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
Support for Relevancy of Issues Addressed
Support for the relevance of issues addressed in the Second Edition of How to Succeed in College Mathematics, includes:
•Remarks in the book from successful college mathematics students on what worked for them, and from unsuccessful college mathematics students on what did not work for them.
•Remarks in the book from college mathematics students on their response to these questions on course evaluation forms: What did you like about the course and instructor? What did you dislike about the course and instructor?
•Suggestions to the author from experienced college mathematics instructors on issues that should be included in the book.
•Remarks by reviewers. (CLICK REVIEWS.)
•Richard M Dahlke’s formal academic training, scholarship, and extensive college teaching experiences in mathematics and mathematics education. (CLICK ABOUT RICHARD M. DAHLKE.)
•No one can argue against the relevancy of students understanding mathematics, and instructors teaching mathematics for understanding. What this means, and how it can be accomplished, along with important short- and long-term benefits of understanding mathematics, is presented and discussed in the book. There is hardly a section in the book that does not relate, in some way, to supporting “understanding” for students and instructors.
Mathematics students who struggled in the author’s classes, mentioned that mathematics was always difficult for them. These students appeared to have one thing in common: They did not study mathematics for understanding. They learned content rotely and viewed most aspects of mathematics as isolated pieces of information. Their main efforts in their mathematics study were to memorize pieces of information and to mindlessly manipulate symbols. To succeed, they needed to make three changes: (1) have a strong desire to understand, (2) know what needs to be changed in their study to understand, and (3) persevere in their efforts to understand. A key responsibility of instructors is to support them in doing this.
A concise overview of topics in the book that relate to understanding mathematics is presented below.
Understanding specific mathematics means being able to connect or relate that mathematics to other things you know. The more things you can relate to what you are trying to understand, the better your understanding will be. The questions that a learner needs to answer when learning a specific topic in mathematics include these: (1) where did it come from, (2) what is its purpose, and (3) how is it applied? Thus, this necessitates students approaching their mathematics study from one of understanding, which includes working with other students. In addition, instructors need to support them in their efforts to get at understanding through exposition, conducting in-class discussions, making appropriate assignments, and evaluating students’ understanding of mathematics.
Perhaps the most important thing an instructor can do to improve students’ understanding of mathematics is to have them write about mathematics. These writing exercises should be included in assignments, study guides and examinations. In most exercises of this type, students are asked to write about how things are related or connected.
Understanding can be fleeting, and that is why it needs maintenance. Meaningful review of mathematics not only enhances maintenance; but it also advances understanding, since topics understood earlier are re-related to knowledge that has been better understood after the topics were initially developed.
Problem solving has to be the focus of mathematics study, and it, along with understanding, does not take place in a vacuum. What this means is that all that is studied in a mathematics course, including concepts, principles, and computational techniques, is done with the thought that this will help in solving problems. And this thought is acted on by solving problems, including those in a real world context. Mathematics work must point to solving problems, which needs to be the basic mathematical activity in a course. The more knowledge and understanding you have of specific concepts and principles, along with computational proficiency and a repertoire of problem solving skills, the better problem solver you will be. However, it is also the case that having problem-solving skills helps in understanding mathematics content. They can be applied in developing concepts, constructing theories, generalizing, and improving one’s ability to abstract. So there you have it, a two-way street—being proficient in problem solving helps you understand mathematics content, and understanding mathematics content helps you become a better problem solver. That’s a win-win situation.
This is not a book on quick fixes or on sound bites—such gimmicks for learning do not help students be successful. Is the content of the book relevant? Bet the farm on it!
Support for Credibility of Issues Addressed
Sources used in writing the Second Edition of How to Succeed in College Mathematics that lend credibility to the topics that are included and the advice given, include:
•Findings of educational psychology.
•Reports and journals of professional mathematics or mathematics education organizations, including the Mathematical Association of America (MAA), and the National Council of Teachers of Mathematics (NCTM).
•Research papers written by experts in the fields of mathematics, mathematics education, and education.
•The credibility of the author as evidenced by his formal training, teaching experience, and scholarship on the teaching and learning of mathematics (CLICK ABOUT RICHARD M. DAHLKE).
•Astute quotations. Carefully selected quotations serve many purposes, including (1) providing evidence for the relevance, credibility, and authority of the ideas they comprise, (2) giving cogent summaries of these ideas, (3) stimulating thought and discussion, (4) illuminating meaning and understanding, (5) giving perspective, (6) creating interest, and (7) preserving wisdom gained throughout the years. Look forward to being motivated and inspired by quotations carefully selected for the book.