Newsletter of the Section on Statistical Education Section of the American Statistical Association

Contents of Volume 3 Number 1:

The more involvement there is from the Section's members, the more we will accomplish this year. Please contact me with your ideas for initiatives that we might undertake. Here are some specific ways that you can become involved now.

All the above could be signs that Robert V. Hogg--yes, Hogg of the famous Hogg and Craig team that wrote the ground-breaking book "Introduction to Mathematical Statistics"--is on the move and impacting students right and left.

Called "outstanding" by colleagues in the fields of teaching, research, publishing and speaking, he is famous nationally despite the fact that his career has been based entirely out of the university from which he received his master's and doctorate degrees. It is an unusual feat in this day and age where climbing to success seems to require moving from one learning institute to another. What is the key to such a successful communicator in statistics?

"Well, the good Lord gave me the mathematical abilities and I got my sense of humor and gift of gab from Mother," he explains. What that means practically is that he is one of the few statisticians who can communicate the science with the ease of talking to a best friend.

"I'm fairly relaxed. I really believe in interaction with the students," he said. "There are not many in academics interested in feedback. But students' complaints are blessings because they say, 'I'm doing something wrong.' But before they can complain they've got to trust you."

To build that trust, Hogg continually does the unusual and really opens up to the students. Laying his own personality on the line, he tells his class throughout the year that Wheaties is the cure to every ill known to man; it is the answer to every nagging question; the way to improve anything; you can, in fact, cure cancer with the cereal. Then to complete the inside lecture-joke he shows up to class in the "Green Wheaties Suit." Or he may begin singing one of the many tunes he has revised like "There's no Theorem like Bayes' Theorem." It's an unusual approach that not every statistician could employ.

"He is outlandish just to get the students riled up," quipped Ron Randles, chair of the Department of Statistics at the University of Florida. "Students remember his class. He loves people. He particularly enjoys working with students and colleagues. He is a very friendly guy--very bubbly. And he is very effective. The rest of us have to adapt--but he does it very, very well."

Randles knows of whom he speaks, having researched and published with Hogg. Hogg, in fact, labels Randles as being one of the two great partners in research--Craig being the other.

"I don't do research any more--but I had two great partners," Hogg explained. "Those two guys did a lot with me. You're lucky if you find one or two people in a lifetime to work with. I had two. We were concerned about students. We tried to do better. We talked a lot," he said.

Although Randles believes there is "a lot of ham in that Hogg," and notes that the theatrical styles employed by Hogg are effective, it is more than just a show that has led to Hogg's successes.

"His textbook is a classic and has brought him much fame," Randles says. "There are few within the profession like him. And I think one of the things is that Bob always has a positive outlook and in doing that he always inspires the best in people."

Sometimes doing what's best in people is painful, too. Hogg is admired for his tact and caring attitude about dealing with students. He has been overheard telling students in conference sessions that either they were in the wrong major or needed some revision in their commitment. These are not easy words to communicate without making people feel threatened, but words that are necessary if you really care as a teacher.

And sometimes the discomfort can be two-way. He is known for his "minute papers." These slips of paper are handed out the last minute of class, with the request that students relate the "muddiest" topic in class. The next day, the first five to ten minutes of class are devoted to reviewing these comments.

Even in large classes, he encourages students to "wave their hands if I'm going too fast." He has even had them use signs: green means "too slow, you can speed this up" and red means "slow down--this is tough stuff."

But the classroom isn't the only place Hogg has had success. Committees, national conventions and other campuses have also been the host of Hogg's wisdom and charm.

"When he is in a meeting--you know it," Randles said. Jim Calvin, associate professor of statistics at Texas A & M, concurs, "He's never met a crowd he wasn't willing to win over."

"He has a tremendous reputation as an instructor," he said. "The reputation in Iowa is he did not fear to use humor as part of his educational repertoire. He can teach the material and keep the students' attention."

Calvin experienced this first-hand when Hogg visited his university and agreed to give an hour lecture to his graduate statistics students. Although Calvin "thinks the world of Bob!" he assumed his "lecture" would really be a 20-minute joke session. What he got was the "most well-organized, prepared, sequential lecture I've ever heard," he said. Filled with references to articles and historical perspectives, Calvin said he looked down at his watch expecting just a few minutes to have passed and the hour was up.

