Statistical Education: Research, Methods, and Improving Outcomes

Introduction

Statistical education trains students in the science of collecting, displaying, analyzing, and interpreting numerical data. It is often referred to as "the science of doing science." Students encounter statistical ideas in their daily lives — for example, in political polls, music charts, and unemployment rates. Basic statistical education is important in helping students make sense of the abundance of numerical information presented daily by the media. In particular, students need statistical education to help them recognize attempts to mislead them through statistical information and diagrams.

In schools, statistical education is primarily taught in mathematics, yet students use statistical ideas in other subjects, including science and economics. Therefore, teachers and researchers are constantly working toward improving statistical education, generating a great deal of research in the field.

Statistical education has become an important part of curricula at all levels. At both the undergraduate and graduate levels, statistical literacy is now a key objective in many classrooms. As a result, statistics is being taught across various disciplines and is rapidly becoming a prerequisite course for graduation, regardless of a student's major. Many U.S. states now emphasize and include statistical thinking in their statewide curriculum guidelines.

However, teaching and learning statistics continues to be a major challenge for statistical educators across the nation. One significant challenge is the instruction factor itself: statistics is both a difficult subject for students to understand and a difficult subject for instructors to teach. Thus, the statistical education literature is filled with research advising teachers on how, when, and what to teach in the statistics classroom.

Another great challenge involves student achievement and student attitudes regarding statistics. There is a considerable body of literature suggesting that students struggle with very basic statistical concepts and that student attitudes about statistics — despite creative instructional approaches — are generally negative.

Because of this increased interest in statistical education, researchers and teachers are constantly conducting research on how to improve achievement and attitudes by examining new learning theories, implementing alternative pedagogy, and using innovative technology. As a result, statistical education is rapidly becoming a distinct field (Vere-Jones, 1997), and there is a growing body of experience in conducting research into statistical education. However, a strong need remains to achieve academic recognition across various disciplines of statistical education. Jolliffe (1998) and Batanero et al. (2000) suggested that statistical education has reached a point where it would be possible to develop general principles about what background knowledge researchers need in order to conduct quality research in the field, and how researchers should be trained to conduct that research.

According to H. G. Wells (as cited in Garfield, 2000), "Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write." Statistical education provides the foundation for the analysis and communication of quantitative information involving variation, across all aspects of society. Statistics is similar to other applications of mathematical thinking in the broad sense: it both gives and receives in its interaction with other areas. Therefore, the interaction among statistical developers, users, and recipients must closely influence — and be influenced by — statistical education at all levels, recognizing that statistical understanding is a key facilitator across modern society.

Theories of Learning

Like mathematics, statistics has the qualities and duties of transferability and enablement. Mathematics serves as an enabler for statistical understanding, development, and hence education (Garfield, 2000). In both the business and engineering fields, statistics education is not only increasingly important but also benefits immensely from constant interaction with statistical usage and real-world problems. Consulting with engineers, for instance, can transfer into statistics education through undergraduate and school-level curricula. Statistics and statistical education have long been of prime importance in the health and life sciences, and therefore must meet new challenges in those areas. At the same time, many statisticians have concerns about the partial subordination of statistics within information technology, and yet a major need in information technology is the improved identification and development of quantitative educational components in this evolving area.

Many statisticians currently teach statistics either formally in a college classroom or informally in an industrial setting (Garfield, 2000). Regardless of the setting, a major concern in statistical education is how to ensure that students understand statistical ideas and can apply what they learn to situations outside the classroom. While statistical educators are aware of the difficulties students face in learning and applying course material, many are unaware of the growing body of research related to teaching and learning statistics.

Prior to examining research on learning statistics, one must consider how students learn in general (Garfield, 2000). Learning in a course is more involved than simply reciting what students have read or been told, and educators have found that students do not necessarily learn by having teachers explain how problems are solved. Many teachers are concerned when they work out a problem clearly — explaining each step thoroughly — only to find that few students actually understand it.

Many teachers rely on informal learning theories that guide their teaching approaches (Garfield, 2000). Some theories of learning are well defined, such as behaviorism or cognitivism. In analyzing how students learn, these theories serve as a basis for theories of instruction that draw conclusions about how instruction is best performed. What is taught in a course can be seen as an interaction among the teacher's goals for the class, views of students' characteristics and abilities, theories of how students learn, and assumptions about how students should be taught.

A widely accepted recent theory of learning in education communities derives from earlier work by Jean Piaget and is known as constructivism (Garfield, 2000). This theory describes learning as the active building of one's own knowledge. Today, it is the primary theoretical framework for the majority of research and reform in mathematics and science education. Constructivists see students as bringing to the classroom their own ideas, experiences, and beliefs, which affect how they learn new material. Rather than simply memorizing class material, students restructure new information into their own cognitive frameworks. Thus, they individually construct their own knowledge rather than copying information "transmitted," "delivered," or "conveyed" to them. A teaching theory grounded in constructivism focuses on developing students' understanding rather than on skill development alone, and views teaching as a means of providing opportunities for students to actively construct knowledge.

Theories of learning are strongly linked to teachers' goals for what they want students to learn. Most teachers indicate that they would like students to understand basic statistical concepts and ideas, to become statistical thinkers, and to be able to evaluate quantitative information, rather than simply recite material on a test.

