One of the delights of learning as rich a subject as mathematics is the never-ending scries of challenges available to the student. Some of the most interesting ones are to be found in the areas of statistics and probability.

### Natasha E. Gerstenschlager and Jeremy F. Strayer

Short, mathematical discussions can elicit students' reasoning and focus on foundational ideas.

### Gail Burrill

Statistics—the collection, organization, and interpretation of data; the art and science of an-alyzing information—was until the late 1960s the domain of those gifted in mathematics or those few who needed limited knowledge to make inferences within their chosen field. The school curriculum furnished little background for the (“science of numbers.” Statistics was a vast array of symbols, formulas, and rules that seemed to have little relationship to reality. During the 1960s, a combination of circumstances indicated a need to change the role of statistics in society: the development of computers with the capacity to create, store, and analyze large quantities of data; the formation of new, simple, and effective data-analysis techniques; and the occurrence of rapid changes in personal and working environments of society.

Help MT readers gain new perspectives on dynamic approaches involving students in the process of wrestling with data and chance.

Help MT readers gain new perspectives on dynamic approaches involving students in the process of wrestling with data and chance.

### Carmen Batanero and Luis Serrano

In the experimental study reported here we intended to examine possible differences in secondary students' conceptions about randomness before and after instruction in probability, which occurs for the Spanish students between the ages of 14 and 17. To achieve this aim, we gave 277 secondary students a written questionnaire with some items taken from Green (1989, 1991). With our results we extend Green's previous research to 17-year-old students and complement his results with the analysis of students' arguments to support randomness in bidimensional distributions. Our results also indicate that students' subjective understanding of randomness is close to some interpretations of randomness throughout history.

### Jennifer Noll and J. Michael Shaughnessy

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.

### Julia A. Mason and Graham A. Jones

The NCTM's *Curriculum and Evaluation Standards for School Mathematics* (1989) recognizes the importance of having all students develop an awareness of concepts and processes of statistics and probability. In particular it proposes that experiences in statistics and probability should be offered that enable students to “formulate and solve problems that involve collecting and analyzing data” (p. 54) and “model situations by devising and carrying out experiments or simulations to determine probabilities” (p. 109).

### Harris S. Shultz and Bill Leonard

In recent years we have seen numerous recommendations that statistics and probability should be integrated into the mathematics curriculum at all levels. A major rationale for this new emphasis is the acknowledgment that in everyday life we repeatedly encounter data and information from which we must make intelligent ceonomic and political decisions.

### Clark Kimberling

When students first meet the concepts of the mean and standard deviation of a set of numbers, they are told that the numbers are called *data* and that the two ways of measuring the data, called the *mean* (or *average*) and the *standard deviation*, are of great importance in the study of statistics and probability.