Algebra and Trigonometry 3rd Edition by Cynthia Y. Young

Book Preface

Distinguishing Features

Four key features distinguish this book from others, and they came directly from my classroom.

PARALLEL WORDS AND MATH

Have you ever looked at your students’ notes? I found that my students were only scribbling down the mathematics that I would write—never the words that I would say in class. I started passing out handouts that had two columns: one column for math and one column for words. Each Example would have one or the other; either the words were there and students had to fill in the math, or the math was there and students had to fill in the words. If you look at the Examples in this book, you will see that the words (your voice) are on the left and the mathematics is on the right. In most math books, when the author illustrates an Example, the mathematics is usually down the center of the page, and if the students don’t know what mathematical operation was performed, they will look to the right for some brief statement of help. That’s not how we teach; we don’t write out an Example on the board and then say, “Class, guess what I just did!” Instead we lead our students, telling them what step is coming and then performing that mathematical step together—and reading naturally from left to right. Student reviewers have said that the Examples in this book are easy to read; that’s because your voice is right there with them, working through problems together.

SKILLS AND CONCEPTS (LEARNING OBJECTIVES AND EXERCISES)

In my experience as a mathematics teacher/instructor/professor, I find skills to be on the micro level and concepts on the macro level of understanding mathematics. I believe that too often skills are emphasized at the expense of conceptual understanding. I have purposely separated learning objectives at the beginning of every section into two categories: skills objectives—what students should be able to do; and conceptual objectives—what students should understand. At the beginning of every class I discuss the learning objectives for the day—both skills and concepts. These are reinforced with both skills exercises and conceptual exercises.

CATCH THE MISTAKE

Have you ever made a mistake (or had a student bring you his or her homework with a mistake) and you go over it and over it and can’t find the mistake? It’s often easier to simply take out a new sheet of paper and solve it from scratch again than it is to actually find the mistake. Finding the mistake demonstrates a higher level of understanding. I include a few Catch the Mistake exercises in each section that demonstrate a common mistake that I have seen in my experience. I use these in class (either as a whole or often in groups), which leads to student discussion and offers an opportunity for formative assessment in real time.