According to research, most teachers want students to gain an understanding of the following ideas (Garfield, 2000):

1. The idea of variability of data and summary statistics.
2. Normal distributions are useful models, though they are seldom perfect fits.
3. The usefulness of sample characteristics (and inferences made using these measures) depends critically on how sampling is conducted.
4. A correlation between two variables does not imply cause and effect.
5. Statistics can prove very little conclusively, although they may suggest things; therefore, statistical conclusions should not be blindly accepted.

A second area of research, conducted mainly by statistical educators, focuses less on basic patterns of thinking and more on how statistics is learned. Some of these studies have contradicted ideas presented by psychological research (Garfield, 2000). For example, some studies indicate that students' use of heuristics — including representativeness and availability — often varies with problem context.

Garfield (2000) examined the performance of students in an introductory course on a variety of parallel problems designed to draw out use of the representativeness heuristic. The results indicate that students do not rely solely on the representativeness heuristic to solve similar types of problems. One researcher suggested that various perspectives students use to reason cause inconsistencies in their responses: students seem to understand and reconstruct a problem in different ways, leading them to apply different strategies. Another researcher described additional reasons for inconsistencies, including the constraints imposed by artificial experiments and the ambiguity of questions used. Thus, alternative methods of teaching could be greatly beneficial to statistical education.

For example, according to Harrington (1999), "Case study method has long been held as an effective tool for increasing student engagement in statistics. The practice of bringing realistic applications and cases into statistics education is growing in general. Improved statistical computer packages and the expansion of Internet-based access to data sets have significantly broadened the opportunity for statistical applications to business problems, particularly those germane to economics. Reports from a number of authors confirm the importance of active student involvement in the learning process. Students regularly report that case projects require considerable effort but are a key component of their learning. Case studies are particularly well suited for business majors because they are primarily interested in the study of business and economic problems rather than mathematical statistics. Students are presented with situations that require statistical and economic analysis to solve a realistic problem. In the cases, students must first apply economic and business analysis to identify key issues and formulate the analysis. Written and oral reports addressed to policy makers are particularly powerful teaching and learning strategies when used with the case study."

Statistical educators include the ideas above as key goals for student learning. A list of specific topics is provided by Hogg (1991) based on a discussion at a workshop of statisticians about what the goals for introductory statistics courses should be. Moore (1991) specified core elements of statistical thinking in terms of what students should be learning in statistics classes.

In addition to concepts, skills, and types of thinking, most statistical educators have attitude goals for how they would like students to view statistics as a result of their courses. Such attitude goals include (Garfield, 2000):

Conclusion

This means that statistical educators must change their strategies to enhance student learning and revitalize statistical curricula by facilitating student engagement in the learning process. In order to implement these changes, further research is clearly needed.

Because statistics education research is still relatively new to the educational world, researchers come from diverse disciplines, educational backgrounds, and training. Research in psychology has focused primarily on identifying student misconceptions and faulty reasoning, while research in statistics education has tended to focus on comparing instructional modes — such as laboratory environments versus traditional lectures — and on predicting student achievement based on various factors.

Still, researchers must attempt to expand this focus — to new questions, across all age groups, and toward research on statistics instructors — and tie the research more closely to actual classroom practice. Currently, the majority of research has not focused primarily on statistical reasoning or on other issues unique to statistics education. For the most part, however, statistics education research is increasing in visibility: there are many ongoing, collaborative projects (many international in scope), and statistics education research is gaining more prominence at conferences and in journals.

However, many of these conferences meet only twice per decade, making it difficult to maintain momentum and communication between meetings. Thus, it can be difficult for a new researcher to find an obvious central focal point for these efforts. There needs to be more discussion and reflection on acceptable research methods and a prominent research agenda. If researchers want to establish the validity and legitimacy of statistics education as an area of research, a well-developed research literature is needed.

While research in statistics education is still emerging, many questions must still be tackled before researchers can form clear hypotheses and proceed to systematic investigations. By gathering information from a variety of sources, researchers can formulate more informed research questions. The first step is to define models of valid research studies that can be held up as examples and that differentiate research in statistics education from other disciplines.

In pursuing this goal, researchers must remain open to alternative research methodologies so that they choose the methods and design most appropriate for the research question at hand. Researchers must also continue to collaborate across disciplines and countries, and train future researchers not only in statistics and randomized experiments but also in learning theory and measurement — including both qualitative and quantitative techniques.

Batanero, C., Garfield, J. B., Ottaviani, M. G., & Truran, J. (2000). Research in statistics education: Some priority questions. SERN Newsletter, 1(2), with discussion in SERN Newsletter, 2(1) and 2(2).

Garfield, J. (2000). How students learn statistics. International Statistical Review. The General College, University of Minnesota.

Harrington, C. (1999). Facilitating student engagement in the introductory business statistics course. University of Southern Indiana Press.

Hogg, R. (1991). Statistical education: Improvements are badly needed. The American Statistician, 45, 342–343.

Jolliffe, F. (1998). What is research in statistics education? In L. Pereira-Mendoza, L. Seu Kea, T. Wee Kee, & W. K. Wong (Eds.), Proceedings of the Fifth International Conference on Teaching of Statistics (Vol. 2, pp. 801–806). IASE.

Vere-Jones, D. (1997). The coming of age of statistical education. International Statistical Review, 63(1), 3–22.