A Cooperative Teaching Approach to Introductory Statistics

Deborah J. Rumsey
Kansas State University

Journal of Statistics Education v.6, n.1 (1998)

Copyright (c) 1998 by Deborah J. Rumsey, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the author and advance notification of the editor.


Key Words: Cooperative learning; Statistics education.

Abstract

Many of today's university undergraduate curricula include two seemingly conflicting themes: (1) increase the quality of teaching to include emphasis on pedagogical elements, such as active learning, in the undergraduate statistics classroom; and (2) cope with a decrease in teaching resources. In this paper, a means by which a department of mathematics or statistics can maintain and increase its standards of teaching excellence in introductory statistics while coping with ever-increasing budgetary pressures is proposed. This process involves promoting what we call cooperative teaching, applying the concepts of cooperative learning to a group of instructors.

1. Introduction: General Education and Statistics

1 A current and pervasive call for increased emphasis on the basic pedagogical elements of undergraduate education is being made by legislators, parents, students, and educators alike. In response to this call, many colleges and universities have established general education programs, including pedagogical elements in their courses such as active learning, making connections between disciplines, and drawing upon the students' experiences. These elements provide a natural environment for teaching introductory statistics; indeed, this framework echoes the calls for statistics education reform (see Cobb 1992, Hogg 1992, Cobb 1993, and Hoaglin and Moore 1992, for example).

2 Most statistics educators readily agree that introductory statistics courses following a general education framework are very important and should be implemented (see Cobb 1992 and Hogg 1992, for example). The accompanying increase in time, effort, facilities, and resources is also recognized (Cobb 1993). Yet, many universities are experiencing a tightening financial situation including reduced budgets, limited resources, and downsized departments. To many departments, a wish list including computer labs, multimedia classrooms, interactive statistical software, and one or two additional faculty seems unrealistic, at least for the time being.

3 This leads to the question, how might statistics educators rise to the challenge of including pedagogical elements in our courses that involve active learning, making connections, and drawing upon personal experiences, in light of budget and time limitations? In this paper, our progress toward answering this question is described. It is our hope that these ideas will be helpful to statistics educators in other programs who are faced with similar issues, and are wondering where to start.

4 The discussion throughout this paper involves graduate teaching assistants led by faculty coordinators; however, the model can be generalized for use by educators in other situations. Examples include: (1) mathematics departments in universities or community colleges where one or two statisticians lead mathematicians in teaching introductory statistics or mathematics courses; (2) institutions where part-time instructors teach lower-level math and statistics courses; and (3) a network of universities or colleges offering distance learning courses on the Internet.

5 Since implementing these pedagogical elements requires a significant commitment of time, energy, and creativity on the part of instructors, an organized system providing guidance and support is in order. A general overview of the system we developed is presented in Section 2. In Section 3, the cooperative teaching approach is described; details regarding how we use this approach to increase teaching quality under budgetary constraints are also presented. In Section 4, a general assessment of our progress after the first two years is given. Final comments and recommendations are presented in Section 5.

2. Getting Started: Challenges and First Steps

6 The target audience of the introductory statistics courses offered by Kansas State University can be stratified into the following groups: (1) business majors (five to six sections of 50 students each); (2) social science majors (five to six sections of 50 students each); (3) physical and natural science majors (one section of 50 students); and (4) others (four to five sections of 50 students each). Each group has its own introductory statistics course offered by our department. Instructors are typically graduate students in either the Masters or Ph.D. program, although occasionally faculty teach these courses. Some have previous teaching experience; some do not. Foreign students must pass a spoken English exam before being allowed to teach. Most graduate student instructors teach one class in addition to taking a nine-hour courseload. They assume full responsibility for the course(s) they teach, including writing and grading of all homework and exams. Each of these courses had been taught, relatively independently, by a group of four or five instructors, led by a faculty mentor. In order to reorganize and restructure these courses while recognizing the limitations in faculty time, consolidation of course coverage and content was a priority. Two faculty members volunteered as faculty teaching coordinators, replacing the faculty mentor system, and the process began.

7 Our first step as teaching coordinators was to reorganize the structure so that each of our four introductory courses would cover the same fundamental concepts in the same order, recognizing that the applications, and perhaps the mathematical abilities of the student audiences, would differ. In the spirit of general education, we broadened the scope of the courses to focus on the big picture: (1) statistics is an important part of each student's professional development; and (2) statistics is an important part of each student's everyday life (Iversen 1985, Moore and Roberts 1989, Moore and Witmer 1991). Six statistical themes were developed as a foundation for these courses: data awareness, variability, sampling, decision-making, scientific investigation, and relationships between variables (correlation, cause-effect).

8 This new approach involved promoting a change in the philosophy of teaching introductory statistics. That is, de-emphasize the traditional approach (typically focussing on formulas, step-by-step procedures, and computations) and shift the focus to the basic statistical ideas that are present in everyday life and in practice (see Hoaglin and Moore 1992). For example, instead of showing the computational formula for sample variance, the idea can be motivated through an in-class project, where students are given a series of distinct, small datasets, and the object is to find ways to measure the spread. Through a discovery approach supported by the instructor, students can develop an intuitive idea regarding variance that follows the definition formula. Moreover, the computational version of the formula is not needed since we do not stress heavy use of hand-computations, especially for large, real-world datasets; once the overall concept of variance is understood and practiced using the definition formula, the student can use the computer to find variance and can then focus on the interpretation of variability and its role in statistics.

9 With this new philosophy in mind, we chose a textbook for each course containing relevant, real-world examples and exercises pertaining to each audience, real-world datasets of varying sizes, and text written in the spirit of the general education themes. (The texts we chose are Aczel 1995, Brase and Brase 1995, and Sincich 1996). It was important to us that each text chosen offered the topics in the same order. We developed one common syllabus to be used for all four courses, using the six statistical themes as a foundation (see Appendix). These changes helped us to consolidate our coordination time and efforts, and promoted a sense of consistency among the courses.

10 The general education pedagogical themes of active learning, making connections, and drawing upon experiences provide a natural fit for statistics (Cobb 1991, Snee 1993, Magel 1996, Bradstreet 1996). Restructuring the courses thereby involved developing guidelines for the implementation of these themes in the classroom. This was achieved through the incorporation of activities such as in-class experiments and projects, written reports, discussions, opportunities for cooperative learning, evaluation of articles, relevant examples, and computer analysis of real-world datasets.

