SECOND EDITION

HOW TO SUCCEED IN COLLEGE MATHEMATICS

A COMPREHENSIVE STUDY AND REFERENCE BOOK

FOR STUDENTS AND INSTRUCTORS

SECOND EDITION

HOW TO SUCCEED IN COLLEGE MATHEMATICS

A COMPREHENSIVE STUDY AND REFERENCE BOOK

FOR STUDENTS AND INSTRUCTORS

Reviews

At first glance I was skeptical of the length of this book … but it is chock full of clear exposition of excellent advice, with careful sectioning and bolding of important points, and it would be hard to point to anything to omit. Much of the advice applies to college in general, but much is specific to mathematics, including how courses are sequenced, how to get credit by examination, and how to obtain assistance. Author Dahlke explains the benefits of learning mathematics and what it means to think mathematically, as well as how to read, write, discuss, listen to, and work problems in mathematics. Rationales accompany the advice and this renders it more credible. Dahlke makes it clear how and why college differs from high school. I have two sons approaching college; I’ll be giving them this book.

Mathematics Magazine (Journal of the Mathematics Association of America)

As an educator and non-mathematician who has long been concerned about the dismal state of math education in America, I find this book is a most welcome account of how students should approach the study of math at the college level. This is a timely, serious “how to” book about a national educational disgrace by an author who has obviously spent a lifetime teaching mathematics at the university level. Dahlke’s reflections represent the intellectual residue and wisdom of over thirty years of teaching. There is no other book like it on the market...period! It deserves to be in every college library, on every math teacher’s bookshelf, and required reading for all math students. It could stand alone as a text for a short course on “How to Study Mathematics.” (University admissions officers, are you listening?) Dahlke provides an accessible “straight talk-tough love” account of how to systematically approach the study of mathematics. He advances practical steps that students must take to develop the study habits needed for triumphing in the classroom. The study habits highlighted and encouraged are also many of the same habits that apply to the mastery of other subjects, and, frankly to life itself. In this latter sense, the book is as much about developing a good philosophy of life as it is about math education! This is most refreshing in a “How to do it” book.

Finally, what Dahlke does not address is the 800-pound gorilla in the room - how is it that America has spent more dollars on K-12 education than ever before while producing one of the weakest cohorts of math students in the western world? American students graduating from high school are amazingly self-satisfied with their low level of math skills. Where ignorance is bliss, what’s to worry about? Given the aversion of so many American students and educators to the practical “tough love” needed to bring our students up to the requirements of an increasingly sophisticated high tech society, we should not be surprised to see this book picked up in rising countries like China, India, and Japan where mathematics is taken seriously. America, are you listening?

Andrjeichuk, Ann Arbor, Michigan

Many liberal arts students fear the dreaded subject known as mathematics. “How to Succeed in College Mathematics: A Guide for the College Mathematics Student” is a thoroughly ‘user friendly’, practical, and effective guide for those students wanting to master this harrowing and difficult subject with academic success. With advice about absorbing all the knowledge one can in these classes, fighting off anxiety, and just plain dealing better with math classes, it’s a complete and comprehensive guide that is ideal for the non-specialist general reader wanting to improve his or her ability and understanding of mathematics. But most of all, “How to Succeed in College Mathematics” is especially recommended to anyone engaged in or planning on enrolling in a college level math course.

Midwest Book Review, Oregon, Wisconsin

This book not only addresses how to succeed in college mathematics, but also how to succeed as a college student, regardless of one’s field of study. Many non-mathematics issues are discussed that all college students face, and many suggestions given for studying mathematics can also be applied to studying other disciplines.

As a counselor and academic support person, many of my colleagues and I can attest to the fact that the foremost issue students come to us with, concerns problems they are having with their mathematics courses.

It is especially gratifying to see a discussion of vital psychological issues that affect so many of today’s college students.

Monica Porter, Ph.D., Psychologist and Director of Women’s

Resource Center, University of Michigan, Dearborn

I begin my comments on Dahlke’s book, How to Succeed in College Mathematics, by placing in perspective how my involvement with it these past two years came about. At SUNY Fredonia, I teach the course MATH 100 Mathematics First-Year Seminar. MATH 100 is a 1-credit course and is offered every fall semester. It is recommended, but not required, for entering first-year (freshmen) mathematics majors. In a typical year, SUNY Fredonia enrolls 25 to 35 first-year mathematics majors, and 15 to 20 choose to take MATH 100. The course meets once per week for 50 minutes.

