics entails rating the key aspects of the books. The table below indicates the comparison of the books based on various aspects. Rating Books Clarity Accuracy Consistency Interface Appropriateness Overall Average Abstract Algebra: Theory and Applications 5.0 5.0 5.0 5.0 5.0 5.0 A First Course in Linear Algebra 4.8 5.0 5.0 5.0 4.8 4.8 Collaborative Statistics 3.8 4.8 4.6 n/a 3.7 3.9 Based on the above table, it is clear that Abstract Algebra: Theory and Applications has the highest rating implying that in terms of improving the mathematics skills of the college students it is the best over the other two. In all the bases of rating, Abstract Algebra: Theory and Applications has the maximum rating while Collaborative Statistics has the worst rating. Conclusion In order curb with the deteriorating performance in mathematics among the US students and other learners, it is essential for the authors to publish books that cover modern concepts that are demanded by the global economy. The paper has covered various weaknesses and strengths of the three books namely Abstract Algebra: Theory and Applications, A First Course in Linear Algebra and Collaborative Statistics. Additionally, the paper has covered critique of the instructional approach of the textbooks. Based on the high demand for technology in all sectors on the economy, it is vital for the publishers to cover the aspects of technology and innovation in the math text books. As indicated in the paper the rating that is done by the students is a major aspect that makes certain books to be preferred to others. References Barbara, I and Susan, D. (2012). Collaborative Statistics. California: De Anza College. Benson, C. (2000). The Moment of Proof: Mathematical Epiphanies. New York: Oxford University Press. Ibrahim, A. (1992). The Origins of Cryptology: the Arab Contributions, Cryptologia, vol. 16, no. 2 (April 1992), pp. 7–26. Robert, B. (2012). A First Course in Linear Algebra. New York: Congruent Press. Thomas, W. (2013). Abstract Algebra: Theory and Applications. New York: Orthogonal Publishing. Read More