11 We immediately recognized the challenge that this new approach would bring upon individual instructors. Indeed, the idea of including a wide variety of activities in the introductory statistics classroom is welcomed enthusiastically by most instructors in our field; that is typically not the issue. Rather, how does one find the time and energy to undertake the process of collecting, organizing, and implementing these elements into the classroom on a week-to-week basis? This can prove to be a daunting and perhaps unnerving task for even the most experienced teachers who operate under a more traditional format. As Cobb (1993, p. 2) stated, "The need for curricular resources in statistics is acute, arguably more acute (at the college level) than in any other subject." The provision of support and guidance to statistics instructors in the successful implementation of general education themes into the classroom is critical (Hogg 1991). In view of this, two important decisions were made regarding coordination: (1) provide a teaching resource notebook for each instructor; and (2) organize and conduct weekly teaching meetings.

12 While a large volume of statistics teaching resource material exists, we wanted one organized place where information was presented in a consistent manner, relevant to the needs of the instructor, and available for easy retrieval. We therefore created a teaching resource notebook, starting with a collection of all of the best ideas from a committee of three faculty and two instructors. This notebook has since grown to a 300-page collection of teaching resources for introductory statistics. The teaching resource notebook contains a large collection of examples, experiments, projects, articles and accompanying discussion questions, handouts for using the computer, as well a listing of existing resources for additional ideas and information (such as statistics links on the World Wide Web). As an additional level of support for instructors, the teaching resource notebook is accompanied by three components: (1) an exam question pool, created through the contribution of instructor questions and maintained by department staff on our computer network; (2) a collection of low-cost equipment for in-class experimental use; and (3) one common set of easy-to-use statistical tables for use in all introductory statistics courses. More details regarding each of these support materials are given in Section 3.

13 We do not want instructors to waste time individually "re-inventing the wheel" to find good ideas for covering each item on the syllabus. The normal amount of time spent teaching and preparing for a three-hour class is expected to run 16-20 hours per week; the additional time necessary to find, develop, and include general education elements can easily double that amount if no support is offered. Our goal is to keep preparation time as close as possible to what it was before, including the added materials and new approach. With a common resource for ideas already in place, and a forum for sharing ideas in a cooperative environment, instructors can concentrate on developing their own teaching styles, and putting the ideas into practice. This also results in the development of additional resource materials, strengthening the support system.

14 Our second decision as teaching coordinators was to organize and conduct weekly meetings with all instructors as a group. We have conducted weekly teaching meetings for two years; they are an essential part of our teaching program. The purpose of the weekly meetings is three-fold: (1) discuss the statistical concepts to be covered in the upcoming week; (2) present ways to teach these concepts in the spirit of general education; and (3) test new teaching ideas. Through this format, instructors learn to view statistics in a way that is perhaps different from the way they were first exposed to it. A level of cooperation and collaboration between instructors is also established. Details regarding our weekly teaching meetings are given in Section 3.

15 This approach to the coordination of undergraduate statistics instruction is different from that taken by many universities in which common exams, homework, and activities are presented using a lecture-recitation approach. In such a system, a professor typically teaches two or three days per week in a large lecture format, with graduate students grading homework and exams, leading labs from a pre-written lab manual, and/or answering questions in a recitation format. While this type of format may serve the purposes of the professor, department, and even the students, it does little to develop the teaching and leadership skills of the graduate students. Hogg (1991, p. 343) observed, "it is clear that all of us would profit more if professors would serve as mentors to graduate students in teaching as well as research."

16 With our system, only three basic guidelines exist: (1) the sequence and selection of topics is to be covered according to the syllabus; (2) at least two writing assignments, two experiments/projects, and two computer activities must be included in each course each semester; and (3) exams written by new instructors must be approved by a faculty coordinator before being administered to a class.

17 The specific percentage of class time devoted to each of the various educational components (activities, discussions, projects, group work) varies by instructor; however, we encourage incorporation of non-lecture items on a weekly, if not daily, basis. Some of the more experienced instructors lecture hardly at all, while new instructors tend to supplement lectures with activities and discussions in increasing amounts over time, depending on their previous teaching experience and level of statistical knowledge. Within these guidelines, each instructor has the responsibility to decide how he/she will present the topics and assess student performance, as well as the freedom to develop his/her own teaching style in a supportive environment.

18 This approach to teaching introductory statistics reflects an investment in future generations of statistics educators and team leaders in industry and government. We call this approach cooperative teaching; it is described in detail in the next section.

3. The Cooperative Teaching Approach

3.1 What Is Cooperative Teaching?

19 Cooperative teaching applies the ideas of cooperative learning to a group of instructors. Garfield (1993) gives a series of recent definitions for the concept of cooperative learning, as it applies to students in the classroom. One definition (Davidson 1990) describes cooperative learning as including a task for group discussion and resolution (if possible), requiring face-to-face interaction, an atmosphere of cooperation and mutual helpfulness, and individual accountability. Another definition describes cooperative learning as an activity involving a small group of learners who work together as a team to solve a problem, complete a task, or accomplish a common goal (Artzt and Newman 1990). If we view a group of instructors in the above setting, it makes sense to talk about cooperative teaching, an environment where teachers share ideas and experiences, support each other, and work together toward a common goal of quality teaching. Individual accountability is reflected by the performance and effectiveness of each instructor.

20 Advantages of cooperative learning noted by Garfield (1993, par. 8) include "better group productivity, improved attitudes, and sometimes, increased achievement." Students "actively and individually construct their own knowledge" (Garfield 1993, par. 10) Garfield (1993) also points out that additional benefits of cooperative learning include experience with teamwork and problem-solving (marketable skills for a statistician especially), and an increased respect for other viewpoints and other approaches to solving a problem. The advantages of the cooperative teaching approach are similar, with an added bonus: the benefits of cooperative teaching reach two levels, the instructors and their students.

21 Operating independently each instructor might find it difficult and time-consuming to find relevant examples, datasets, computer projects, and articles for discussion for the variety of topics on the introductory statistics syllabus. But if each instructor, or team of instructors, is responsible for locating and sharing ideas for only a few topics, everyone benefits. Johnson, Johnson, and Smith (1991) showed that when students work together, they often accomplish more, and at a higher level, than they could individually; we have experienced similar results with our instructors under this new program. For example, two of our instructors have been working together to investigate different computer packages and report back to the rest of us; they have also developed and demonstrated projects for using spreadsheets in the classroom. Another team of instructors combined their woodworking skills to construct a game in which marbles are dropped down through a series of nails and into slots according to a binomial distribution.

