# Theory

• ### Three kinds of statistical literacy: What should we teach?

Statistical literacy is analyzed from three different approaches: chance-based, fallacy-based and correlation-based. The three perspectives are evaluated in relation to the needs of employees, consumers, and citizens. A list of the top 35 statistically based trade books in the US is developed and used as a standard for what materials statistically literate people should be able to understand. The utility of each perspective is evaluated by reference to the best sellers within each category. Recommendations are made for what content should be included in pre-college and college statistical literacy textbooks from each kind of statistical literacy.

• ### Data Driven Activities: Teaching Statistics Through Mathematics

Real data and statistical techniques can motivate many traditional mathematical topics at the secondary level. Collectively, the important statistical ideas and ways of reasoning can be developed in the context of studying mathematics. The study of formulas, linearity, centers, inequalities, matrices, and logarithms can be embedded in data and statistics and used to lay the foundation for the mathematics and to demonstrate the relevance of statistics to the world. Data Driven Mathematics provides teachers and students with application based activities that makes this happen and that can be used in conjunction with a standard mathematics course or to design a data based statistics course.

• ### Emergent Modeling As The Basis For An Instructional Sequence On Data Analysis

This paper discusses an instructional design heuristic called "emergent modeling", with an instructional sequence on data analysis as an example. The emergent modeling approach is presented as an alternative for instructional approaches that focus on teaching ready-made representations. In relation to this, a distinction is made between modeling as "translation" and modeling as "organizing". Emergent modeling fits the latter. Within this perspective, the model and the situation modeled are mutually constituted in the course of modeling activity. This gives the label "emergent" a dual meaning. It refers to both the process by which models emerge, and the process by which these models support the emergence of more formal mathematical knowledge. This is reflected in the exemplary instructional sequence, in which the model co-evolves with the notion of distribution as an entity.

• ### Elementary Statistics International Travel Lab Component

A travel lab component in elementary statistics is envisioned as a statistics lab within the context of a foreign setting. This paper will focus on why this is important and how the learning of statistics can be enhanced due to participation in such a lab. The travel lab component to Nicaragua in 2000 dealt with the extreme poverty among women and children. In Cuba in 2002, it will be on the status of women in contemporary Cuba. Many students appear to have an interest in humanitarian issues and even expect to see values discussed in their college courses. Thus they find this application of statistics in social context not only interesting but also relevant. I believe that through this type of travel component the utility of statistics becomes evident and students are better able to appreciate statistics studied and used in context.

• ### A New Approach to Learning Probability in the First Statistics Course

The probability unit in a first statistics course is difficult to teach because there is not much time, the concepts and mechanics are difficult, and the students do not see the relevance of learning it. Research by Cosmides and Tooby (1996) supports our findings that instructors should avoid fractions and decimals and capitalize on students' affinity for counting things. In addition, we avoid the use of normal tables at the beginning of our discussion of continuous random variables by using uniform and triangular distributions. These ideas may be used in traditionally structured classes or in group-based and activity-based classes.

• ### Statistics Course Web Sites: Beyond syllabus.html

Student-instructor and student-student interaction outside of the classroom are very important to learning statistics. A successful statistics course Web site increases these interactions by creating a forum for the instructor and students to communicate with statistical language. The development of a successful statistics course Web site involves determining the Web site's purpose, deciding what Web pages are needed, organizing the Web pages, implementing the Web site, and assessing the Web site. The purpose of this article is to discuss the development of a statistics course Web site for a Web-enhanced or Web-centric course and to provide a detailed example of one such course.

• ### Determining the educational potential of computer based strategies for developing and understanding of sampling distributions

An analysis of the steps involved in forming the idea of an empirical sampling distribution and the nature of the methods and/or images used in most computer based strategies to teach this idea suggest that this way of using the computer adds little insight to the usual text based explanations that they are designed to complement. This analysis suggests reasons why a more recent approach which uses the computer to model and dynamically display the processes that underlie the idea is more likely to be successful. (orig.)

• ### Does the computer help us understand statistics: Hilft der Computer uns statistische Ideen zu verstehen

The present paper is intended to illustrate by means of examples what can be accomplished in an environment where students have access to statistical computing package and also where they are familiar with a simple computing language. The authors have identified three broad areas in which the computer is helpful: reducing the need at lengthy manual calculations, facilitating graphical data analysis, and illustrating statistical concepts by means of simulation experiments. The first two categories tend to be well supported in the available packages, and they present here some representative examples. The last category seems not to be well developed in the standard texts, and their treatment here is more extensive, including both manipulations with standard packages and programming exercises.

• ### Training Teachers to Teach Probability

In this paper we analyze the reasons why the teaching of probability is difficult for mathematics teachers, describe the contents needed in the didactical preparation of teachers to teach probability and analyze some examples of activities to carry out this training. These activities take into account the experience at the University of Granada, in courses directed to primary and secondary school teachers as well as in an optional course on Didactics of Statistics, which is included in the Major in Statistical Sciences and Techniques course since 1996. The aim is encouraging other colleagues to organize similar courses at their universities, either as part of their official programs or in their postgraduate training.

• ### Components of Statistical Thinking and Implications for Instruction and Assessment

This paper focuses on a third arm of statistical development: statistical thinking. After surveying recent definitions of statistical thinking, implications for teaching beginning students (including non-majors) are discussed. Several suggestions are given for direct instruction aimed at developing "habits of mind" for statistical thinking in students. The paper concludes with suggestions for assessing students' ability to think statistically. While these suggestions are primarily aimed at non-majors, many statistics majors would also benefit from further development of these ideas in their undergraduate education.