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# Chapter

• ### Getting More Data into Theoretical Statistics Courses

At many small colleges the only statistics course offered to a mathematics major is the standard sequence in probability and mathematical statistics. This paper offers concrete suggestions on infusing this course with more data and applications so that students coming out of the course better appreciate the nature of statistics as a discipline separate from mathematics.

• ### Calibration of probabilities: The state of the art to 1980

The experimental literature on the calibration of assessors making probability judgments about discrete propositions is reviewed in the first section of this chapter. The second section looks at the calibration of probability density functions assessed for uncertain numerical quantities. Although calibration is essentially a property of individuals, most of the studies reviewed here have reported data grouped across assessors in order to secure the large quantities of data needed for stable estimates of calibration.

• ### A longitudinal study of the effects of undergraduate education on reasoning

Does an undergraduate education improve reasoning about everyday-life problems? Do some forms of undergraduate training enhance certain types of reasoning more than others? These issues have not been addressed in a methodologically rigorous manner (Nickerson, Perkins, &amp; Smith, 1985). We consequently have little knowledge of whether reasoning can be improved by instruction, yet this question has long been regarded as central the theories of cognitive development.

• ### Effects of Age and Instruction on Combinatory Ability in Children

The aim of the study was to investigate the effect of direct instruction on the ability to handle permutations and arrangements, as an example of a problem at the level of formal operations. 60 Bucharest school children, 20 aged 10 years, 20 aged 12 and 20 aged 14, tested individually, were first asked to estimate the number of possible permutations with 3, 4 and 5 objects. Results showed that these subjective estimates improved with age, with a threshold (or marked improvement) at age 12, though there was serious underestimating at all ages. A step-by-step teaching strategy using generative "tree diagrams" was then used. Even the 10-years-olds learned the use of the tree diagrams and the appropriate procedures for permutations and arrangements. Reprinted from The British Journal of Educational Psychology 40 (1970), Part 3.

• ### Belief in the law of small numbers

Apparently, most psychologists have an exaggerated belief in the likelihood of successfully replicating an obtained finding. The sources of such beliefs, and their consequences for the conduct of scientific inquiry, are what this paper is about. Our thesis is that people have strong intuitions about random sampling; that these intuitions are wrong in fundamental respects; that these intuitions are shared by naive subjects and by trained scientists; and that they are applied with unfortunate consequences in the course of scientific inquiry.

• ### Data, discernment and decisions: An empirical approach to introductory statistics

This article presents one point of view on what data analysis concepts should be taught, how to teach those concepts and why this emphasis is important.

• ### Providing a statistical "model": Teaching applied statistics using real-world data

In this paper, we describe how we use real data in the classroom and we identify characteristics of data sets that make them particularly good for teaching. We also identify advantages and disadvantages of this approach, and offer suggestions for overcoming the obstacles. In a separate section of this volume, we provide an annotated bibliography that lists several hundred primary and secondary data sources that teachers may use in their own courses.

• ### Low-tech ideas for teaching statistics

This paper describes ideas for teaching introductory statistics courses.

• ### Student-conducted projects in introductory statistics courses

The present paper offers some ideas for student projects that can be used in the introductory statistics class.

• ### Hands-on activities in introductory statistics

This paper describes different ideas that key on most of the important topics of the introductory statistics course.