Joan B. Garfield
University of Minnesota
First, I want to share with you some of my reactions upon being invited to participate in this symposium. I thought there had been a mistake because, after all, I am not involved in a graduate statistics program, and I do not teach statistics courses to graduate or even upper-undergraduate majors in statistics. I am an educational psychologist whose area of research has focused on the teaching and learning of statistics, primarily at the introductory level. What could I possibly contribute to a discussion of modern interdisciplinary statistical education? However, John Tucker convinced me to give it a try and share with you some of my perspectives on teaching and learning statistics as they relate to the theme of this symposium. I must admit that I am glad he did convince me to accept his invitation, because I have had the opportunity to read some very interesting papers and find out that there are some very dedicated statistical educators who share some of my concerns and beliefs about educating students. I have already learned a great deal by reading the advance papers and listening to the presentations today, and will try to frame some of my reactions to the presentations we have heard in the context of my work on teaching and learning statistics.
Let me briefly summarize what I have heard so far: The purpose of this conference is to instigate change in upper-undergraduate, graduate, and postdoctorate statistics education. The focus is what changes in statistics education are needed to incorporate interdisciplinary training into these programs, bring curricula up to date, and improve the apprenticing of statistics graduate and postdoctoral students.
We began by listening to some excellent papers on what different customers are looking for in the statisticians they hire, hearing from the different areas of industry, academia, and government. Then we heard two papers on what the implications of these needs are for statistics education, and have learned about an exciting program at Carnegie Mellon that is trying to address these needs in some innovative and laudable ways. I heard some recurrent themes interwoven into these papers. I want to highlight a few, beginning with the needs perceived by the customers.
We heard about the need for:
Teamwork and collaboration: the need for statisticians to be able to work together, solving problems and working on projects, and the need for them to bring to these teams not only their statistical expertise, but also their knowledge of other disciplines involved so that they may contribute as full partners in the research effort.
Communication skills, both oral and written: the need for statisticians to be able to write and speak effectively about the methods and results of statistical analyses and the conclusions of projects undertaken.
Solving real problems with real data: the need for statisticians to be able to apply skills to a variety of contexts, know how to frame meaningful research questions, and help select appropriate methods.
These themes were echoed in the two papers that addressed what statistical education should be as viewed from academia and in a larger perspective. In addition, those presentations addressed two other themes:
The increased amount of knowledge to be learned (in the area of statistics as well as specialized knowledge in different disciplines, and particularly in science).
The need for internships and real-world experience in analyzing data and working on projects.
In the two papers just presented, we also heard much about what the content of statistics education should be to prepare future statisticians to meet the needs of our customers. Now, I wish to focus on the process of educating statisticians.
Keeping in mind the five themes I just outlined, I would like to share with you some findings from educational research that have implications for teaching and learning statistics. Then I will return to these five themes and relate them to the findings from educational research.
Learning is a constructive activity. Students learn by constructing knowledge and by being actively involved in learning activities. This contradicts the model of a student as an empty vessel or a blank slate, waiting to be filled with knowledge, as if knowledge is something that can be given or transmitted. Instead, the theory of constructivism describes learning as the process of integrating new information into students' previous knowledge and beliefs, as students construct their own representations of what is being learned. Much research in the areas of cognitive science, mathematics education, and science education supports this theory of learning.
Students learn to do well only what they practice doing. Research has shown that students become better problem solvers only if they have had frequent opportunities to solve problems. They become better communicators if they have had a great deal of practice trying to communicate their ideas and understanding.
Students learn to value what they know will be assessed. Students are astute at figuring out what they will be tested on and how they will be tested. Even if instructors profess to have other educational goals, such as learning to work together cooperatively or being able to understand important ideas, these will be taken seriously only if they also are included in assessment and grading.
Students seem to learn better when they are able to work in small groups on structured learning activities, when they are able to work on open-ended problems, when they are encouraged to write about what they have learned, when there is an emphasis on problem
solving and higher-order reasoning skills, and when they receive consistent and helpful feedback on their performance.
How do these suggestions relate to the themes mentioned previously? Students learn by constructing knowledge. Good students may be fairly adept at constructing knowledge from a lecture. By the time they have been accepted into a graduate program in statistics, they have already succeeded in undergraduate education, most of which consists of passively listening to lectures. However, students tend to learn better if they engage and struggle with material, rather than having it ''delivered" to them. This works best when they are able to interact and discuss their learning with others. Not surprisingly, cooperative learning activities have been shown to be an effective way to learn, because students are actively engaged in constructing knowledge. If students develop experience learning to read and learn on their own or in collaborative situations, they come to realize that a lecture is not the only (nor the optimal) way to learn, and they should be more able to continue learning on their own outside of formal education. This is one way to deal with the theme mentioned earlier of too much content and too little time to learn it in the confines of an undergraduate or graduate program.
This leads us to the theme of teamwork and collaboration. Since students learn to do well only what they have practiced doing, teamwork and collaborative activities need to be an ongoing part of students' educational experience, and not just one isolated class in which students work on projects. Teamwork and collaboration should also be modeled by the sharing of experiences by faculty involved in cross disciplinary projects.
Encouraging collaboration and teamwork may not be an easy component to add to courses. Remember that students are used to being in competitive academic environments, where they are used to competing against each other, rather than working collaboratively with each other. Some may resist working on group projects, especially with group grades assigned. Students may be concerned about working with others who appear different from themselves. I would encourage you to consult some of the excellent literature on collaboration in higher education for suggestions and guidelines on how to successfully incorporate cooperative group activities into your classes (Artzt and Newman, 1990; Davidson, 1990; Garfield, 1993; Goodsell et al., 1992; Johnson et al., 1991; Weissglass, 1993).
