Teaching and ActivStats

Lecture-based Classes

Experience has shown that ActivStats is best used as part of a full range of teaching tools and methods. Assign a lesson of ActivStats to introduce a subject as preparation for class. Then discuss that subject in class. You will find that you can spend less time teaching formulas and definitions because the students have had time to work with them, visualize their consequences, and apply them to real data. This leaves more time for examples, discussion, remedial background work, and extra time on the really hard concepts.

You will find that it is not necessary to change your lectures substantially. Rather, you can change the emphasis away from the nitty-gritty of formulas and definitions and towards philosophy, the big picture, and examples.

Most textbooks are hard for students to read without some introduction. Textbook readings seem to be most useful after students have seen the topics in ActivStats and in class. It is a good idea to assign homework exercises from ActivStats and texts only at the time of the classroom discussion to reduce the number of students who try to work the exercises first and then look back to see what they need to know to work the problem.

One way to improve compliance with the assigned computer work is to require students to hand in their answers to the "Study Questions" that appear periodically in the middle of Animated Activities. Because the questions are in the middle of a narrated activity, it is easier for students to work through the activity than to search for the questions directly. Another method is to administer a brief quiz at the start of a class meeting.

One classroom model that has worked well is this: We assign an ActivStats lesson in preparation for lecture, expecting students to spend about an hour with the computer. Class meetings consists of:

• 5 minutes of organizational discussion. It pays to review where we are and where we are going frequently.
• Optional 5-minute quiz or review of the required study questions, designed to ensure that students keep up with the ActivStats-based assignments. Especially at the start of the course, it is important to convince students that there is value both to working with the software and to classroom attendance. We have heard both "I don't need to come to class; it's all on the DVD" and "I don't need to do the computer work, it's all in the lectures and text." We have found that undergraduate students may need some "encouragement" until they see the synergies among the learning modes for themselves.
• 10–15 minute review of the "big ideas" to be found in the ActivStats lesson. We review these below.
• The remainder of the time can be spent working examples, enriching the material with additional information, providing background mathematics, class projects, etc., as appropriate to the size, maturity, and capabilities of your class.

Of course, as with all rules about teaching, these are meant to be broken—and we will recommend some ways to break them in the lesson-by-lesson discussions below.

Discovery Learning, "Workshop" Classes

Many ActivStats activities employ discovery learning concepts. In particular, lessons on randomness, probability, and the reasoning of inference turn the computer into a "randomness laboratory" that can be more vivid and effective than classroom activities with coin flipping, dice rolling, and balls in urns. If you are teaching a workshop-style class, you will want to judge when team-based classroom activities are the best way for students to discover a concept and when individual computer-based work may be better.

When team projects introduce a subject, ActivStats can provide summaries of the key definitions and formulas to consolidate students' understanding. Topics in data analysis (summarizing data, depicting relationships, etc.) may work best in this way. When individual work with ActivStats leads, team discussions and applications of the concepts can reinforce understanding. Topics in randomness, probability, and inference may work best this way. Applications of inference methods to real data may again work best when motivated by real-world projects first with ActivStats serving as a reference and reinforcement.

Distance Learning

ActivStats is an ideal core for a distance learning statistics course. The narrated expositions provide some "human provided" instruction and the independent explorations let students discover much of the course on their own. In a distance learning course offered by Cornell University, students had the ActivStats disc, a textbook, e-mail, and access to a course web site. The web site provided administrative information for students, a discussion board, assignments, homework solutions (posted after the homework was graded and returned), and occasional supplementary material.

Pace and Workload

With 27–30 lessons, ActivStats matches the pace of a typical college semester or quarter, which typically offer 26-32 class meetings. An average pace of one ActivStats lesson per class meeting leaves time for extra attention, discussion, and review when needed. Push students to move quickly through the early lessons; they establish much foundation material, but are not as dense in new ideas as later lessons. Leave extra time for discussions of sampling distributions and the reasoning of inference.

The Table of Contents is Pided into six major Sections. The end of each Section is a good place to pause for review (and possibly an exam).

Generally, students report spending between 2 and 4 hours of computer contact time on a lesson, including time to complete computer-based homework. Your mileage may vary. (And, of course, the distribution is skewed to the high end. Some students spend much more time than that, but these students usually report that ActivStats enabled them to learn the material and do well in the course.)

Classroom Demonstration

You will want to incorporate ActivStats into classroom presentations (both lectures and group discussions of team-based activities). Use the Resources tab to browse through different types of activities in ActivStats. You will see a list of all the Videos, Teaching Applets, Tables, and Datasets used throughout the course.

Often you will need nothing more for class than access to a visualization tool or to Data Desk. Data Desk is available directly by clicking its icon in the toolbar.

Some visualization tools are invaluable to illustrate classroom presentations. The Normal and t-distribution density tools make discussions of confidence intervals and hypothesis tests clearer. The scatterplot tool used for correlation illustrates the sensitivity of correlation to individual values and the importance of linearity. The least squares tool makes regression line fitting clear and demonstrates that there is a unique least squares solution even to classes for whom minimizing the residual sum of squares analytically is inappropriate.

You may also want to demonstrate data analyses with Data Desk in class. This is an excellent way to bring more real-world examples into the classroom or to work with data collected by the class.

For classroom demonstration you will need a computer projector. If you wish to play any of the activities you will need to amplify the sound from your computer. Often there is no need for this; students have the soundtracks when they work with ActivStats individually. Note that the Preferences (in the Edit menu) let you set the size of the type in the Lesson Book for better projection.

