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 come across statistical ideas in their daily lives. For example, a student may see statistics used in political polls, music charts and unemployment rates. Basic statistical education is important in helping students to make sense of the abundance of numerical information that is presented on a daily basis 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 towards improving statistically education, leading to a great deal of research in the field. This paper aims to examine existing research to determine how statistical education research can be improved in the future.

Introduction

Statistical education has become an important part of curriculums in all levels of education. At both the undergraduate and graduate levels, statistical literacy is now a key objective in many classrooms. As a result, statistics is now being taught across various disciplines and is rapidly becoming a prerequisite course for graduation, regardless of a student's major.

The teaching and learning of statistics has recently increased dramatically in many schools. As a result, 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 major 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 ridden with research telling teachers how, when, and what to teach in the statistics classroom.

Another great challenge has been student achievement and student attitudes regarding statistics. Thus, there is a great deal of literature suggesting that students are struggling with understanding very basic statistics concepts and that student attitudes about statistics, despite creative ways of providing instruction, are generally negative.

This paper will examine existing research on statistical education to determine which aspects are beneficial to students and which areas need improvement. There will be a strong emphasis on statistical education research, as it will continue to advance and improve the field.

Hypothesis

Because of this increased interest in statistical education, researchers and teachers involved in statistical education 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 field (Vere-Jones, 1997) and there is a good deal of experience in the world about conducting research into statistical education. However, there is still a strong need to achieve academic recognition in various disciplines of statistical education. Jolliffe (1998), and Batanero et al. (2000) suggested that statistical education is now at a point where it would be possible to develop some general principles about what background knowledge researchers need in order to conduct quality research in statistical education, and how researchers should be trained to conduct research in statistical education.

Literature Review

According to H.G. Wells (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 as it both gives and receives in its interaction with other areas. Therefore, the interaction between statistical developers, users and recipients must closely influence and be influenced by, statistical education at all levels, recognizing that the process of learning is not just a cliche in statistics and that statistical understanding is a key facilitator across modern society.

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 actual problems across these areas.

For example, consulting with engineers can transfer into statistics education through undergraduate and into health and life sciences, and therefore must meet new challenges in these areas. On the other hand, many statisticians have concerns about partial subjugation of statistics within information technology, and yet a major need in information technology is improved identification and development of the quantitative educational aspects in this evolving area. This paper will discuss challenges for statistical educators.
Many statisticians are currently teaching 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 of the classroom. While statistical educators are concerned about difficulties students have learning and applying course material, many are unaware of the increasing body of research related to teaching and learning statistics. This paper will attempt to summarize this literature and apply it specifically to improving learning outcomes in college-level statistics courses. It will also examine existing research to determine how improvements can be made in the future.

Theories of Learning

Prior to examining research on learning statistics, one must examine 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 discovered that students do not necessarily learn by having teachers explain to them how problems are solved. Many teachers are concerned when they work out a problem clearly, explaining each step thoroughly, only to find out that few students actually understand it.

Many teachers have 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, theories of learning 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 between the teacher's goals for the class, views of students' characteristics and abilities, theory of how students learn, and assumptions about how students should be taught.

A recent theory of learning that has been widely accepted in education communities comes from earlier work by Jean Piaget, and is known as "constructivism (Garfield, 2000)." This theory refers to learning as actively building one's own knowledge. Today, this is the direct theory 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 just memorizing material in class, students restructure the new information into their own cognitive frameworks. Thus, they individually construct their own knowledge, rather than simply copying information "transmitted," "delivered" or "conveyed" to them. A teaching theory focuses on developing students' understanding, rather than on skill development, and looks at teaching as a means of providing opportunities for students to actively construct knowledge rather than having knowledge simply given to them.

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

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

The idea of variability of data and summary statistics.

Normal distributions are useful models though they are seldom perfect fits.

The usefulness of sample characteristics (and inference made using these measures) depends critically on how sampling is conducted.

A correlation between two variables does not imply cause and effect.

Statistics can prove very little conclusively although they may suggest things, and therefore statistical conclusions should not be blindly accepted.

Improving Statistical Education

Statistic educators include these ideas 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 statistic educators have attitude goals for how they would like student to view statistics as a result of statistics courses. Such attitude goals include (Garfield, 2000):

It is important to learn some fundamentals of statistics in order to better understand and evaluate information in the world.

Anyone can learn important ideas of statistics by working hard at it, using good study habits, and working together with others.

Learning statistics means learning to communicate using the statistical language, solving statistical problems, drawing conclusions, and supporting conclusions by explaining…