The second theme I mentioned was communication skills. How do we know what our students have learned, and how do we know how well they are able to apply what they have learned? One important way to determine this is by giving them frequent opportunities to communicate their learning or performance, via written reports or oral presentations. By incorporating these types of activities into a class, we are actually doing several things:
Collecting information to help us see what students have learned and how well they can apply their knowledge, and using this information to provide feedback about the quality of their learning and application;
Giving students experience in learning to communicate effectively, by offering feedback on communication skills; and
Demonstrating that communication is an important part of statistical work.
In addition, incorporating "writing to learn activities," in which students are asked to explain their understanding or interpretation of what they are learning, not only tends to improve their learning but also provides additional practice for students so that they may improve their written communication skills. Therefore, I believe that it is important to build written and oral communication skills into most of the classes students take, to help them develop these important skills needed by our customers, as well as to improve their own learning process.
The third theme I mentioned was solving real problems. We heard recommendations for courses to be built on real problems, real data, taught by people with experience analyzing real data, who can provide role models in data analysis. We agree that students need to experience solving or seeing problems solved in a variety of different disciplines and settings, involving resources or resource people from those disciplines. Again, these kinds of experiences can build collaboration and teamwork, give students practice in solving problems, and help them construct knowledge of how problems are solved in different contexts and disciplines.
I believe that students need to develop experience in solving open-ended problems, ones that may not be well defined and need to be clarified before they can be solved. In working on open-ended problems where a variety of approaches may be taken, based on different methods and assumptions, students should be encouraged to defend their selections, argue for their approach, and question other approaches and conclusions. These types of activities can help them develop higher-order thinking and reasoning skills as well as give them practice in problem solving.
If statistics educators agree that all of these different types of experiences are really valued, then we should make sure that students' educational programs include many experiences applying and improving their problem solving and communication skills and ability to work collaboratively with others. They should be assessed on their performance in each area and given appropriate feedback so that they may work toward improving their performance in each area.
This leads to a very different view of teaching, as the teacher's role becomes more that of a designer of activities, and facilitator of assessment and learning. This is a departure from the traditional role of teachers, viewed typically as "givers of knowledge," a view that is incompatible with the constructivist theory of learning.
Let me now attempt to summarize what I see as the implications of these issues for teaching statistics.
Statistics teaching can become more effective if teachers determine what it is they really want students to know and do as a result of their courses — such as the things we have been discussing today — and then provide course work, activities, and educational experiences designed to develop the performance they desire. The key here is knowing what students should be able to do as statisticians and making sure that students' educational experiences are aligned with these desired outcomes. It is interesting to note that the desired outcomes expressed by the speakers from the three different areas of industry, academia, and government did not specify particular content that students should know, but instead specified particular skills and experiences students should have.
Appropriate forms of assessment need to be incorporated into the learning process so that teachers and students can determine if these goals are being achieved.
Statistics educators need to take teaching seriously and assess their own personal theories of learning and teaching in light of the evidence classroom experience provides. If students are not developing the desired skills, or are not achieving the level of performance desired, teachers should rethink their notion of effective teaching and experiment with alternative methods, carefully evaluating the impact of these methods on student outcomes.
Students should be encouraged to assess their own learning and performance. An important goal of educating students should be to help them become better at assessing their own level of learning and performance, so that they may develop the appropriate standards for the discipline.
One aspect of being a good statistics teacher is modeling good teaching for the next generation of statistics teachers. One of the most exciting things I learned in reading John Lehoczky's paper was that graduate students in statistics at Carnegie Mellon University who serve as teaching assistants have to go through a comprehensive teacher training program.
I am inclined to believe that despite the different settings in which statisticians work, it is nevertheless important for them to be aware of good teaching and learning techniques, so that they may continue in their own lifelong learning, dealing with the continual increase of new information to be learned, and also so that they may teach others, whether in an academic setting with students or in another type of setting in government or industry. To this end, I think that course work and experience in teaching should be required of all graduate students in statistics, as well as for students in other disciplines.
However, I have some concerns about teacher training programs that focus exclusively on lesson plans, syllabi, handouts, and lectures. In keeping with the suggestions for good teaching I have described, I would like to see teacher training programs help graduate students learn about the teaching and learning process, learn how to develop and facilitate cooperative learning activities, become experienced with the role of assessment (and alternative forms of assessment), and learn about current ways to improve teaching in their discipline (that is, the use of software as a teaching tool, the use of projects, and so on). The development of programs such as these could lead to a new generation of improved statistics teachers and statisticians who are able to work more effectively in any type of setting. I look forward to seeing this happen.
Artzt, A., and C. Newman. 1990. How to Use Cooperative Learning in the Mathematics Class. Reston, Va.: National Council of Teachers of Mathematics. 73 pp.
Davidson, N., ed. 1990. Cooperative Learning in Mathematics: A Handbook for Teachers. Menlo Park, Calif.: Addison Wesley.
Garfield, J. 1993. Teaching statistics using small-group cooperative learning. J. Stat. Educ. 1(1). [An electronic journal.]
Goodsell, A., M. Maher, and V. Tinto. 1992. Collaborative Learning: A Sourcebook for Higher Education. University Park, Pa.: National Center on Postsecondary Teaching, Learning and Assessment.
Johnson, D., R. Johnson, and K. Smith. 1991. Cooperative Learning: Increasing College Faculty Instructional Productivity. ASHE-ERIC Higher Education Report No. 4. Washington, D.C.: George Washington University.
Weissglass, J. 1993. Small-group learning. Am. Math. Mon. 100(7):662-668.