22 A second advantage to the cooperative teaching approach is that it establishes a level of consistency from section to section within the same course. With a common syllabus, and one set of goals and guidelines, instructors are more cohesive as a group, and interact more with each other. This corroborates Garfield's (1993, par. 17) reference to students: "Working together towards a mutual goal also results in emotional bonding where group members develop positive feelings towards the group and commitment towards working together." Although this may be a bit optimistic to expect for a group of instructors, it is true that through an open forum for discussion, they make decisions together regarding issues such as how to grade exam questions involving short answers and opinions, or how to evaluate group work. They also have the opportunity to solicit and give feedback in a peer environment; an atmosphere of teamwork and collaboration is created. New instructors in particular enjoy a more supportive, less isolating environment with less start-up time.

23 An additional advantage of a cooperative teaching environment is that instructors experience ways in which others are teaching the same material; there is a continual emergence of fresh, new ideas. This encourages instructors to become more open about trying new things and gives them more options to offer their students. Research has shown that a wide variety of teaching techniques reaches the largest possible number of students (Higbee, Ginter, and Taylor 1991). As an example, some of our instructors have previous employment experience outside of academia; their insight into the practical nature of statistics provides an important viewpoint in our discussions.

24 The disadvantages of cooperative teaching seem to be few. It does demand a somewhat large initial time commitment on the part of teaching coordinators as well as instructors. On the other hand, once the program is established, the individual time commitment diminishes, and takes on more of a maintenance role. Increasing the quality of teaching by nature will require a larger amount of effort on the part of the instructor; our aim is to minimize that amount of additional effort.

3.2 Facilitating Cooperative Teaching Among Statistics Instructors

3.2.1 Weekly Teaching Meetings

25 Throughout the first two years of this endeavor, we experimented with various formats for our weekly teaching meetings, although our primary goals remained the same throughout -- to offer a forum to confirm statistical concepts, discuss and present ways to teach the concepts in the spirit of general education, and provide a testing ground for new ideas. In this subsection, different formats that we tried are described, as well as our future plans based on what we have learned.

26 During the first semester, groundwork was laid. The first part of each meeting included an overview of the material for the upcoming week as shown on the common syllabus. The philosophy of general education was presented and discussed in depth; that is, move away from the traditional approach to teaching statistics (hand computations and formulas, the flow-chart approach to working problems, daily lectures, and small, contrived datasets and examples) and move toward an environment of discovery, hands-on activities, critical thinking, and making connections to the students' everyday lives and professional careers through relevant, real-world examples. This philosophy follows the spirit of statistics education reform (Moore 1992, Hoaglin and Moore 1992, Cobb 1993). Examples include class discussions and projects involving data quality and ethics in data collection and presentation, developing the intuitive ideas of variability and margin of error early on, and discussing sampling procedures and design of experiments throughout the whole semester, not just during one part of it.

27 The rest of our meeting time that first semester was spent discussing how each instructor planned to implement the pedagogical themes of general education in his/her classroom. Items for discussion included conducting in-class experiments and projects, choosing articles and questions for in-class discussion, and exploring ways to incorporate computer instruction. Each instructor was encouraged to participate in a round-table discussion format. Most of them did; some did not. As an example, one discussion involved how to break a class into groups; it was generally agreed that some type of randomization scheme for assigning groups works best, since isolation of students and clique-formation are controlled.

28 Additional topics of discussion included the additional teaching skills that the general education approach demands. Instructors are asked to use the textbook only as a guide, not as the main teaching tool. They are asked to facilitate a new environment in the classroom, where students are actively involved, not just lecture spectators. Basically, they are asked to be real leaders in the classroom. For new instructors, and non-U.S. instructors who still find the language challenging, this can be especially intimidating. Support for instructors includes open discussions, tips and advice, and classroom visits where appropriate.

29 Areas for improvement were noted after the first semester. A survey of our undergraduate students found that a moderate percentage were not able to describe an example of how statistics was related to their major. Many instructors of statistics courses find that coming up with truly relevant examples is somewhat of a challenge, not being experts in the individual fields themselves. Many textbooks lack a good selection of relevant, real-world exercises and examples, as well as datasets. We decided that our weekly meetings for the second semester would focus on finding and presenting practical, interesting applications relevant to the student audience (business, social sciences, natural sciences, and all others); these examples would be added to the teaching resource notebook.

30 Thus, the format of the weekly teaching meetings for the second semester was modified somewhat. After the initial part of the meeting, where the upcoming material for the week was discussed, we broke into four groups based on the course taught; each group worked together to find ways of reinforcing statistical relevance in their classes. Resulting ideas included: (1) ask students to provide additional examples from newspapers and journal articles in their field, and to critique these examples; (2) incorporate on-line resources such as EESEE (available through the Ohio-State Department of Statistics homepage) and the Chance Database (Snell and Finn 1992); and (3) include additional datasets which were created and shared among instructors. Regarding relevant examples, some inroads have been made regarding this issue; however, it continues to be a challenge. As more textbook publishers join the statistics education reform movement, things will improve. Regarding this weekly meeting format, since the groups were smaller than they were the first semester, each instructor participated more often. However, we missed the cohesiveness of the whole group; we decided to go back to the large group format and find a way to promote increased participation from all members.

31 While instructors should always be encouraged to speak their minds regarding how the material is to be covered in class, a few guidelines help to maintain focus and productivity. Our guidelines were: (1) the material on the syllabus is not negotiable until the end of the academic year, when revisions are considered; and (2) how the material is covered is up to each instructor, as long as the course includes at least two written assignments, two computer assignments, and two in-class projects and experiments.

32 In the third semester of our new program, we added another level to the cooperative teaching approach: presentation of teaching ideas and activities in a peer environment. The first year we spent a great amount of time establishing what general education is and discussing ways to implement it in the statistics classroom. We knew that most of the experienced instructors had the basic idea, but some of them still needed practice actually carrying it out in their classrooms. In addition, our new instructors could benefit from this experience.

