Literature Index

In April 1983, the Madison Commission on Excellence in Education reported that we are a "Nation at Risk" in that we are setting for mediocrity in education and that our students are insufficiently prepared in mathematics, science, and other related areas. This report included the recommendation that high school students must be equipped to understand probability and statistics. In Educating Americans for the Twenty-First Century, the National Science Board on Precollege Education in Mathematics, Science and Technology (1983) expressed its concern that "statistics and probability should now be considered fundamental for all high school students." The National Council of Teachers of Mathematics' Agenda for Action: Recommendations for School Mathematics of the 1980's concluded that school mathematics must focus on problem solving and should integrate "the problem-solving capabilities of the computer" into the classroom in order "to implement new strategies of interaction and simulation.

In this paper I consider the characteristics of a statistically literate (a "statisticate") person. I suggest that a statisticate person should be able to read and understand statistical arguments of moderate complexity, and to carry out statistical analyses to some degree. Significantly, the truly statisticate person should also have developed the habit of thinking quantitatively. Furthermore, he or she does not rely on rigid rules to make statistical decisions, but uses informed judgment. In particular, he or she should understand the concepts of modelling and selection between models, and recognise their importance. Consideration is given to one of the major barriers to developing statistacy: the vocabulary used, in particular, the common use of two words that should only be used with the greatest of care (if used at all). These words are "prove" and "true". An important illustration of the way that vocabulary hinders the development of understanding is the case of hypothesis testing, a vital statistical tool that is widely misunderstood. It represents a mode of thought that is fundamental to statistical analysis, and so belongs in the kit bag of any statisticate person.

Results of analysis of responses to a first-year undergraduate engineering activity are presented. Teams of students were asked to develop a procedure for quantifying the roughness of a surface at the nanoscale, which is typical of problems in Materials Engineering where qualities of a material need to be quantified. Thirty-five teams were selected from a large engineering course for analysis of their responses. The results indicate that engagement in the task naturally led teams to design a sampling plan, use or design measures of center and variability, and integrate those measures into a model to solve the stated problem. Team responses revealed misunderstandings that students have about measures of center and variability. Implications for instruction and future research are discussed.

The term `cartoons' usually suggests humorous, animated drawings, along the lines of Mickey<br>Mouse or Charlie Brown. However, a much older use of the word refers to the prototypes or trial<br>drawings of artistic masters such as Michelangelo, in preparation for the finished work to follow.<br>In a broad sense, graphical insight into statistical ideas connects with both these meanings; the<br>aim is to give students a means of exploring concepts until they are comfortable with their roles,<br>while the ability to animate adds an extra dimension which can often spark additional interest and<br>which can sometimes raise a welcome smile.<br>This talk will discuss some of the ways on which animated graphics can help in the understanding<br>of statistical ideas at elementary, intermediate and advanced levels. The `rpanel' package for R<br>will be used as a vehicle but other systems will also be mentioned. Over the years there has been<br>considerable focus on illustrations of elementary statistical concepts and there are many good<br>examples at that level. However, the scope for tools addressing more advanced topics, such as<br>likelihood and spatial sampling, will also be discussed.<br>The advent of R as a standard computing environment in statistics, with increasing connectivity to<br>other systems, makes it entirely feasible for lecturers to construct their own cartoons, rather than<br>simply use those designed by others. The talk will argue for the importance of this mode of use.