Laboratory Setup

Many classes provide ActivStats in a statistics laboratory. You can license a laboratory so that several students can share a single ActivStats serial number, or have students use individual copies. Some schools may provide computers but have students purchase their own copies of ActivStats.

ActivStats need not be installed on the hard drive of a computer to work. Indeed, with over 1 GB of material on the DVD, few labs will want to devote the disk space needed to install ActivStats on individual machines. Students using individual copies of ActivStats will ordinarily need their DVD and a place to store their Student Progress File. At first use, students launch ActivStats and enter their individual serial ID numbers. The Student Progress File can be stored on a hard disk or floppy disk. Subsequently, they can open the student file (by dragging its icon over the ActivStats icon and releasing, or by opening the ActivStats icon, choosing Open Student File from the startup screen, and selecting the student file.) When they quit from ActivStats, students can save their student progress files on their floppy disk and easily resume at the same place next time even if it is on a different computer.

Note that the DVD itself must be in its drive for ActivStats to work.

Students will also need headphones. Ordinarily, this is not an additional burden; most students seem to be attached to headphones already. However, the computer vendors' habit of locating the headphone plug at the back of the computer can make it difficult to reach the plug. Extension wires may be needed for the lab computers. It is also easy to find "splitter" plugs that will let two students use a single computer together, each with an individual headset.

Homework

Each ActivStats lesson includes homework exercises. Many of these include data; a click on a button takes the student to Data Desk with the data present and the questions repeated for convenience. Most of these exercises ask students to interpret what they see in the data when they apply the methods being taught.

We have secured permission to quote homework exercises and include datasets from a number of leading textbooks. ActivStats thus has a larger collection and greater variety of homework exercises than most other texts. Wherever possible, we selected problems with real data and include the data. At times, we altered the original question to work with the entire datasets rather than a pencil-and-paper sized subsample. The "numbering" of the homework exercises indicates their original source.

Each ActivStats lesson also includes projects. Projects are typically activities that generate their own data rather than using data already provided. Many of the projects in ActivStats are quoted (with permission) from Alan Rossman's book Workshop Statistics.

Assessment and Tracking

ActivStats offers personal review quizzes so that students can assess their own progress and understanding. These are not intended to be graded or reported to the teacher. ActivStats has no built-in student tracking features. This was deliberate. One of the great advantages of multimedia learning materials is that they allow students to move at their own individual paces. Students should feel free to repeat an activity several times if necessary without fearing that "Big Brother" is watching and will think them stupid.

We recommend that exams include "screen shots" of both Data Desk and ActivStats with requests that students interpret what they see. Both programs can copy images to the clipboard (on both Macintosh and Windows) for pasting into a word processor.

As noted earlier, students can be asked to hand in solutions to the study questions found periodically (but unpredictably) in the middle of activities as a way to show that they have worked through the activities.

Scope and Sequence

The scope of ActivStats is the material commonly covered in an introductory statistics course. Indeed, few college courses cover all of the material provided. The most common omissions are conditional probability, inference for proportions, and contingency tables. Although all of these are valuable topics, the material has been designed so that any of these lessons can be omitted without loss of continuity.

The scope of ActivStats also conforms to the syllabus for the Advanced Placement exam in Statistics.

Statistics authors (and thus statistics teachers) have not settled on a single standard sequence for the introductory material. Consequently, ActivStats offers to reorder lessons to correspond to any of several leading textbooks. Several of these might be called the "Traditional, probability first" sequence. In this sequence, students are introduced to data and simple data description, then study probability in some depth. Subsequent discussion of inference build on the probability basis and the treatment of real data analysis grows out of inference. Texts by Triola; Weiss; McClave, Dietrich, and Sincich; Johnson; Devore and Peck; and others follow this approach. ActivStats offers detailed matches to the first four of these, but any of them will be close enough to use with other texts that take this approach but are not on the list.

The other sequence could be called the "Modern, data analysis" sequence. This sequence emphasizes data analysis, leading students through descriptions and interpretations of variables and relationships among variables through regression, and emphasizing intelligent data collection. Only then is probability introduced. Inference methods are then offered for the various data patterns seen in the first part of the course. Texts by Moore; Rossman; Moore and McCabe; Seigel and Morgan; Yates, Moore, and McCabe; and Freedman, Pisani, and Purvis follow this sequence. ActivStats offers complete matching with the first four of these, but any of them will be close enough to use with other texts that take this approach.

When ActivStats is purchased in a bundle with a textbook, it ordinarily comes configured for that book automatically. For other books, students need only open Preferences (in the Edit menu), select the appropriate text, and then save their student file.

The detailed lesson-by-lesson discussion below is in the Modern data analysis order of Moore's Active Practice of Statistics. A version in the Traditional, probability first order of Triola's Elementary Statistic is available from Addison Wesley.

Notation Notes

No two statistics texts agree entirely on notation, and none agrees entirely with any statistics package. The notation choices made in ActivStats reflect a preference for the notation of the Advance Placement Statistics exam, tempered by a desire to minimize the use of subscripts (which can be hard to make and read on a computer screen) and the mixing of Greek and Latin characters (also difficult on the computer.)

It is worthwhile to be aware of notation differences and to point out to students differences between ActivStats' notation and those of whatever texts they are using. The detailed lesson-by-lesson notes that follow discuss specific notation and terminology issues as they arise.