33 The format for the third semester did not include the initial time spent discussing the upcoming material that the previous semesters had. Instead, each week one team composed of both new and experienced instructors (chosen randomly) gave a 40 to 50 minute presentation on ways to cover the material for the week in the spirit of general education. Teams were created using a stratified random sampling approach; no one was chosen more than twice. A few guidelines were given to add a bit of structure and focus: (1) each member of the team must participate; (2) examples of written homework assignments, computer assignments, and/or in-class activities and experiments should be included; and (3) the topic for the week is the upcoming material on the syllabus. Instructors not involved in presenting material for the week contributed to discussion and offered feedback. Teaching coordinators came prepared with items to lead discussion.

34 This approach seemed to work very well; most presentations were of very high quality and served as an excellent forum for sharing ideas regarding teaching. There was also more balance in participation, since everyone contributed. One particular presentation involved an in-class project to compare the strength of two brands of facial tissue by placing a tissue in an embroidery hoop and adding one-ounce weights, one at a time, until the tissue broke through. The instructor leading the presentation asked us to find out how many one-ounce sinkers would be needed in order to conduct this in-class experiment with a class of 45 students, in groups of about four students each. Our group had fun conducting the experiment using several different methods, and developing an estimate of how many sinkers would be needed. And the instructor was better prepared to conduct this experiment in her classroom, because in the process of answering her question, we also provided important feedback regarding the conduct of the experiment itself.

35 The fourth semester of our work focussed on the presentation and testing of new teaching ideas in a peer environment. One particular in-class project involved sampling fish from a `pond' (generated by a computer and drawn on paper); each fish had a code number, and corresponding data, such as weight of the fish, were included in a file for use after the fish was `caught' (using one of several different sampling techniques) and identified. Objectives of the project included estimating the total number of fish and total weight.

36 The presentation format used during the third and fourth semesters of our program has resulted in some very exciting projects and discussions. However, we realize that instructors just entering our program during this time did not have the same opportunity for building a foundation that was offered during the first year. A two-tiered system for providing support to our instructors is therefore needed. (This will be true in any program where graduate students teach courses, since the turnaround rate for instructors is very high.) The first tier should focus on helping new instructors understand and implement the fundamentals of general education in statistics, and strengthen their knowledge of the topics to be covered in their classes. The second tier should focus on helping experienced instructors develop personal teaching styles, gain experience with higher-level educational topics, such as assessment, and develop more advanced teaching resources.

3.2.2 The Teaching Resource Notebook

37 The first edition of the teaching resource notebook was developed during the summer of 1995, through a small grant from the Kansas State University General Education Plan. The development committee included two graduate teaching assistants, the two faculty teaching coordinators, and Ray Waller, who spent a semester with us as a visiting professor. The committee first pooled together projects, experiments, examples, discussions, and newspaper articles that had been used in our classes; later, other materials were developed and added.

38 The notebook is organized into sections, according to each of the six statistical themes: data awareness, sampling, variation, decision-making, scientific investigation, and correlation/cause-effect. A seventh section, entitled `Additional Resources,' includes a reference list of items such as journal articles, books, workbooks, manuals, Internet addresses, and websites pertaining to statistics teaching resources that are already available. Sections are further divided into subsections according to type of resource material, such as projects, in-class discussions, examples, and datasets.

39 Each individual teaching resource item includes a detailed description of ways to use it in the classroom. This is a great advantage of the resource notebook; it not only gives ideas, but it explains how to carry out those ideas in the classroom. Grading tips are also described. For example, a newspaper article shows the results of a couples survey, indicating that money was the most-often cited issue for couples experiencing marital problems. The article goes on to imply that money problems cause divorce, without discussing any other possible confounding variables, such as communication skills or length of the marriage. A copy of the article and the source are included in the teaching resource notebook under the cause-effect section. Accompanying the article is the following explanation of how this article might be incorporated into a class discussion or a short written report: "Ask students to read this article and answer the following questions: (1) What was the source of the study? (2) How were the data collected? (3) Are there any problems with bias or lack of precision? (4) What statistical results were reported? (5) Do you agree with the conclusions made in this article? Explain your answer." Tips for grading reports are given.

40 Additional examples of teaching resource materials include the following: (1) discovery projects to learn how government statistics, such as unemployment rate, are calculated; (2) outlines for discussion of statistics heard in the news (examples provided); (3) class activities with student-generated data; (4) in-class experiments to test and compare product; (5) sample /resample projects; (6) simulation activities to illustrate the central limit theorem and confidence intervals; and (7) regression projects with stock market data.

41 Regarding the computer, much work remains to be done. We do not have our own computer lab, and we have no access to a computer teaching lab. Student accessibility to computers in public labs with the appropriate software is somewhat limited, as maintenance of statistical software adds to the already overburdened university computing network. Hence, there is a limited amount that we can ask of our students.

42 Given the state of the public computing situation, we must explore other options. Using the cooperative teaching approach, we can at least maximize the effectiveness of the computer resources we do have available. We have established a basic set of handouts to be used with our current statistical software package, SYSTAT, for inclusion in the teaching resource notebook. These handouts provide instructors and students with the basic knowledge to get started on the computer, in a step-by-step manner. Several projects have also been developed by our instructors specifically for our situation, for both the teaching and the practice of introductory statistics topics using the computer. Examples include random number generation, estimating the mean of a generated distribution using confidence intervals, and projects involving data displays and simple analyses.

43 Areas of promise include the use of graphing calculators for some of the basic computations; some textbooks now offer instructions involving the use of graphing calculators (for example, Brase and Brase 1995). Spreadsheets, although known to have some limitations (Nash and Quon 1996), may be the most practical and accessible computing resource for programs that do not have their own teaching labs.

44 Our work with in-class activities has revealed some important ideas. First, there are two distinct types of in-class activities: (1) activities designed to discover a concept; and (2) activities designed to put a concept into practice. For example, a series of small datasets can help students formulate measures of centrality and spread, while a project involving a series of attempts at drawing a 3-inch line without the use of a ruler is an exercise in quality control that uses measures of center and spread. Both types of in-class activities are important tools for implementing active learning in the classroom, and both are included in our teaching resource notebook.

45 Second, we have found that in-class activities that are straightforward, and that include directions that are very clear to the students, as well as to the instructor, are generally more successful. Reinforcement of the statistical concept(s) behind the activity is crucial; yet this reinforcement is easily neglected in the details of carrying out the activity. The teaching resource notebook is very helpful in this regard; it provides well-organized and clearly explained ideas for reinforcing the statistical concept(s) in the form of questions and ideas for group discussion, written reports, in-class follow-up discussions, and exam questions. Special "instructions for use" are included that give the instructor enough detail to easily carry out the project, yet leave enough room for project customization.