MATH 100 seeks to help students utilize campus resources effectively, learn useful academic skills, especially those relevant to mathematics, develop a support network, become more self-aware, promote personal health and wellness, and better connect with the campus. The course introduces students to the culture of the Mathematical Sciences Department and the mathematics community in general. Students taking MATH 100 need to be concurrently enrolled in a precalculus or calculus course.

MATH 100 has been offered every fall since 2001, with the exception of 2003. I have been the instructor each time, with one exception. As I recall, around 2000 there was an initiative on campus to develop freshmen seminars, in the hopes that such courses might improve student retention. In 2006, the development and strengthening of new student learning initiatives was made an explicit goal of the campus’ strategic plan.

I have used Dahlke’s book in MATH 100 each of the last two years, with considerable success. Student comments have been overwhelmingly positive. Before using Dahlke’s text, I used Math Study Skills Workbook, 3rd edition, by Paul D. Nolting. This is a fine resource, but it is aimed at students taking mathematics courses to satisfy general education or cognate requirements, but in addition to these students, Dahlke’s book also applies to mathematics majors.

I first learned of Dahlke’s text in 2008, and considered adopting it for that fall’s course. However, the length of the text – 622 pages – made me a bit uneasy – and I was afraid my first-year students would find it intimidating. So, I decided to “scout it” that year, using it as a resource. The more I used it, the more impressed I was! I came to realize that the length of the text was deliberate, and the result of an intentional design consideration. To quote from the introduction, “Most topics associated with learning mathematics are linked together … . The book is organized so as to be sensitive to this linkage; thus, when you are reading about one link in the chain, you are often referred to other links in the chain. Hardly a section of the book stands alone, yet most sections can be read out of order.”

When I mention the number of pages in Dahlke’s book, it should be pointed out that my students don’t find the book large at all, especially compared to their calculus text. And the cost? There is no comparison! At our university bookstore last fall, [the first edition of] Dahlke’s book cost $27.95, which is astonishingly inexpensive considering its size and content value—our calculus book, with WebAssign, cost $222.00.

As alluded to above, I really appreciate the flexibility Dahlke’s text provides in terms of how I want to structure my course. I begin the first week with “Getting Off to a Good Start,” covering Chapter 1 (Introduction), and Chapter 2 (College Mathematics Environment). The discussion for the second week is focused on “Class Preparation and Taking Notes,” and the students are asked to read Chapter 14 (Learning Mathematics Through Reading, Writing, Listening, Discussion, and Taking Notes) and Chapter 15 (Reading a Mathematics Textbook). Notice how I’ve jumped way ahead in the text. However, because of the text’s design, this does not cause a problem. In week 3, we visit the university’s Learning Center (I spring for pizza), and the focus is on “Time Management.” For this topic, the students are asked to read Chapter 7 (Managing Time) and Chapter 23 (Obtaining Assistance in Mathematics).

At this point in the semester, I figure the students are approaching the first hour exam in their mathematics course. Thus, we cover Chapters 26 and 27 on preparing for and taking mathematics exams. These chapters are especially well written and offer a great deal of useful advice. Other chapters that my students find particularly helpful include Chapter 13, on different learning and teaching styles, and Chapter 25, on evaluating progress in a course. I cover the latter chapter just before the students receive their mid-semester grades; shortly thereafter, the students must decide whether to withdraw from any courses and they are also determining their course schedules for the following semester.

In preparing to write this review, I surveyed about a dozen public and private colleges in New York State to see if any of them had a course similar to MATH 100. To my surprise, I found only one: MATH 101 Welcome Mathematics Majors, at SUNY Geneseo. MATH 101 is also a 1-credit course, but it focuses more on the nature of mathematics rather than on study skills. I think that Dahlke’s text would work well for this type of course, also, and could see covering Chapter 8 (Nature of and Evolution of Mathematics), Chapter 19 (Learning Mathematics Notation), Chapter 20 (Technical Aspects of Writing Mathematics), and Chapters 21 and 22 on problem solving, among others.

