Writing Math Research Papers: A Guide for High School Students and Instructors (4th Edition)
reviewed by Mary M. Capraro & Mahati Kopparla - October 21, 2015
Title: Writing Math Research Papers: A Guide for High School Students and Instructors (4th Edition)
Author(s): Robert Gerver
Publisher: Information Age Publishing, Charlotte
ISBN: 1623968631, Pages: 298, Year: 2014
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Through Writing Math Research Papers: A Guide for High School Students and Instructors, Robert Gerver speaks to both high school students and their teachers, providing valuable insights and suggestions for instructors seeking to make mathematics more engaging and meaningful. The book puts into practice the words of Aristotle: What we have to learn to do, we learn by doing (Broadie & Rowe, 2002). Chapters One through Twelve are mainly for high school students, while Chapter Thirteen is a guide for instructors and administrators. The authors expertise in research and mathematics is evident throughout the text. He uses a broad literary strategy that provides students, teachers, administrators, and even lay readers with clear takeaways. The unique style allows for various audiences to experience the message through the eyes and experiences of others.
Writing Math Research Papers takes on the important topic of developing a mathematics research paper while simultaneously training students to be good researchers. The author emphasizes that curiosity and interest in a chosen topic are basic characteristics of a researcher. In addition to mentioning some of the existing research topics in mathematics, Gerver also explains the process of developing a students research agenda and the requisite questions that inform that research. The content of the book can be broadly classified into that which discusses mathematical content knowledge and practices, guidelines for conducting research, and organization and presentation of research. Acquiring mathematical content knowledge relevant to a research topic is a critical aspect of conducting research. The author touches upon multiple mathematical topics and practices, and makes excellent use of the extant literature base by recommending the reader toward more in-depth discussions and other sources of information for more elaborate and/or specific information. The author describes the process of conducting research and mentions the difficulties that might eventually arise. He also provides guidelines for every step of the research endeavor to make research more organized and enjoyable, as well as for an applied paradigm for presenting mathematical information in an authentic format. Because research needs to be communicated in many forms, the author also provides a format for preparing for an oral presentation.
Chapters One, Three, and Seven are rich in mathematical content, but are presented skillfully to engage the reader in deeper, thought-provoking ways. Providing plenty of examples, the author occasionally pushes the reader to think outside the box. Though questions occur naturally to all of us, the author emphasizes that finding a solution may require patience and perseverance, and that strategies that seem suitable in theory may not be so in practice. The author provides a glimpse of a mathematicians world and directs the reader toward mathematical thinking, dismissing the notion that mathematics is about finding a single correct solution for a question. To kindle the reader's interest, simple yet intriguing questions from basic mathematical concepts are presented, some of which are solved with great difficulty and some left unsolved.
Given that solutions to mathematical questions are not always readily available, effective problem solving strategies are presented in Chapter Three. The strategies explained by the author are based on Polyas four steps of problem solving (1945). These strategies guide students to take up unfamiliar and challenging problems that are the very essence of research. Even though educators argue whether or not to include proofs in school mathematics, proofs are the core of mathematics research and therefore an integral part of the current book. Chapter Seven introduces the reader to theorems, conjectures, and proofs. A variety of approaches to proof are discussed in the context of fairly advanced mathematical content; however, the authors description is simple, so the difficulty level should not be a roadblock for students, instructors, or administrators.
The book is focused on conducting mathematics research; however, chapters about finding a topic, keeping a research journal, structuring a research paper, and preparing for an oral presentation are applicable to researchers in general. Since research involves gathering and processing a large quantity of information, taking notes and keeping track of progress are critical for optimizing time and effort. Moreover, as research is a lengthy process, maintaining a research journal is an efficient way to keep track of information and references. Chapter Five elaborates on adding annotations at various stages to make the content more readable and understandable. The author also provides examples of how parts of the research process can be turned into class activities, thereby keeping students on task.
Communicating research is as important as conducting the research itself. Chapter Four briefs the students on communicating ideas particularly in mathematics. Presenting mathematical research in a written format is different from other subjects because of the symbols, equations, diagrams, and proofsthe syntax and semantics of mathematics. Chapters Six and Nine serve as style guides for presenting mathematical research; the author discusses the technicalities of mathematical writing and language usage and provides an outline for the structure of the research paper.
In Chapter Ten the author helps the novice researcher prepare oral presentations of their research. This is extremely useful for high school students as well as novice researchers at the masters level or doctoral level. The authors also make excellent use of strategy development for effective presentations. The author mentions the use of other aids such as posters, models, and manipulatives to make the presentation more engaging and participant-friendly without sacrificing rigor. The step-by-step instructions make the text easy to follow and accessible for novice researchers.
Chapters Eleven and Twelve are complementary to the rest of the text, with an example of a mathematics research paper and a list of resources for the reader. Along with providing information and guidelines for students writing a research paper, the author extends some guidelines to teachers and administrators for introducing a mathematics research course in Chapter Thirteen. In addition, teachers are provided with instructions to prepare for the course and assess students work.
As the title suggests, the book walks the reader through every step of writing a mathematics research paper. The roles of the student, instructor, and the school administration are specifically addressed, and the book is rich in content knowledge, research practices, and presentation techniques.
Broadie, S., & Rowe, C. (2002). Nicomachean ethics, translation, introduction, and commentary. Oxford, UK: Oxford University Press.
Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.