# Theory

• ### Sequencing topics in introductory statistics: A debate on what to teach when

We discuss various perspectives on the sequencing of topics to be studied in an introductory statistics course, debating the merits and drawbacks of different options. We focus on the introduction of data collection issues; the study of descriptive statistics for bivariate data; the presentation order of inference for mean and proportions; and the placement of tests of significance and confidence intervals. Our goals is not to declare final resolution on these issues, but to stimulate instructors' thinking about this important aspect of course design. We conclude by identifying a set of core recommendations emerging from our points of agreement.

• ### Statistical literacy: Thinking critically about statistics

Statistical literacy is the ability to read and interpret data: the ability to use statistics as evidence in arguments. Statistical literacy is a competency: the ability to think critically about statistics. This introduction defines statistical literacy as a science of method, compares statistical literacy with traditional statistics and reviews some of the elements in reading and interpreting statistics. It gives more emphasis to observational studies than to experiments and thus to using associations to support claims about causation.

This article has four main sections. Section 2 summarizes the state of academic mathematics and statistics and argues that, in most institutions, the two disciplines need each other. It would repeat false starts from the past to think primarily of statistics departments, or even of large research universities more generally. I believe that growth of undergraduate statistics programs in other institutions will generally require the cooperation of the mathematics department, and that mathematics may be ready for more cooperation. Section 3 presents some market research--data on trends that ought to influence our thinking about statistics for undergraduates. Section 4 offers some cautionary findings from research in mathematics education. The unifying theme of these three sections is the need for realism in discussing programs for undergraduates.

• ### Making sense of graphs: Critical factors influencing comprehension and instructional implications

Our purpose is to bring together perspectives concerning the processing and use of statistical graphs to identify critical factors that appear to influence graph comprehension and to suggest instructional implications. After providing a synthesis of information about the nature and structure of graphs, we define graph comprehension. We consider 4 critical factors that appear to affect graph comprehension: the purposes for using graphs, task characteristics, discipline characteristics, and reader characteristics. A construct called graph sense is defined. A sequence for ordering the introduction of graphs is proposed. We conclude with a discussion of issues involved in making sense of quantitative information using graphs and ways instruction may be modified to promote such sense making.

• ### The challenge of teaching statistics to non-specialists

Traditional methods of teaching introductory statistics are often viewed as being ineffective because they fail to establish a clear link between statistics and its uses in the real world. To be more effective, it is essential that teaching objectives are clearly defined at the outset and issues of content and methodology are addressed accordingly. This paper proposes that the relevant objectives should aim to develop the following competencies: (a) ability to link statistics and real-world situations, (2) knowledge of basic statistical concepts, (3) ability to synthesize the components of a statistical study and to communicate the results in a clear manner. Towards these objectives, we propose a revamp of the traditional course together with the creation of a new software tool that is currently unavailable.

• ### Statistical or quantitative thinking as a fundamental intelligence

This article presents an expanded view of statistics both in the topics embodied and in the way people employ it. Statistics is proposed as one of the fundamental human intelligences and, using the verbal intelligence as a model, a quantitative parallel to speaking is introduced. This spoken form of the quantitative language is part of everyone's everyday activities and has been used throughout our lives. Informal statistical principles are described as providing a foundation for the formal statistics traditionally taught and promulgated. Recommendations for beginning a radical change in what we teach are offered.

• ### Successful students' conceptions of mean, standard deviation, and the central limit theorem

This paper reports on a preliminary attempt to better understand the development of student knowledge of some fundamental statistical concepts.

• ### Mere literacy is not enough

As computers enhance the value of verbal, visual, and logical skills needed to reason with data, more than ever citizens and employees need skills in quantitative reasoning that create a tapestry of meaning blending context with structure.

• ### Multimedia for teaching statistics: Promises and pitfalls

This article examines the usefulness of multimedia technology for teaching statistics, with attention to both promises and pitfalls. We suggest some principles for the design and use of multimedia, and we offer opinions on the role of human teachers in a multimedia educational environment.

• ### Bridging the gap between students and statistics: Cognition, affect, and the role of teaching method

Traditionally, the introductory statistics course has been one of the most hated and feared courses on campuses across the country. Simon and Bruce (1991) lament, "probability and statistics continues to be the bane of students, most of whom consider the statistics course a painful rite of passage--like fraternity paddling--on the way to an academic degree..." Over the past 30 years, there has been an increase in the professional literature on how to teach statistics with a continuous call for reform of the introductory statistics course. Virtually every American Statistical Association (ASA) president, in the past 10 years, has addressed the topic of statistics education as a key issue affecting the status and image of statistics as a profession. It is rather interesting that, while many have examined the practice of teaching statistics, very little is known about how students learn statistical concepts and reasoning skills. In addition to presenting a review of the literature on what is known about how students learn statistics and an overview of the suggested classroom reforms, this talk begins to examine the extreme gap that clearly exists between the introductory student and the subject matter of the introductory statistics course.