46 Finally, we have learned that an introductory statistics course can contain many exciting and effective in-class activities without the luxury of a high-dollar budget. We are not saying that we would turn down the offer of a multimedia computer lab, or that this simpler approach is better. What we are saying is that a program can make do without a large budget. Our most important resource is our instructors; as long as they are supported and encouraged to develop their teaching skills in a creative, cooperative environment, the overall goals can be accomplished.

47 Future goals regarding the teaching resource notebook include developing an electronic version for eventual availability on the World Wide Web. Work is currently in progress in this area.

3.2.3 Additional Cooperative Teaching Opportunities

48 Our instructors contribute to several additional areas of the education process. In this subsection, we describe some of these additional cooperative teaching opportunities. Through these opportunities, instructors gain additional experience; our teaching program is enhanced as well.

49 One area in which our instructors have contributed is textbook selection. The challenge is finding a textbook that fits the needs of general education, including relevant, real-world datasets and examples, as well as opportunities for activities beyond working homework problems and reading text. To tackle this challenge, instructors help us periodically review and select textbooks. Instructors who are assigned to teach the same course work together reviewing several texts. One group of instructors established the following set of criteria that prove very useful in textbook review.

  1. Does the text present and explain the topics correctly? (Unfortunately this cannot be taken for granted with statistics textbooks.)
  2. Does the text explain the intuitive ideas behind any formulas used?
  3. Are there enough examples, and are they relevant to the student audience?
  4. Does the text provide real-world datasets? If so, in what format?
  5. Are the themes of general education supported?

We feel confident in using textbooks that are chosen through this process.

50 Another cooperative teaching activity involves writing good exam questions in the spirit of general education. Writing a single exam question that requires critical thinking is a very challenging task; creating an entire exam in the spirit of general education is extremely time-consuming, especially for a new instructor. We realized that it would benefit all of us if each instructor would design a few questions, and we put all the questions together as one collection. This resulted in what we now call our Exam Question Pool.

51 Questions in the exam pool are categorized by topic, and include contributions from all of our instructors. To create the initial collection of questions, teams were formed; each team wrote four to six questions on a certain topic. The coordinators edited the questions, and department staff entered them into a WordPerfect file that can be accessed by all of our instructors. Instructors add to the exam pool each semester by contributing their best problems. Through this cooperative effort a large collection of high-quality questions is created; questions can easily be downloaded and edited for exam construction.

52 Consider the following example, involving variation. The student is required to demonstrate an understanding of the concept of variability, and its role in a statistical process.

A brand of oven is built to reach 400 degrees Fahrenheit in ten minutes. We want to know how consistent this brand of oven is, and how well it does at achieving this target temperature in a given amount of time. Fifteen ovens, all of this brand, are randomly selected. Each oven is set at 400 degrees. Ten minutes later, the temperature of each oven is recorded by observing a thermometer set inside each oven.

  1. Does this brand of oven achieve the target temperature overall? What statistic would we calculate to answer this question? Explain.
  2. Is this brand of oven consistent? What statistic would we calculate to answer this? Explain.
  3. Some of the variation in temperatures may be due to the way the measurements were taken. Design a procedure for taking the measurements that would help to minimize this variation.
  4. Name one source of variability in oven temperatures that could not be controlled by the person doing the experiment.

53 Security of exam questions is an obvious consideration. We let our instructors know that the exam pool is not to be used as a substitution for their own exams. In other words, the questions in the exam pool are to be used as a guideline only, not to be cut and pasted verbatim, but rather edited and customized to their own styles and specific coverage in the classroom. We also emphasize that old exam questions should not be re-used. This eliminates cheating problems between and within classes, and promotes individual teaching style and instructor responsibility -- a benefit that a common exam for all classes cannot provide. However, we need to emphasize that it is very important that coordinators look at the exams of new instructors to make sure they understand these issues when writing their exams.

54 In addition to the team effort in writing exam questions, instructors also work together to get their students ready for the final exam. They have composed a common final exam review packet with questions and answers, that is available to students at the university copy center for a nominal fee (helping to reduce the large departmental copying cost for over 900 students). Accompanying this review packet is a televised review session that was taped by the instructors in our on-campus television studio for later broadcast on our local campus television station. The students in each class were surveyed as to the usefulness of the common review; the majority of students surveyed were happy with this review session, and the instructors had a positive experience working to put it together. (It is always important to check out the facilities available to you at your institution; we were pleasantly surprised to learn that this service was available to us.)

55 Another cooperative teaching opportunity arose when we asked instructors to help comprise a list of low-cost equipment needed for in-class experiments. We received a small amount of funding from the Kansas State University General Education Plan for equipment to accompany projects and experiments outlined in the teaching resource notebook. The equipment we purchased includes tape measures, decks of cards, eyedroppers, beakers, weights, embroidery hoops, dice, poker chips, stopwatches, and some reference books, including the Statistical Abstract of the United States (U.S. Bureau of the Census 1995). As new projects are designed, the equipment inventory increases; for example, we have since added boards and several pairs of tongue-depressors for launching pennies under different experimental conditions. All of our equipment is cataloged and kept in the department office for easy access using a sign-out system. This low-cost equipment has contributed to the success and popularity of the in-class activities, as students and instructors alike find it great fun to use the materials in class in a discovery setting.

4. Assessment and Preliminary Results

56 Three areas of our general education approach to introductory statistics have been assessed thus far: (1) student effort and performance; (2) instructor performance; and (3) reaction of students and instructors to the general education program.

4.1 Assessment of Statistics Undergraduate Students

57 A set of expectations by the instructor has been found to be critical to learning, particularly in the cooperative learning setting (Garfield 1994). Our expectations for introductory statistics students are outlined as a part of the common syllabus, distributed to each student on the first day of class. The student expectations are the following:

  1. Read assigned pages from your textbook and other assigned materials.
  2. Participate in class discussions of newspaper/journal articles in which statistics is used and/or misused.
  3. Participate in group projects and experiments in which you will discover several important aspects of statistics with hands-on experience.
  4. Write evaluations of articles discussing current events involving statistics (O. J. Simpson case, AIDS testing, etc.).
  5. Display and analyze real-world datasets using the computer.
  6. Answer questions in which you will apply critical thinking to situations involving statistics.

