The Math Forum’s Dr. Math Gets You Ready for Algebra is a very user-friendly book written with a view to help students make the leap from arithmetic to algebra. It is a well-organized collection of letters from students and answers provided to them by the Math Forum’s "Ask Dr. Math" service. The letters were written by actual students who were having difficulty understanding concepts that are a basis for Algebra. The answers were provided by trained volunteers who were drawn from a pool of college students, mathematicians and teachers in the mathematics community, and referred to collectively as "Dr. Math". The answers are insightful and presented in an elegant and simple manner that makes them accessible to any student.
The book is divided into five parts. Part I begins with interesting questions such as "What is Algebra?" and "How does one start thinking algebraically"? These are difficult questions to answer, but Dr. Math does a very good job of giving simple, to the point, and easy to understand explanations. This part also includes a discussion of variables, exponents, scientific notation, infinity, order of operations, the distributive property for polynomials, etc..
The notion of a variable is explained in different ways, including references to real life situations where the use of variables to represent numbers we do not know yet is crucial. Dr. Math explains how understanding the definition of an exponent easily leads to the various properties of exponents. "He" then illustrates the use of exponents and scientific notation to simplify the process of doing numerical calculations by hand and to express some very large or very small numbers. For instance, it is shown how 1.05120 can be calculated by hand with only 9 multiplications.
Infinity is a difficult concept for students to grasp. Dr. Math gives an interesting explanation of infinity, emphasizing that infinity is not a number. "He" then goes deeper to explain how infinite sets are categorized into countably and uncountably infinite, which I’m sure students would find interesting. Dr. Math does an excellent job of explaining that PEMDAS is merely a good convention for the order of the fundamental operations and that you can use different orders of operations and come up with a perfectly consistent mathematical system. To explain why the distributive property for polynomials works the way it does, Dr. Math neatly models multiplication of polynomials after multiplication of numbers so that it looks familiar.
In Part II, Dr. Math explains the concept of integers. A detailed account of how the fundamental operations work with integers is given. To answer the frequently asked question, "Why is a negative number times a negative number positive?", Dr. Math gives several good explanations, as there is no single visualization that works for everyone. This part ends with a discussion of absolute value, along with some practical applications of this concept.
In Part III, Dr. Math introduces students to real numbers. A simple and interesting discussion of why 0.999... = 1 and of what it means for a decimal to repeat forever is given. The concepts of prime factorization, greatest common factor and least common denominator are explained thoroughly. Dr. Math shows how one can approximate square roots by hand by repeated use of division and averages. This leads to a discussion of irrational numbers, including a brief history of π. The authors then help students visualize the relationships between the sets of whole numbers, integers, rational and irrational numbers as subsets of real numbers with the aid of Venn diagrams.
In Part IV Dr. Math explains the importance of being able to solve equations and gives highly detailed step-by-step instructions for solving linear equations. Moreover, a neat explanation of why we can subtract one equation from the other when solving a system of two equations in two unknowns is given.
Part V, the concluding part of the book, aptly discusses applications that demonstrate the uses of numbers, equations and variables. Some of the problems described here deal with ratio and proportion, area and perimeter, distance, rate and time, and rate of work. Students having trouble with distance, rate and time problems would definitely benefit from this section. Dr. Math introduces these concepts with carefully chosen examples and does a great job of explaining some tricky problems posed by students on this topic.
In conclusion, this book cannot be used as a textbook but would certainly be a very good reference for Prealgebra/Beginning Algebra students and teachers. Its unique question and answer format makes it interesting for students to read. The language is simple and explanations are clear and precise. Prealgebra students will be able to read this book by themselves. They will also be able to relate to many of the questions in the book because they are likely to have encountered similar questions during their course. Students who do not have difficulty in understanding prealgebra will also benefit from this book, as it will get them to think more deeply about the concepts and clarify some misconceptions they might have.
This book includes many great questions asked by students, questions which would require some thought on the teacher’s part to answer effectively on the spur of the moment. This makes the book a good reference for prealgebra teachers. Moreover, numerous web resources that provide practice problems, group activities, real life applications etc. have been listed at the end of each part of the book. Instructors could take advantage of these web resources to enhance teaching and learning in the classroom.
Hema Gopalakrishnan (GopalakrishnanH@sacredheart.edu) is assistant professor of mathematics at Sacred Heart University