"You know how you hear people say they hope they will have that much energy when they're that age? Well, I wish I had that much energy now!" Calvin muses.

And "energy" is exactly the adjective that describes Hogg. He has attained numerous successes in publishing and teaching. He has received honors and filled prestigious positions at both the university level and in national statistics organizations. Now, at 72 years of age, he is in "phased retirement," meaning a half-time position. What this means, in reality, is a full-time schedule this fall semester and a 27-university speaking and research tour in the spring. Leaving January 13 and concluding May 2, Hogg plans to start in Arizona and conclude in Minnesota, offering university statistics departments a choice of six lectures. And when he is not speaking he will be researching his own personal quest to see how Total Quality Management can be applied to university teaching. This drive is stimulated by his on-going desire to improve education in America.

"Unfortunately, in America today, mathematical skills are not as good as they should be. We've missed the boat," he said. He refers to the 1983 "Nation at Risk" revelation that the United States wasn't doing enough in math, chemistry and science. "We're even in worse shape," Hogg said. "They (students) are playing with computers but I get worried about basics. Maybe we should shut the TV off and the computer off. There's got to be a balance--and these guys that do (have a balance) get great things. But they know their basics."

This concern is the focus of his energy right now. After experiencing the mathematical and teaching success he has attained and after expending a lot of energy in his personal life with the loss of his first wife Carolyn, his marriage to Ann in 1994, raising four children and working professionally with some of them, he has the luxury of picking what he really wants to spend his time doing. And his choice is trying to fix the future of mathematical education.

"He is working on this because he's a man that has concerns. With his accomplishments, he must judge it as the most important thing he can accomplish," Calvin said.

This accomplishment would be the realization by society that we must not only get back to basics but also use those skills to reach out to other areas and a lot more people with training. "Unless we get involved," Hogg warns, "we'll have trouble. It's OK to do the math--but it's very important to reach out and get truly involved...not just consulting, but really involved."

He suggests degrees in statistical sciences with the emphasis in science. He suggests statistics majors get involved in other areas of interest and work in other fields. "Maybe even politics," he said, "but that's really going out on a limb."

Editors' Note: Bob has graciously given us a copy of his speaking tour schedule. Please check with the person listed in parentheses at each university for further details.

• Jan 19-22, Arizona State (D. Montgomery)
• Jan 22-24, U. of Arizona (J. Ramberg)
• Jan 26-29, Texas-El Paso (J. Rojo)
• Jan 29-Feb 1, Texas Tech (W. J. Conover)
• Feb 2-4,Texas-San Antonio (J. Keating)
• Feb 5-8, Texas-Austin (T. Sager)
• Feb 9-12, Rice U. (Scott)
• Feb 12-14, Texas A&M-College Station (J. Calvin)
• Feb 16-18, Louisiana State (L. Escobar)
• Feb 24-26, Florida State (D. Meeter)
• Feb 26-28, U. of Florida (R. Randles)
• Mar 5-7, U. of S. Carolina (W. Padgett)
• Mar 9-11, Duke (D. Berry)
• Mar 12-14 or 17-19, U. of N. Carolina (G. Koch)
• Mar 20-22, N. Carolina State (T. Gerig)
• Mar 23-25, VPI (K. Hinkelman)
• Mar 26-28, George Mason (E. Wegman)
• Mar 31-Apr 1, U. of Maryland-College Park (F. Alt)
• Apr 2-4, Penn State (T. Hettmansperger)
• Apr 6-8, Roch. Inst. Tech. (E. Schilling)
• Apr 9-11, Cornell (G. Casella)
• Apr 13-16, Waterloo (J. MacKay)
• Apr 16-18, U. of W. Ontario (D. Bellhouse)
• Apr 20-22, U. of Michigan (T. Raghunathan)
• Apr 23-25, U. of Wisconsin-Madison (B. Miller)
• April 30, Winona State (C. Blumberg)
• May 1-2, U. of Minnesota-Twin Cities (G. Oehlert)

Sandy Weisberg has organized a session titled "Using Graphics to Teach Statistics and Statistics to Teach Graphics", which promises to provide a different and thought-provoking perspective on the way in which we teach statistical concepts. Session participants will include Jan de Leeuw, Sandy Weisberg, Dennis Cook, Forrest Young, Robert McCulloch, and Dianne Cook.

