Teaching with Statistics in Action

We’ve designed Statistics in Action: Understanding a World of Data to help you accomplish three objectives. Your students will

• learn the fundamental logic and tools of statistics
• learn about the actual practice of statistics in real-world situations
• be well prepared for the Advanced Placement Statistics examination

Statistics in Action is different from other textbooks because your students will learn by doing. They’ll discover the important concepts themselves and further develop their understanding by discussing the concepts they have discovered. Your close guidance is indispensable—you’ll help them stay on track, add emphasis to important discoveries, compare cases, distinguish issues, and connect the ideas they accumulate. Simply reading the textbook will not be sufficient; by doing the activities in class or in a lab period, students will have the opportunity to apply ideas, think critically, and articulate issues in group conversation and in debate over discussion questions, just as statisticians do in field practice.

Many of you will find that you’ll follow the textbook quite closely. We have designed Statistics in Action much like a protocol for analysis, if not exactly as a "script" for teaching class sessions. If you guide your class through the material sequentially, doing the activities and addressing discussion questions in order, you’ll find that your students will adopt the healthy skepticism that professionals cultivate and maintain interest and self-motivation for further study. Here’s how you might progress through a section of Statistics in Action.

Preparation

Each chapter of the Instructor’s Guide opens with an overview section that highlights the goals and content to be mastered and provides useful strategies and instructional methods for you to help students reach these goals. At the beginning of each chapter, you’ll also find valuable tools—planning charts for semester and two-quarter college courses, and for traditional schedule, block schedule, and 4-by-4 block schedule AP Statistics courses. In addition, you’ll find a materials list and suggested assignments for each section in the chapter to help you organize and manage the material to be presented.

Introduction

You’ll briefly introduce the lesson using the scenario presented at the beginning of the chapter, bringing students up to date with their work on the analysis so far. The opening exposition is your prompt. That will set the scene for an activity or an example.

Activity

As you circulate around the room, students work through the activity, collecting data, analyzing it—whatever is called for—and answer all the questions it poses. Most activities are designed for students to work with partners or in small groups. (A few activities can be assigned as individual homework with class discussion in the following class session, but you may find that you lose the benefit of students helping and challenging each other.) As work on the activity concludes, you’ll be checking with each group to make sure that the students have answered the questions correctly or sensibly. Finally, you might pose a general question to the whole class that elicits the concept the activity was designed to introduce. Notes for the activities in the Instructor’s Guide offer practical step-by-step guidelines for moving through the activity and present clear and realistic answers supported by plots and computer-generated data. The activity notes, along with all the notes in the Instructor’s Guide, are designed to provide a unique, in-depth focus on the statistical language being explored by highlighting contradictions and complexities behind the vocabulary of the lesson. Doing the activities aligns both the AP Statistics course and the college course with the goal of active engagement of the students in their learning, and helping them develop a powerful quantitative perspective.

Text

Following the activity is expository material that you present to the class, describing the concepts and techniques and working through examples. Occasionally, you’ll assign students to read the material on their own—and we’ve made every effort to make it lively reading—but you’ll want to be sure that they understand when a rule comes into play, what its exceptions are, and how to tell when a computation or a logical step has likely gone wrong.

Increasingly, students have had to read in mathematics classes. Still, there is a great reliance on you, the instructor, to present, explain, and emphasize; in the Instructor’s Guide, we detail and reinforce important points in each section in order to aid your delivery of the subject matter. More and more independent reading and research will be expected of students throughout their education, so we have tried to engage the student on the page with clear and attractive graphics and an optimal amount of text and graphic information on each two-page spread.

However you decide to implement the expository material, you’ll always want to structure your time so that students consider all of the essential and recommended discussion and practice questions.

Discussion

You’ll always want to consider the discussion questions in a whole-class discussion. It is in these discussions that students develop their instincts, support their reasoning, field challenges, and offer creative ideas. Sometimes you can precede a whole-class discussion by small-group discussions that go on while you circulate, giving hints or posing step-wise queries to be sure all groups are on track. Discussion questions are not meant for individual students to answer by themselves because they are often open-ended, with no clear-cut "best" answer. Many questions probe quite deeply into the concepts underlying the topic being discussed. Your guidance will be necessary. The Instructor’s Guide includes a full solution for each discussion question. You won’t usually want students to write out the answers to discussion questions—that would become tedious for both you and your students—and it might defeat the dynamic exchange of views and easy reevaluation of an individual’s position on an issue. However, most students will want to take notes (the answers do not appear in the back of the student book). Occasionally, you can have students write out a summary of the discussion or its upshot to be sure they understand the idea discussed.

Practice

Students should work the assigned practice questions independently or sometimes in groups, either as an assignment or in class, as they run across it. These questions enable both you and your students to check individual understanding of the immediately preceding material. Regular attention to practice questions, which do not introduce new material or rely on complex scenarios, will boost confidence—students will "digest" what they have done or read before going on. Brief textual answers (but not the solutions) are in the back of the student book; solutions for all practice questions are provided in the Instructor’s Guide.

Exercises

At the end of each section is a set of exercises. You’ll want students to work many of these as the class comes to them, for immediate reinforcement, and to catch common errors and misconceptions. Preparing for the chapter exam is another good time to assign exercises, so that students review what they know and realize what they have forgotten or still have questions about. You can assign the rest as review before the AP exam or before the college semester or quarter exam. Typically, exercises are done as individual assignments, although you can assign some of the more difficult questions as collaborative work. Brief answers to selected exercises are in the back of the student book and fully detailed solutions are provided in the Instructor’s Guide.

Technology

Students should have access to a graphing calculator with statistics capabilities. They will need a graphing calculator or a computer to carry out some of the simulations and analyses. However, be sure that students can set up and conduct small-scale simulations without the use of a calculator or computer. On the AP Statistics exam, students will need a graphing calculator for computations, so they should use one to work problems throughout the course. Also, on the AP exam as well as in professional practice, your students will be expected to be able to read a standard computer printout. A variety of program printouts—including Fathom, Minitab, Data Desk, and JMP-IN—are explained in greater detail in the student book and detailed in the Instructor’s Guide to help students acquire this ability.

Ann E. Watkins, Richard L. Scheaffer, George W. Cobb