Preface

Pathways to College Mathematics, Second Edition, provides a general survey of topics to prepare students for success in a variety of college math courses, including college algebra, statistics, liberal arts mathematics, quantitative reasoning, finite mathematics, and mathematics for education majors. The text and MyLabMath course are generally designed for students pursuing non-STEM majors, and who are likely to go into a Liberal Arts Math, Quantitative Reasoning, Statistics, etc. course. However, it does have the necessary topics and rigor required for students who might pursue a STEM path and move into an Intermediate Algebra or College Algebra course.

The book has four major goals:

1. To provide skills necessary for non-STEM and STEM students that can beapplied in future college math courses.

2. To show students how mathematics can solve authentic problems that apply totheir lives.

3. To enable students to develop problem-solving skills, while fostering criticalthinking, within an interesting setting.

4. To provide students with learning strategies that lead to persistence and successin mathematics.

One major obstacle in the way of achieving these goals is the fact that many students do not read their textbook. This has been a source of frustration for me and my colleagues in the classroom. Anecdotal evidence gathered over years highlights two basic reasons why students do not take advantage of their textbook:

“I’ll never use this information.”“I can’t follow the explanations.”

I’ve written every page of Pathways to College Mathematics, Second Edition, with the intent of eliminating these two objections. The ideas and tools I’ve used to do so are described for the student in “A Brief Guide to Getting the Most from This Book,” which appears at the front of this book and are described in the following features. This book is available as a paperback OR as an eBook (in MyLab Math, and through other sources). Either format is suitable, just so that students do utilize the text and all the resources it has to offer!

What’s New in the Second Edition?

• Chapter P, Prealgebra Pathways. Many students enter a pathways course shakyin prealgebra topics. The Second Edition provides an entire chapter dedicated tothese topics, including whole numbers, fractions, decimals, percents, bar graphs, circle graphs, and line graphs.

• Mid-Chapter Check Points. At approximately the midway point in eachchapter, an integrated set of review exercises allows students to review andassimilate the skills and concepts they learned separately over several sections.

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• “Make Sense?” Critical Thinking Exercises. Each Exercise Set containsfour Critical Thinking Exercises that test conceptual understanding by askingstudents to determine whether statements are sensible, and to explain why orwhy not. These exercises can be used for classroom discussion in order to engageparticipation in the learning process. This new feature lets you ask students whatthey think about selected statements, determine whether they understand theconcepts, and give them feedback to clarify any misunderstandings.

• Section 1.1, Sets, Venn Diagrams, and Set Operations. Because the numbersdiscussed in Chapter 1 (Numerical Pathways) are defined using sets, the chapteropens with a new section devoted entirely to this topic.

• New Applications and Real-World Data. I’m on a constant search forreal-world data that can be used to illustrate unique applications of topics ina pathways course. The Second Edition includes 58 worked-out examples andexercises based on new data sets and 23 applications containing updated datafrom the First Edition.

• New Topics for STEM Students. Among the abundance of algebraic topicsaimed at preparing students to continue with STEM-level mathematics, newtopics in the Second Edition include modeling mixture problems with systems ofequations (Section 3.4) and right triangle trigonometry (Section 6.6).

• New Blitzer Bonuses. These enrichment essays provide historical, interdisciplinary, and otherwise interesting connections to the mathematics under study, showingstudents that math is an interesting and dynamic discipline. New Bonuses inthe Second Edition include “Digits, Place Values, and Computers” (Section P.1), “Palindromes and Rational Numbers” (Section 1.3), “Slope and ApplaudingTogether” (Section 3.2), “Three Weird Units of Measure” (Section 5.1), and“Sereen Math” (Section 6.2).

• New to MyLab Math. See page xiii for complete details. The MyLab Mathexercise coverage has been expanded and increased to reflect the changes in thetext. The video program has also been enhanced to include more videos broken upby objective, and assignable questions to accompany the Check Point Videos.

• Enhanced Learning Guide with Activities. The Learning Guide helps studentslearn how to make the most of their textbook, while also providing additionalpractice for each section and guidance for test preparation. With the new edition, we’ve added even more activities per chapter, which are intended for group workin class to help students put the math into real work context. Using these activitieswith students (regardless of class format) can be an ideal approach to help students, especially non-STEM students, apply their newfound knowledge so it sticks. TheLearning Guide is published in an unbound, binder-ready format so that it canserve as the basis for a course notebook.