Capstone experiences will be the theme of an invited session that will examine three different models for capstone experiences in the undergraduate statistics curriculum. John Spurrier, Richard Madsen, and Chris McLaren will present, and Jim Daly will be the discussant for the session.

"What I Did/Didn't Learn in School and How I Have/Haven't Used It in Industry" will be the topic of a panel discussion organized by Aidan Cardella. The panel will feature four recent graduates who will talk about experiences during the first few years in industry and the ways in which their education did and didn't prepare them for life after college.

Stat Ed will also be cosponsoring a session with the Section on Quality and Productivity. This session, titled "Use of the World Wide Web to Support Classroom Instruction", will address the use of course home pages and the way in which they can be used to support classroom instruction in statistics.

A new session format will be introduced this year-the invited poster session. There will be two invited poster sessions, one of which will be organized by the Stat Ed section. Our invited poster session will feature funded projects (NSF, NIH, etc.) that focus on the undergraduate statistics curriculum.

This year for the first time students will be applying to colleges and universities with AP Statistics credit. Colleges and universities that award either credit or placement for AP courses need to start thinking about their policy for AP Statistics. The fact that statistics is often offered by several departments makes this an issue that is somewhat different from that usually encountered when a new AP course is offered and may provide an opportunity to discuss the AP Statistics course with colleagues in other disciplines.

The first AP Statistics examination comes at a time when The College Board is undertaking a comparability study. This involves college and university students taking an examination that comprises a subset of the questions on the AP examination. This study thus provides a way of directly comparing their performance with that of the high school students who write the AP examination. Several thousand college and university students will be involved. Their papers will be graded with the AP examinations at a reading that will take place on June 8-13, 1997 at the College of New Jersey. If you are interested in applying to be a reader for this examination, application forms are available from Pam Esbrandt at Educational Testing Service, Princeton NJ 08541; (609) 734-1127.

This year the ASA has started offering a membership for schools. Advertisements have appeared in Amstat News and other publications. The suggestion has been made that ASA members take this opportunity to give an ASA membership to their local school. This is also an ideal time to make teachers aware of the AP Statistics Course. There are two publications, "The Advanced Placement Course Description -- Statistics" (IN-201694) and "Teacher's Guide to the Advanced Placement Course in Statistics" (IN number not yet available) that are both available from: Advanced Placement Program, P.O. Box 6670, Princeton NJ 08541-6670; (609) 771-7243. The Course Description, published in May 1996, includes the AP Statistics course outline and discusses the examination, giving sample questions and solutions. The Teacher's Guide, which will be available in April 1997, provides advice on how to go about offering an AP Statistics course. It also includes examples of scoring rubrics, sample syllabi, and a list of recommended resources for teaching the course.

Beyond making teachers aware of the AP Statistics Course, there may also be the opportunity to provide support for any teacher who decides to teach the course. Two of the most commonly asked questions are "What textbook should I choose?" and "What software should I choose?" Having someone who can give knowledgeable advice about these and other questions is invaluable.

One of the major issues for AP Statistics is the need for teacher training. A number of AP Statistics workshops were offered last summer, often through the Regional Offices of The College Board. Other initiatives, for example the Teachers Teaching with Technology workshops in AP Statistics, will offer workshops in 1997. These workshops are typically conducted by two instructors, a statistician and a high school teacher. It is important that college teachers support the training and preparation of AP Statistics teachers. Please consider how you can help make statistics education more effective at this level. If you are interested in running your own AP Statistics workshop, the ASA's Center for Statistical Education is keeping a list of high school teachers who are qualified to lead a workshop. You should also gain the approval of the Regional College Board Office so that it becomes an "official" AP Statistics workshop.

