# Teaching

• ### An active learning in-class demonstration of good experimental design

This article presents an active learning demonstration available on the Internet using Java applets to show a poorly designed experiment and then subsequently a well-designed experiment. The activity involves student participation and data collection.

• ### Can we teach mathematical statistics without a probability prerequisite?

This paper describes three courses that could be taught by statisticians in departments of mathematics. These courses have three features in common: (1) they are serious about data and contemporary applications of statistics, (2) they are mathematical enough to count towards a major in mathematics, and (3) they are accessible to sophomore math majors or first-year students with advanced standing.

• ### Instruments to assess statistical concepts in the school curriculum

This paper will document four instruments devised to assess student understanding of statistical concepts. Two are intended for large scale administration and two are for individual differences.

• ### Interactive demonstrations for statistics education on the World Wide Web

The World Wide Web (WWW) is a tool that can be used in many ways for basic statistics education. Using the latest WWW technology, educators can now include interactive demonstrations in the form of Java applets within their WWW materials. Six example applets developed by the authors are introduced and discussed. Suggestions for class are made, and instructions for incorporating the applets within a WWW document are given

• ### Learning statistics by doing statistics

To help students develop statistical reasoning, a traditional introductory statistics course was modified to incorporate a semester-long sequence of projects, with written and oral reports of the results. Student test scores improved dramatically, and students were overwhelmingly positive in their assessment of this new approach.

• ### Using cooperative learning in a large introductory statistics class

This article discusses one active learning technique, cooperative learning, that can be used in large classes. This technique requires that students be divided into learning teams. A method for quickly dividing a large class of students into learning teams is presented. Two examples of cooperative learning exercises used in an introductory statistics class are given. These serve as illustrations of the type of cooperative learning exercises that can be assigned in a large class. In particular, these exercises were used in a class of 195 students. Preliminary findings by the instructor of the advantages of using cooperative learning exercises are discussed.

• ### Decoding a scrambled text: A hands-on project to illustrate sampling and variability

Students crack a simple substitution code using character frequencies in texts sampled from web pages. Frequencies are tabulated by a web-based character counter. This quick and simple project reinforces notions of sampling variability and emphasizes the need to complement statistical techniques with intuition.

• ### Probability concepts: Putting research into practice

The Chance and Probability Concepts Project, directed by the author at Loughborough University from 1978-81 (Green, 1982a) revealed the very limited understanding which 11-16 year old English School pupils have of probability concepts. A previous article in Teaching Statistics (Green, 1983) presented a general report of the research findings and made some recommendations. This article describes an attempt to follow up the research with practical class based activities using the computer to improve pupils' understanding.

• ### Many faces of the correlation coefficient

Some selected interpretations of Pearson's correlation coefficient are considered. Correlation may be interpreted as a measure of closeness to identity of the standardized variables. This interpretation has a psychological appeal in showing that perfect covariation means identity up to positive linearity. It is well known that |r| is the geometric mean of the two slopes of the regression lines. In the 2 x 2 case, each slope reduces to the difference between two conditional probabilities so that |r| equals the geometric mean of these two differences. For bivariate distributions with equal marginals, that satisfy some additional conditions, a nonnegative r conveys the probability that the paired values of the two variables are identical by descent. This interpretation is inspired by the rationale of the genetic coefficient of inbreeding.

• ### Session Seven--Lab Activity

A common experiment in investigating consumer preferences is to give a sample of potential customers two competing products and ask them which they prefer. The statistical inference involves the proportion of the population of potential consumers who prefer a particular product.