58 Each instructor weights each of these activities in the way that he/she chooses. We suggest the following breakdown: homework, projects, activities, and reports (30-40%); three in-class exams and a final exam (60-70%). Most instructors use a system similar to this one. We believe that if students are expected to participate in a variety of activities, an appropriate amount of credit should be given for these activities.

59 General comments from instructors indicate that this assessment system works very well as long as students know what to expect regarding grading, and receive a fair amount of feedback. Students seem to enjoy the in-class activities and the projects. Instructors are generally pleased with the quality of student participation and performance, especially their written reports. Instructors are also very excited to see discovery taking place in their classrooms; connections are made as students bring in examples that are relevant to them.

4.2 Assessment of Statistics Instructors

60 Instructors are also given a description of what is expected of them by the department.

  1. Effectively communicate statistical ideas by providing clear and relevant examples, involving students in discussions, encouraging questions, and following through.
  2. Promote the spirit of general education by including elements that promote active learning, making connections to the students' field(s) of interest and to the world around them.
  3. Exhibit classroom leadership by leading in-class projects and discussions and organizing group activities.
  4. Demonstrate a positive attitude by showing a willingness to be open to new ideas, supporting other instructors, and communicating any concerns or problems to the coordinators.
  5. Effectively evaluate your students by establishing a grading policy that includes weight for general education activities, and letting your students know what to expect.
  6. Fulfill your basic teaching responsibilities (office hours, etc.).

61 The biggest challenges for our instructors, especially new ones, appear to be leading in-class discussions, getting students actively involved, and grading homework and exam questions that involve written answers using critical thinking. During our weekly meetings, we focus on these issues, providing examples and discussing some things to avoid, such as giving vague directions, or asking questions that could have two clearly different interpretations. When checking exams, coordinators watch carefully for potential grading problems.

62 Instructors are required to be evaluated by their students at the end of each semester; student feedback is very important. Many of our instructors found that their evaluations improved under the new system. Sometimes a new instructor will struggle a bit during the first semester, especially under a new system; therefore, the first semester probably does not adequately reflect his/her potential performance.

63 Classroom visits by coordinators are optional, except in rare cases where there is a problem. In such cases, coordinators work with the instructor to address the issue; if things do not improve, the department head may assign a new instructor to the course (only as a last resort). While such action is extremely rare, it is an important option to have, as the overall high quality and consistency of the courses must be preserved. Student complaints are handled by the coordinators, with involvement of the department head only when necessary. Students are not encouraged to change instructors except in special cases.

64 Under this system, instructors show increased productivity, improved attitudes, gains in knowledge about teaching and problem-solving, and an increased respect for other viewpoints. In addition, we feel that they are better equipped to teach and be leaders in other capacities after having had the experience, support, and responsibility that this system provides.

65 Duties of teaching coordinators are described below.

  1. Provide direction and leadership regarding the implementation of general education activities in the classroom through syllabus formulation, provision of a teaching resource notebook, textbook selection, and handling of administrative details for running the courses.
  2. Organize and plan weekly teaching meetings to discuss the upcoming material each week, and help instructors develop and strengthen the skills necessary to meet general education objectives in the classroom. Such skills include leading in-class discussions and activities, conducting experiments, assigning and grading homework and exam questions, and managing the course without doing an extraordinary amount of grading.
  3. Promote the development of individual teaching styles.
  4. Help establish and maintain consistency among instructors regarding exam writing and grading.
  5. Provide support by being enthusiastic, encouraging new ideas, offering constructive feedback, encouraging instructors to voice their concerns, and following through.
  6. Report progress to the college.

66 The amount of work required for the position of teaching coordinator, especially if done by one person, is sufficient to justify a reduction in teaching load by one three-hour course. However, due to budget limitations and extraordinary course demands, this may not be possible. Our department is very supportive of our work, and while a means for compensation is not currently in place, it remains an important goal. As for now, coordination is being done by the same two volunteers; should that position rotate, clear and complete documentation and organization of materials will facilitate that transition.

67 We found that coordinating instructors in this program is a very rewarding experience, personally and professionally. Our work is generally well-received by the instructors. One particular challenge for the teaching coordinators is finding a balance between structure and flexibility. We must `practice what we preach' by providing enough structure to give instructors direction and focus, yet offering enough flexibility and support to promote the development of their own teaching styles. Mentoring, rather than managing, is a much more rewarding approach.

4.3 Assessment of the Approach to General Education

68 At the end of the first semester, we surveyed the instructors and their students regarding their reaction to the way we were now teaching introductory statistics. In this subsection, we describe some general results.

69 The undergraduate students generally fell into two groups based on their reactions. One group (the majority) seemed very excited about the way the class was being taught, and thought it was much more interesting and relevant than they expected it to be. The other group seemed to balk against the active learning environment; they were expecting the usual lecture format, in which they would spectate rather than participate. This was not an unexpected outcome; in fact, we can be encouraged by it. In a sense, if we are not satisfying those students who wish to remain passive about statistics, we might be on the right path.

70 One item of concern is the use of the computer in our classrooms. Some undergraduate students felt that the computer was not incorporated smoothly into the courses; they did not understand how the computer work was related to the rest of the activities and material. This is not surprising, as it is difficult to incorporate computers without access to at least one of them in the classroom. We realize that this will be an ongoing struggle. Our instructors have made progress in this area by writing detailed computer handouts, finding creative ways of using a portable computer system in the classroom, and designing projects using the computer to both teach and illustrate the practical use of statistical topics.

71 A survey of the instructors at the end of the first semester indicated that they were buying into the idea of general education, implementing it in their classrooms, and seeing some positive effects. They appreciated the weekly meetings and the cooperative teaching approach to lighten their workload and provide new ideas; the teaching resource notebook was found to be particularly helpful. Through feedback from the instructors our program will continue to improve.

5. Recommendations and Concluding Remarks

72 Our program for establishing the themes of general education in our introductory statistics courses at Kansas State University is still in the developmental stages; there is still much to learn. However, we have made progress toward our goals of improving the quality of the courses and the teaching experience for our instructors. This has been accomplished through a cooperative teaching approach.

5.1 Tips for Implementing General Education in Introductory Statistics Using the Cooperative Teaching Approach

73 Based on what we have learned over the past two years, our recommendations to a statistics or mathematics program considering adopting a program similar to ours are described below.