The remainder of the article is organized as follows. First, a case is made for radical revision of introductory statistical education as a key leverage point to positively impact the statistics profession as a whole. Next, an overall approach to redesign, based on four areas of revision is presented. These four individual areas will then be explored in detail, and lastly, an overall summary will be given.

The need for radical redesign. The status of the statistics profession has been discussed at great length over the past ten or so years, and has been addressed by virtually every ASA president in this time frame. There is general consensus that we should be more influential in important issues facing our country, such as health care, economic policy, and the evaluation of various social programs. The word "crisis" and phrase "under siege" have been used by some to describe our current situation. While I do not intend to review this vast literature, the following quote from Bailar (1995) is hopefully indicative of the tone of much of the commentary.

"As academic statisticians, we are missing the boat. We are barking up the wrong tree. We do not see what is plainly before us. We are kidding ourselves when we think that 'our' kind of statistics is vital to the welfare of the nation and the world....More and more, despite occasional appearances otherwise, we as academic statisticians are talking to ourselves. Even at this symposium, we talk about how to do the old things better and more broadly, not about what we could offer to society and what needs to be done...The kinds of statistics that we teach in under-graduate and especially in graduate programs have almost nothing to contribute to anything that matters on the scale of these problems."

Unfortunately, many view the problem as one of "image" rather than substance, and do not see a need for us to fundamentally change. In diagnosing why this is so, I believe Carl Morris (1995) gave the correct answer when he said: "Can the needed changes be made? I am pessimistic about this. It is awfully hard to change, because to do so requires performing surgery on ourselves, and that hurts."

If lack of influence is a symptom, what might be the root causes? As has been pointed out by many, the first exposure to formal statistics that most people receive is through introductory statistics courses in college. As someone who has both taught this course, and worked with numerous people in business and industry who went through it, I can testify that it can significantly and permanently impact students' perception of statistics. Unfortunately, this first impression is often negative, and may leave the future engineer or business leader with the impression that formal statistics is to be avoided at all costs. Bob Hogg (1991) spoke for many of us when he stated: "So students frequently view statistics as the worst course taken in college." I firmly believe that as a profession, we have significantly underestimated the long term detrimental impact to us of this perception by introductory students. I would further suggest that radical improvement of these introductory courses may be the single most powerful leverage point to improve the influence of our profession.

Clearly, we are not solely to blame for the poor performance of introductory statistics courses. The lack of quantitative literacy in incoming students, the low value placed on introductory courses by academic administrators, academic reward systems which force non-tenured faculty to narrowly focus their energies on publication, and the frequent use of untrained non-statisticians to teach statistics, all contribute to the problem. Most commentators have acknowledged that we should have the leading role in improving the introductory courses, however, and many positive reforms are under way. My concern is that individually these reforms appear detached from one another, and only address isolated symptoms. In other words, they appear as "one-at-a-time" experiments unguided by theory. What follows is an attempt to view the reforms holistically, and provide a theoretical framework for how they might be integrated.

A suggested approach. If we organize the main reform suggestions which have been made, we are left with four major redesign areas, which are closely interrelated. These provide a suggested course of action, which I would view as a "known solution", in that the individual ideas have been suggested previously, and generally agreed upon.

1. Consciously develop course objectives based on students' and future employer needs, and structure the course to meet these objectives.
2. Radically revise the course content based on the above objectives, which should lead to more emphasis on statistical thinking and less on numerical calculations.
3. Utilize experiential learning more and lecture less.
4. Reverse the organization of the course to teach overall approaches to scientific inquiry first, and individual tools afterwards.

All of these points are referred to in Shon's paradox, mentioned by Ullman (1995). Shon's paradox (gender neutral version) states: "The paradox of learning a really new competence is this:

• that students cannot, at first, understand what they need to learn

• can learn it only by educating themselves, and

• can educate themselves only by beginning to do what they do not yet understand."

I will now discuss the individual suggestions.