In conclusion, if your university does not have a course similar to MATH 100 or MATH 101, consider starting one. Your mathematics majors will find it beneficial. And when you do implement such a course, consider using this book. I recommend it enthusiastically.

H. Joseph Straight, Ph.D., Professor and Chair, Department of Mathematical

Sciences, State University of New York, Fredonia

To give the needed impact to my review of Professor Dahlke’s book, it is necessary to give background information. I came from Poland and have been teaching in the United States for 10 years. My primary educational interest is methodology of teaching and studying. In Poland, I won the top prize for my master's thesis on methodology of teaching awarded by The Polish Physics Society, presented classes on Polish TV for teachers who were working on an Advanced Credential, and was awarded a Silver Cross for achievements in teaching by the Ministry of Polish Education.

I am currently a member of the Math and Computer Department at Chapman University in Orange, California. Chapman University, founded in 1861, is one of the oldest and most prestigious private universities in California. It enrolls more than 6,000 undergraduate, graduate and law students. At Chapman, I am Director of the Math and Computer Science Clinic, responsible for the mathematics tutoring done by Chapman students. We view the primary goal of tutoring mathematics as helping students help themselves. Our mathematics tutors are trained to guide students to become independent learners. In addition, I am teaching mathematics courses full time at Chapman, including introductory and intermediate algebra, precalculus, mathematics for elementary teachers, and a course in mathematics tutoring techniques that I created.

Students who tutor have to take my course in mathematics tutoring techniques. This course counts as a general education course (one that provides service to the community). To be admitted to the course, a student needs to have attained an A in the course he or she wants to tutor, and submit a letter of recommendation by an instructor. There are about 35 mathematics tutors each semester, and they are paid by the University for this work. Tutors do not have to be mathematics majors, but many are.

Before I discovered Professor Dahlke’s book, I was using many different sources in the tutoring course. It was simply amazing to learn how well his book addresses the goals for the course, and is now the main source for the course. Students who know mathematics well think that they can tutor, and tutor well. Nothing could be further from the truth. Knowing mathematics well is one of the conditions of tutoring well, but there is so much more to tutoring, as there is to teaching. I found the book very resourceful for myself, even though I am an experienced teacher with lots of formal training in educational pedagogy.

Many college mathematics instructors have not been formally trained in educational pedagogy and they practically mimic how they were taught, and I have to say, not always according to principles of learning. What they can learn about educational pedagogy from the book has the potential to positively affect how they look at mathematics learning, and how they teach mathematics in the future. All faculty members in my Mathematics Department have this book.

My students read almost the entire book, and had 23 assignments on the reading. (I am delighted to learn that an Assignment Manual will be available for the Second Edition of the book, both of which will be available for Fall Term, 2011.) Students found the book very interesting, thought provoking, practical and enlightening. They appreciated the fact that the author, besides using his vast teaching experiences and formal training in mathematics and mathematics education, used papers on teaching and learning that were written by experts.

Many of the sections of the book were a source of heated discussions among students. In the assignments I was asking them questions to check their understanding of the material they read. Some mathematics majors implied that it would be a challenge to do all that Professor Dahlke was saying, and that they most likely would not. The author makes it clear that they are not expected to, but I was surprised at their attitude; after all they are mathematics majors.... For example one said, "I wasn't reading a mathematics book in high school, and look at me now, I am a mathematics major.” This remark and others like it provided good material for discussion.

I cannot believe that an American educator wrote this book, because the approach is European. He is telling things the way they are, not saying, “Great job” for everything. The book is filled with wisdom and tough love that can only come from an experienced and dedicated educator. I have been waiting my entire teaching career for a book like this. You may put 1000 teachers’ experiences together, and you will not get from them what you get from this book.

When reading Professor Dahlke’s book, I felt like I had known him my whole life. Here is someone who cares, whose wisdom is almost intimidating, and who didn’t lose his passion for education after many years of teaching. Sometimes I think maybe I am too strict because I am European. That this is a different place and I need to adapt. But after reading this book I no longer feel this way. I am inspired by this book to continue on with my work with renewed commitment and passion.