What Familiar Features Have Been Retained in the Second Edition?

• Learning Objectives. Learning objectives, framed in the context of a studentquestion (What am I supposed to learn?), are clearly stated at the beginningof each section. These objectives help students recognize and focus on thesection’s most important ideas. The objectives are restated in the margin at theirpoint of use.

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• Chapter-Opening and Section-Opening Scenarios. Every chapter and every section open with a scenario presenting a unique application of mathematics in students’ lives outside the classroom. These scenarios are revisited in the course of the chapter or section in an example, discussion, or exercise.

• Innovative Applications. A wide variety of interesting applications, supported by up-to-date, real-world data, are included in every section.

• Detailed Worked-Out Examples. Each example is titled, making the purpose of the example clear. Examples are clearly written and provide students with detailed step-by-step solutions. No steps are omitted and each step is thoroughly explained to the right of the mathematics.

• Explanatory Voice Balloons. Voice balloons are used in a variety of ways to demystify mathematics. They translate mathematical language into everyday English, help clarify problem-solving procedures, present alternative ways of understanding concepts, and connect problem solving to concepts students have already learned.

• Check Point Examples. Each example is followed by a similar matched problem, called a Check Point, offering students the opportunity to test for conceptual understanding by working a similar exercise. The answers to the Check Points are provided in the answer section in the back of the book. Additionally, Check Point Videos and assignable exercises are available in MyLab Math.

• Concept and Vocabulary Checks. This feature offers short-answer exercises, mainly fill-in-the-blank and true/false items, that assess students’ understanding of the definitions and concepts presented in each section. The Concept and Vocabulary Checks appear as separate features preceding the Exercise Sets.

• Extensive and Varied Exercise Sets. An abundant collection of exercises is included in an Exercise Set at the end of each section. Exercises are organized into seven categories, a format that makes it easy to create well-rounded homework assignments.

• Practice Exercises follow the same order as the section’s worked examples. This parallel order enables students to refer to the titled examples and their detailed explanations to successfully achieve each section’s objectives.

• Practice Plus Exercises contain more challenging practice exercises that often require students to combine several skills or concepts. These exercises provide the option of creating assignments that take practice exercises to a more challenging level.

• Application Exercises give the option of assigning realistic, relevant, and unique applications consistent with your students’ needs and interests.

• Explaining the Concepts Exercises ask students to provide written or oral responses to questions covering each of the section’s objectives.

• Critical Thinking Exercises require students to employ analytic skills that go beyond applying each section’s basic objectives. The exercises ask students to make sense of complex problems and persevere in solving them.

• Technology Exercises enable students to use technological tools to explore and deepen their understanding of concepts.

• Group Exercises contain projects and collaborative activities that give students the opportunity to work cooperatively as they think and talk about mathematics.

• Brief Reviews. The Brief Review boxes summarize mathematical skills that students should have learned previously, but which many students still need to review. This feature appears whenever a particular skill is first needed and eliminates the need for you to reteach that skill.

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• Great Question! This feature presents a variety of study tips in the context of students’ questions. Answers to questions offer suggestions for problem solving, point out common errors to avoid, and provide informal hints and suggestions. As a secondary benefit, this feature should help students not to feel anxious or threatened when asking questions in class.

• Achieving Success. The Achieving Success boxes at the end of most sections offer strategies for persistence and success in college mathematics courses.

• Detailed Chapter Review Summary Charts. Each chapter contains a review chart that summarizes the definitions and concepts in every section of the chapter. Examples that illustrate these key concepts are also included in the chart. For further review, the chart refers students to similar worked-out examples, by page number, from the chapter.

• End-of-Chapter Materials. A comprehensive collection of review exercises for each of the chapter’s sections follows the review chart. This is followed by a chapter test that enables students to test their understanding of the material covered in the chapter.

I hope that my love for learning, as well as my respect for the diversity of students I have taught and learned from over the years, is apparent throughout the Second Edition of Pathways to College Mathematics. By connecting mathematics to the whole spectrum of learning, it is my intent to show students that their world is profoundly mathematical, and indeed, π is in the sky.

Robert Blitzer

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