Course objectives. As noted in Shon's paradox, students do not know what they need to learn. Therefore, student evaluations cannot provide much guidance on what we should try to accomplish in the introductory course. I believe that much of the disagreement on course design is due to having different views of what we are trying to accomplish. As the old saying goes, if we don't know where we are going, any road will do! Despite the vast literature on reforms to the introductory course, precious little meaningful discussion over proper objectives has occurred. This point has been made previously:

Hogg (1991): "In some of these beginning courses, we must carefully consider the goals which differ from one group of students to another. Certainly, students in the liberal arts, taking statistics only to satisfy some 'quantitative reasoning' requirement, do not need to know about t and F tests....but no matter what the first course is under consideration, it is important to state the goals and give an appropriate course."

Wild (1994): "We need to give careful consideration to the aims and objectives of every part of our programs. If we have not thought through very carefully what we are trying to achieve, we are in no position to assess the quality of what we provide. Unfortunately, so much of what we do is not thought through from a careful consideration of customers, aims, and objectives; it just grows in an ad hoc way over the years, building on what has been done before."

In summary, we can't agree on a course because we haven't agreed on (or even discussed) objectives. Hopefully, however, all would agree that trying to make students experts in all statistical tools is not a realistic objective. It is interesting to look at typical introductory courses and texts, and think inductively about what set of objectives would lead one to develop this course. Such an exercise would seem to add credence to Wild's point.

Content. Again, as noted in Shon's paradox, the student is not in a good position to suggest content. Clearly the content should be directly based on the objectives. It has been convincingly argued, however, that any reasonable set of objectives would lead one to stress good conceptual understanding of statistical concepts over memorization of formulas. The following comments are illustrative.

Cobb (1991): "Emphasize statistical thinking: any introductory course should take as its main goal helping students to learn the basic elements of statistical thinking. Many advanced courses would be improved by a more explicit emphasis on those same basic elements."

Hogg (1991): "The course should focus on the process of learning how to ask appropriate questions, how to collect data effectively how to summarize and interpret that information, and how to understand the limitations of statistical inference .… Good statistics is not equated with mathematical rigor or purity, but is more closely associated with careful thinking."

Wild (1994): "These characteristics concern mental habits (rather than technical skills), which play a large part in statistical thinking...It would be very beneficial to society as a whole if these mental habits could be instilled early and widely, beginning with Stat 101."

Bradstreet(1996): "Our profession must decide if we want to teach people to compute before we ask them to think."

In summary, any reasonable set of objectives would lead to emphasizing statistical thinking over statistical techniques. The formal techniques can then be more rigorously addressed in subsequent courses. This is the approach typically used in other disciplines, such as economics, engineering, psychology, physics, and so on.

Since statistical thinking has become somewhat of a "buzzword", I would like to clarify that I am using the term in the sense of the definition published by the Statistics Division of ASQC (1995):

Statistical thinking is a philosophy of learning and action based on the following fundamental principles:

• All work occurs in a system of interrelated processes,

• Variation exists in all processes, and

• Understanding and reducing variation are keys to success.

This definition is discussed in greater detail in the Special Publication on Statistical Thinking (1996).

Experiential learning. Shon notes that students can only learn by educating themselves. While there are various learning styles, it is virtually impossible to develop a new competence without actually doing it yourself. For example, imagine trying to learn to play chess or bridge solely by studying the rules in a class. Again, the suggestion to move towards less lecturing and more experiential learning has been made by many.

Hogg (1991): "Instead of asking students to work on 'old' data, even though real, is it not better to have them find or generate their own data? Projects give students experience in asking questions, defining problems, formulating hypotheses and operational definitions, designing experiments and surveys, collecting data and dealing with measurement error, summarizing data, analyzing data, communicating findings, and planning 'follow-up' experiments suggested by the findings."

Garfield (in Cobb 1991): "I do not lecture at all."

Snee (1993): "We all learn more from what we do than from what we watch. Value comes from using statistics in one's life ... collection and analysis of data is at the heart of statistical thinking. Data collection promotes learning by experience and connects the learning process to reality."

In summary, this reform appears obvious, and more progress has probably been made on this one than the others. Considering the previous two points, however, using experiential learning to teach the wrong content is of little value.