It is clear that the general level of mathematics education in the United States is less than adequate, to say the least. I see this book as a lifesaver for mathematics education in this country. There is so much talk about money needed for education, which gets me upset. We need good teachers first, and this book will help promote this if it is read and discussed.

In conclusion, the book is not only useful for students who have problems in mathematics, but also for students who are doing well in mathematics and want to deepen their understanding of it. The book is invaluable for every student taking mathematics in college, including mathematics majors, and for every mathematics instructor. An added bonus is that much of the advice given in the book applies, directly or indirectly, to taking courses in the other hard sciences.

Halina Goetz, M.S., Director of Math and Computer Science Clinic, Chapman

University, Orange, California

Students are finally made privy to what trained teachers receive; namely, what students need to do to learn mathematics and why they need to do it. Reason has to rule the day in the life of a college student, and it rules the content of this book.

The book is written for students and they will benefit greatly from it, but I would also encourage inexperienced and experienced mathematics instructors to use it as a resource to support their teaching and their students’ learning.

Problem solving is a fundamental part of mathematics—many college students struggle with it and don’t know what they can do to improve. I was a student in Professor Dahlke’s problem-solving course and it has served me well. His two chapters on problem solving are comprehensive, lucid, and useful.

Daniel Buchanan, M.S., Mathematics Instructor, Henry Ford Community

College, Dearborn

Richard Dahlke brings to this rather prolix book thirty-four years of teaching lower-division courses at the University of Michigan in Dearborn. Its 600 pages cover a range of topics that include both useful information and sound advice to help students get the most out of their university experience: the college environment, organization of courses and programs, prerequisites, admission and internal examinations, time management and study skills, confidence building, the nature of mathematics, reading mathematics texts, working exercises and solving problems, [and] balance of responsibilities of teacher and student. Although written for an American audience, a Canadian student will find much that is useful. However, its length means that it cannot be read from cover to cover. It is intended to be a resource book, and chapters and sections of chapters stand alone.

Despite this, the author views almost everything in the life of a college student as related, so that actions in one direction can affect other areas. The table of contents and index make the book convenient to navigate.

There is much in this book that I have said myself to incoming university students, and the author covered the fundamental points for students to heed if they are to be successful. Basically, students are invited to a maturity that engenders accepting resonsibility for their learning, grasping their interests and capabilities, formulating their goals, working independently but knowing when and how to access assistance and what they can reasonably expect from their instructors. I was pleased to note Dahlke’s insistence on having an attitude towards mathematics that leads them to probe for meaning and coherence. However, there are a few points that bear emphasis. An important issue in any teaching-learning situation is the alignment of what the student can bring with what the instructor can deliver. Often, a productive relationship is confounded by a clash of expectations about the outcome. Students come with ideas about learning along with mathematical conceptions that may be inadequate, fuzzy or just plain wrong. A good instructor will take this into account, observing that teaching may have destructive as well as constructive aspects, so that they can make contact with students; correspondingly, students must expect that their notions will be challenged and deepened. Furthermore, no matter how inspired the teaching and articulate the textbook, for robust learning to occur, students need to put the material through “their own sieve”, coming to terms with it in their own way. The failure of some students to appreciate this is exemplified in some of the student comments, which the author uses and analyzes to good effect.

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This comprehensive and practical book is a worthwhile purchase for any student embarking on a university career who wants to get a leg up on what to expect and how to manage the experience. It can also find a place on the bookshelves of advisors, undergraduate reading rooms and libraries.

CMS Notes—Newsletter of the Canadian Mathematical Society,

(by Ed Barbeau, Ph.D., University of Toronto, Ontario)

Aside from a new subtitle, this second edition of the 2008 book with the subtitle of “A Guide for the College Mathematics Students” added an Appendix on Online Learning and an Assignment Manual. It contains quotes from nine laudatory reviews of the first edition, including two in publications of the mathematics societies in North America. In addition to mathematicians and mathematics educators, reviewers have backgrounds that include psychology and academic support.