  1. Establish an administrative structure that everyone can live with. We found that it works best if all instructors are treated equally, without a hierarchical, competitive system in which some have greater responsibilities than others. What seems to work for us is a team approach where each team includes a random selection of one or two experienced instructors, working with a random selection of one or two new instructors. An open communication line between faculty teaching coordinators and the department chair is important; any problems and/or complaints must be handled together.
  2. Be very clear about your own philosophy regarding general education and introductory statistics. This helps to provide the initial direction and establish a general tone for instructors to follow; it also helps to maintain focus.
  3. Be clear about expectations. Since this is a new approach to teaching statistics, it is important to let students and instructors know what is expected of them. These expectations can then be referred to from time to time, to self-assess the program at all levels.
  4. Be flexible and creative. Lively discussions, a high level of participation and enthusiasm, and an openness to other viewpoints and ideas are instrumental toward the implementation of general education into the statistics classroom. This applies to teaching coordinators as well as instructors.
  5. Include instructors in the process wherever possible. We approach this in the spirit of teamwork, with the idea that we are all in this together. Instructors are always encouraged to give input and feedback to the teaching coordinators, and to each other. Everyone benefits from a cooperative approach.
  6. Offer support and guidance to instructors without being controlling. One of the greatest advantages to the cooperative teaching approach is that it promotes and cultivates the teaching style of each instructor within a supportive, semi-structured environment. Weekly teaching meetings help greatly in this regard.
  7. Be organized. One objective of the cooperative teaching approach is to conserve time and resources by limiting the amount of time an instructor spends looking for resource materials. This demands a well-organized system.

    A collection of ideas that is readily accessible to the instructor is very helpful, and serves as an organizational foundation to operate from. Our teaching resource notebook is unbound; it is kept in a wide three-ring notebook so items can be added, deleted, and edited easily; there is also room on the back of each page for individual notes. Many portions of the teaching resource notebook are also available in WordPerfect format on our departmental computer system.

    The second major area of organization involves a collective source of exam questions. Our exam question pool is maintained by department staff in WordPerfect files on the department computer system; readers can copy and edit questions for their own use. There is a special security mechanism included on these files, for obvious reasons.

    Finally, an agenda for the weekly meetings should be established to maintain focus and productivity, and to provide opportunities for all instructors to participate. The meetings should be organized into two separate components, one for new instructors, and one for those having prior experience with the program.

  8. Be sure to follow through. Throughout the course of a semester, several activities may be going on at once (maintaining the exam question pool, updating the teaching resource notebook, and preparing for weekly teaching meetings, for example). It is important to keep abreast of all activities, and establish a timeline for following through. Taking notes during meetings and establishing deadlines will help in this regard.

5.2 Looking to the Future

74 The cooperative teaching approach allows us to implement the pedagogical themes of general education in a way that minimizes the overall amount of additional time and effort. This is accomplished through teamwork and cooperation among instructors as they develop and share ideas, receive and offer feedback, and work together toward the common goal of teaching introductory statistics in the best way possible. We are very happy with the progress we have made in establishing a teaching resource notebook and a weekly teaching meeting structure; ideas are collectively developed, presented, tested, and written down in an organized form for easy retrieval and use. Our instructors have the responsibility and the freedom to develop their own teaching styles and leadership qualities; this is an important investment in the future of statistics education.

75 Much work remains to be done. Textbook selection remains a challenge, since many textbook publishers have yet to adopt the new general education philosophy. We are still not certain as to what role the computer should have, or how best to deal with limited computing resources. And we continue to improve the structure of our weekly meetings. We look forward to the opportunities that the World Wide Web brings; in particular, a place for an electronic version of our teaching resource notebook. Future research includes investigating additional forms of assessment of general education in introductory statistics and the cooperative teaching approach.

76 We believe that the call for educational reform will continue, and that budget limitations will also continue. This is the time to make the best use of all resources available, the most important of which is our instructors. Toward this end, let us as statistics educators commit ourselves to two goals: (1) Increase the quality of introductory statistics courses without greatly increasing the need for resources. (2) Support the development of introductory statistics instructors; they are the future of statistics education. It is our hope that the ideas in this paper provide some means toward realizing these goals.

77 For additional information regarding the teaching resource materials described in this paper, please contact the author.

Acknowledgments

The author wishes to acknowledge the support and partnership of James J. Higgins throughout this endeavor, as well as helpful comments and support from Ray Waller, John Boyer, and Dallas Johnson. Also, the hard work and enthusiasm of the graduate teaching assistants at Kansas State University must be recognized; special thanks to Lynda Ballou and Marjorie Bond for helping to create the original version of the teaching resource notebook. This work was partially supported by two grants from the Kansas State University General Education Plan.


Appendix: Syllabus for Stat 330

Stat 330 Syllabus
Elements of Statistics for the Social Sciences

Text: Understandable Statistics
by Brase/Brase

Format for the Course

This course has been designed with the University Guidelines for General Education in mind; that is, in addition to the typical lecture-textbook format, we will be enhancing your experience by including other activities and ideas that draw on your personal background and experience, and better prepare you for future coursework, research, and application of statistics in your field.

General Topics

We have outlined six general topics to be stressed throughout the course, using the methods we've outlined above:

  1. Awareness of Statistics: how statistics is presented to you on a daily basis; use and misuse of statistics.

  2. Variation: measuring variability, accounting for variability, and attempting to reduce variability; the role of probability in variation.

  3. Sampling: how to collect sample data, sampling distributions, margin of error, the Central Limit Theorem.

  4. The Decision-Making Process: designing and carrying out a scientific experiment in order to help you make a decision; the role of statistics in this process.

  5. Scientific Investigation: What questions to ask; how to collect the data (sampling, experimental design); what conclusions you can draw; do's and don'ts.

  6. Correlation and Cause-Effect: how to look at relationships between different items of interest; what we can and cannot say.

Expectations

We provide many different media through which you can learn to understand, apply, question, evaluate, and communicate ideas in the many situations where statistics plays a role. These different methods may include the following:

Suggested readings from a textbook chosen on the basis of its clarity, relevance, and applicability to your field(s) of interest, designed to supplement the other forms of learning you will gain from this course.

In-class discussions of newspaper/journal articles where statistics is used and/or misused.

Group projects in which you will discover several important aspects of statistics with hands-on experience.