Organization of the course. This is probably the reform area which has received the least attention in the literature. This is unfortunate, as it is well known in educational and behavioral research that the sequence in which material is presented significantly impacts understanding and retention. For example, it is known (Forrester 1990) that students learn most easily by seeing the big picture first, and then learning the details (whole to parts); by seeing a tangible example before learning the theory behind it (tangible to abstract); and by first grasping the concept of what they are doing, and then developing technical capability to do it (gross to fine). These points provide a proven theory to guide reform efforts. Statistics, especially at the introductory level, tends to use just the opposite approach:

• teach isolated tools and (perhaps) try to tie them together at the end (parts to whole)

• teach the theory and formulas, and then show an example (abstract to tangible) and

• emphasize calculating the correct answer, and hope the students grasp why they are calculating this number (fine to gross skills).

There are obvious tie-ins to content here. The overall process of scientific inquiry is a "whole". Real, sequential case studies can be used to introduce new techniques. In fact, Harry Roberts has been making this suggestion for years. "Gross" conceptual understanding is used with statistical thinking, while "fine" technical competency is used with statistical techniques.

One potential explanation for the statistical community's resistance to utilizing this theory is the current overemphasis on mathematics (See Box 1993). Anything mathematical is often viewed as "rigorous" or "pure", while the overall process of investigation, sequential case studies, and conceptual understanding, although certainly scientific, are often viewed as extraneous, or "fluff", because they cannot be rigorously mathematicized. What is really "meat", and what is "fluff" obviously depends on the objectives.

Shon's point that students "...can educate themselves only by beginning to do what they do not yet understand" refers to the need for gross understanding prior to technical competence, i.e., students need to begin applying what they have learned before they have fully mastered it. This point also explains why it is not a problem to show students techniques in a case study which they have not yet been formally taught. They can still get a gross understanding of what the technique is doing, and why it is being applied. This also creates "suction" from the students, in that after seeing the technique used, they are anxious to learn more about it.

Several authors have also noted the need to explicitly teach the overall process of scientific inquiry prior to teaching individual tools. This provides an overall context for the tools, so that students understand why they need to learn a particular tool, and how it fits in with the rest of the course. For example: Wild (1994): "The process of investigation as a whole should be the heart of any statistics program, particularly of the basic introductory course, Stat 101. It is something one should never lose sight of, and should always come back to." And Hogg (1991): "In particular, students should appreciate how statistics is used in the endless cycle associated with the scientific method..."

In summary, students' understanding and retention could be significantly enhanced by teaching the overall process of investigation before the tools, by using tangible case studies to introduce and motivate new topics, and by striving for gross understanding of key concepts (statistical thinking) before fine skills to apply numerical tools. It should be obvious that this would require virtually a complete reversal of the traditional course and text.

Conclusion. Revitalizing the introductory statistics courses may be the single most impactful thing we can do in the long run to enhance the influence of our profession within US society. There is enough theory and specific examples to guide radical revision of these introductory courses. Individually, the reforms have been proven effective. Integrating them would lead to the following overall approach:

1. Clarify our objectives. Suggestion - the main objectives should be to develop capability to apply statistical thinking and the overall process of investigation to everyday situations.
2. Base the content on the objectives. Suggestion - emphasize statistical thinking versus statistical techniques.
3. Utilize experiential learning. Suggestion - sequential, real projects of the students' choosing are excellent vehicles for learning the process of investigation.
4. Reorganize the course in light of educational and behavioral science. Suggestion - a potential sequence might be: Why are we studying this topic? (Gross understanding); What is it? (Part 1, Tangible whole - real case studies); What is it? (Part 2, Abstract whole - overall framework or model); How do I do it? (Fine skills in the tools).

Once the overall suggested approach was presented at a high level, details of the individual points (How) were discussed. The reader will have to decide whether this approach was more effective than if the article had begun with details of the individual reform areas, and then tried to tie them together at the end, without ever discussing why this subject is important. Such an approach would be consistent with the typical introductory statistics course.

Since how to change is basically known, the key question becomes will we? As noted by Hogg (1991): "Probably each of us thinks the others should change, but it is important that we must start with ourselves." Now is not the time to point fingers at one another, rather it is time for those who are willing to "belly up to the bar" and "perform surgery on ourselves". Good luck with your surgery!