The author organizes his advice to mathematics learners distilled from over 35 years of teaching experience into over twenty chapters of “how-to’s” with detailed instructions/suggestions for a student. Written for students in the United States, it starts withthe “shocking” college mathematics environment: more work & little admonishment to do it; more freedom & more decisions to make; faster pace courses & more content details left to you; less grading of assignments & less feedback in class; no in-class reviews for exams & no in-class feedback on graded exams; more lecturing, less discussion, and less personal interaction; more complex content; greater necessity to read the textbook & take notes; fewer, longer, & more difficult examinations; less opportunity to improve poor test scores, and lower course grades. The “more” or “less” are in comparison with most students’ high schools experiences in the U.S., where student retention in the first two years of mathematics courses in the universities is a problem. In fact, one of the reviewers quoted used the book as a text (“with considerable success”, he reported) for a mathematics first-year seminar for entering students to introduce students to the culture of the mathematical sciences department and the mathematics community in general.

A chapter (12 pages) on the nature and evolution of mathematics offers 30 characteristics (among them: solving problems; deductive; inductive; symbolic, spoken & written language; abstract; compact) and nine less tangible aspects (inspired by nature, power, etc.).

The author then proceeds to inform the student of the benefits of learning mathematics through “understanding and thinking in mathematics”, listing 23 skills among which, “one gains increased ability to be more flexible in your thinking”. By understanding, he means “to know”, not to be confused with “to be familiar with”: “Understanding something comes from connecting or relating that thing to other things you know (p.120).”

Premised on the belief that each student can succeed in learning mathematics (stated in the postscript of “About the Author”), the book tells the student: “Nothing works unless you do (p.5).” Detailed guidance is given on various facets of an Americanstudent’s life: having course prerequisites; scheduling activities including jobs, managing time. It goes further: changing beliefs, attitudes, and study habits; increase confidence & motivation and decrease procrastination & anxiety, and choosing a mathematics instructor based on learning and teaching styles. Specific to learning mathematics, there are chapters on: learning through reading, writing, listening, discussion, and taking notes; managing problem assignments; learning notations; technical aspects of writing mathematics; remembering, reviewing and summarizing mathematics; self-evaluation of progress; preparing for final exams. Some of the author’s advice reflects his beliefs that “a math course needs to be . . . a conversation course” (p.626), and that “when writing, you are telling a story” (p. 402). He states that nothing he did in his teaching has equipped his students to understand mathematics as much as requiring them to “write about mathematics” (p. 247). Often cited to support his arguments are writings by Paul Halmos and Alan Schoenfeld.

As a reference book also for instructors, there are sections on instructor responsibilities and students’ complaints about their instructors. Scattered in many chapters are student comments that the author has collected or solicited. On the robust institution of student evaluation of teaching practiced in the American universities, he tells thestudent: “You have a responsibility to be fair . . . . Be critical, but truthful in your evaluations.

Rationale for his suggestions to the students are drawn from writings from a range of fields including philosophy, educational psychology, and cognitive psychology, as well as from reports & recommendations by mathematics & mathematics education organizations. The chapter on choosing a mathematics instructor is based on the Myer-Briggs Type Indicator. The closest he gets to the vast literature of research in mathematics education is Schoenfeld’s work on problem-solving.

Teaching and learning of mathematics have social and cultural aspects, and indeed local classroom culture may affect student learning. Mathematicians do have an international forum in the gatherings of International Commission on Mathematics Instructions. In addition to its intended purpose, the book may provide some topics for discussions on “practices that work”, and it may also prompt some investigations in the mathematics education research community.

Zentralblatt MATH Database (by Pao-Sheng Hsu, Ph.D., Columbia Falls, Maine)—The database is produced by the Berlin editorial office of FIZ Karlsruhe and edited by the European Mathematical Society, FIZ Karlsruhe, and Heidelberger Akademie der Wissenschaften.

My job has just become easier with the availability of this book. Before, my mathematics colleagues and I had nothing to refer our students to that discussed the many ways they could improve their performance in mathematics.

It takes a lifetime of passion, caring, experience, and dedication to one’s profession and students to write a book like this. Students need to do themselves a favor and read it, use its ideas, and realize its potential—in college and beyond. As a parent whose children are out of college, I wish this book had been available for them when they were ready to enter college.

Robert Fakler, Ph.D., Mathematics Professor, University of Michigan, Dearborn