Written evaluation of articles discussing current events involving statistics (O. J. Simpson case, AIDS testing, etc.).

Computer activities involving display and analysis of real-world data.

In-class experiments conducted by groups, the results of which will be written up in a final report.

Homework problems and exam questions in which you apply critical thinking (beyond computations) to situations involving statistics.

If you have any problems or conflicts regarding this class, first try to resolve the issue with your instructor. If the problem is not resolved, please contact Dr. Rumsey, GTA coordinator, at 532-0523.

                      Course Schedule

Class  Topic                                 Section    Pages

1      Introduction/Motivation               1.1-1.3    1-19

2      Data Quality/Ethics
       with Statistics                       1.1        7-14

3      Sampling                              2.1        23-33

4      Data Display -- Frequency
       Distribution, Other Techniques        2.2-2.4    37-83

5      Centrality Measures                   3.1        107-116

6      Variation Measures                    3.2        120-134

7      Identifying and Controlling
       Variation                             3.4        152-161

8      Data Display Using the Computer       Handouts   ----

9      Probability -- Definitions, Rules
       and Variation Connection              4.1        185-194

10     Conditional Probability --
       Contingency Tables/Independence       4.2        197-210

11     Independence (continued)              "          "

12     Review                                ----       ----

13     Exam 1                                ----       ----

14     Random Variables, Probability
       Distributions, Expected Value and
       Standard Deviation:  An Example       4.4        237-245

15     Binomial Distribution                 5.1-5.3    261-288

16     Binomial Distribution (continued)     "          "

17     Normal Distribution and Control
       Charts                                6.1        325-349

18     Normal Distribution                   6.2-6.3    350-381

19     Sampling Distributions/Central Limit
       Theorem -- Class Demonstration        7.1-7.2    401-416

20     Central Limit Theorem --
       Problems/Concepts of a Confidence
       Interval                              7.2/8.1    443-454

21     More Confidence Intervals/
       t-distribution                        8.2        459-466

22     Class Demonstration on                ----       ----
       Confidence Intervals

23     Confidence Intervals for
       Proportion/Sample Size                8.3-8.4    470-485

24     Review                                ----       ----

25     Exam 2                                ----       ----

26     The Decision Problem --
       Concepts                              9.1        529-543

27     Test for a Mean                       9.2-9.4    547-580

28     Test for a Proportion                 9.5        585-591

29     Scientific Experimentation --         ----       ----
       Concepts

30     Paired Comparison Experiments         9.6        594-603

31     Test for Means:  2 Independent
       Samples                               9.7        610-624

32     Contingency Table Analysis:
       Chi-Squared Test for Independence     11.1       747-757

33     Contingency Table Analysis and Test
       for Goodness-of-Fit                   11.2       761-766

34     Goodness-of-Fit:
       In Class Demonstration                ----       ----

35     Review                                ----       ----

36     Exam 3                                ----       ----

37     Alternative Measures
       of Association                        handouts   ----

38     Regression:  Introduction to Paired
       Data and Scatter Diagrams             10.1       655-662

39     Linear Regression and Confidence      "          "

40     Bounds for Prediction                 10.2       665-681

41     Correlation and Cause/Effect:
       Concepts and Computation              10.3-10.4  687-709

42     Class Discussion of Car Data --       handouts   ----
       Regression/Correlation

43     Review                                ----       ----

44     (Floating Day)

45     (Floating Day)

       Final Exam


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----- (1992), "Teaching Statistics," in Heeding the Call for Change: Suggestions for Curricular Action, ed. L. Steen, MAA Notes No. 22, Washington, D.C.: Mathematical Association of America, pp. 3-23.

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----- (1994), "Beyond Testing and Grading: Using Assessment to Improve Student Learning," Journal of Statistics Education [Online], 2(1).
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Hoaglin, D., and Moore, D. (eds.) (1992), Perspectives on Contemporary Statistics, MAA Notes No. 21, Washington, D.C.: Mathematical Association of America.

Higbee, J., Ginter, E., and Taylor, W. (1991), "Enhancing Academic Performance: Seven Perceptual Styles of Learning," Research Teaching in Developmental Education, 7, 5-10.

Hogg, R. (1991), "Statistical Education: Improvements are Badly Needed," The American Statistician, 45, 342-343.

----- (1992), "Report of a Conference on Statistical Education," in Heeding the Call for Change: Suggestions for Curricular Action, ed. L. Steen, MAA Notes No. 22, Washington, D.C.: Mathematical Association of America, pp. 34-43.

Iversen, G. (1985), "Statistics in Liberal Arts Education," The American Statistician, 39, 17-19.

Johnson, D., Johnson, R., and Smith, K. (1991), Cooperative Learning: Increasing College Faculty Instructional Productivity, ASHE-ERIC Higher Education Report No. 4, Washington, D.C.: The George Washington University.

Magel, R. (1996), "Increasing Student Participation in Large Introductory Statistics Classes," The American Statistician, 50, 51-56.

Moore, D. (1992), "Teaching Statistics as a Respectable Subject", in Statistics for the Twenty-First Century, eds. F. Gordon and S. Gordon, MAA Notes No. 26, Washington, D.C.: Mathematical Association of America, pp. 14-25.

Moore, T., and Roberts R. (1989), "Statistics at Liberal Arts Colleges," The American Statistician, 43, 80-85.

Moore, T., and Witmer, J. (1991), "Statistics within Departments of Mathematics at Liberal Arts Colleges," The American Mathematical Monthly, 98, 431-436.

Nash, J., and Quon, T. (1996), "Issues in Teaching Statistical Thinking With Spreadsheets," Journal of Statistics Education [Online], 4(1).
(http://www.amstat.org/publications/jse/v4n1/nash.html)

Sincich, R. (1996), Business Statistics by Example (5th ed.), Upper Saddle River, NJ: Prentice Hall.

Snee, R. (1993), "What's Missing in Statistics Education?," The American Statistician, 47, 149-154.

Snell, L., and Finn, J. (1992), "A Course Called Chance," CHANCE: New Directions for Statistics and Computing, 5, 12-17.

U. S. Bureau of the Census (1995), Statistical Abstract of the United States (15th ed.), Washington, D. C.


Deborah J. Rumsey
Department of Statistics
Dickens Hall
Kansas State University
Manhattan, KS 66506

rumsey@stat.ksu.edu


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