Teaching

• Mean or meaningless?

This article describes actitivies that can be used to teach elementary school students about the concept of the arithmetic mean.

• Assessing statistical knowledge as it relates to students' interpretation of data

The chapter examines the nature of interpretive skills that students need to acquire in statistics education, with a special focus on the role of students' opinions about data. Issues in the elicitation and evaluation of students' opinions are examined, and implications for assessment practices and teacher training are discussed.

• Visualizing hypothesis tests

Three software modules were created to help students learn to visualize hypothesis tests, based either on scenarios or on a Do-It-Yourself control panel to set up the experiment. The one-sample and two-sample modules illustrate tests of means or variances. For each sample, there is a dot plot with optional overlays of the populations or sampling distributions, table of statistics and parameters, confidence intervals, and theoretical distribution of the test statistic with the rejection region shaded. The ANOVA module offers stacked dot plots, ANOVA table, and sample statistics. Each module allows replication experiments to estimate empirical Type I or II error. There is an extensive help system. Software has been tested on students. The modules are part of an NSF-supported project to enhance quantitative reasoning and motivate students.

• Eight features of an ideal introductory statistics course

This paper discusses the following features of the author's ideal introductory statistics course: (1) a clear statement of the goals of the course, (2) a careful discussion of the fundamental concept of 'variable', (3) a unification of statistical methods under the concept of a relationship between variables, (4) a characterization of hypothesis testing that is consistent with standard empirical research, (5) the use of practical examples, (6) the right mix of pedagogical techniques: lectures, readings, discussions, exercises, activities, group work, multimedia, (7) a proper choice of computational technology, and (8) a de-emphasis of less important topics such as univariate distributions, probability theory, and the mathematical theory of statistics. The appendices contain (a) recommendations for research to test different approaches to the introductory course and (b) discussion of thought-provoking criticisms of the recommended approach.

• Fourth graders invent ways of computing averages

The purpose of this article is to describe what fourth graders can do when they are encouraged to invent their own ways of getting the average. The article also shows the teacher's active role in constructivist teaching.

• A learning and assessment model in teaching statistics

This report deals with the use of portfolios in assessing student performance in statistics. It gives a background on the use of portfolios, information on portfolio development, and issues surrounding portfolio assessment. It also provides a sketch of what a portfolio in statistics might look like.

• Resampling: A tool for everyday statistical work

This article discusses the use of data to "simulate" sampling from a population. The authors claim that their approach, termed "resampling", offers a powerful heuristic for solving statistical problems.

• What every high school graduate should know about statistics

Statistics is not about numbers, statistics is about numbers in context. Statistics is not the same as probability. But some probability is necessary to understand certain statistical topics, while other statistical topics do not depend on probability. Statistics is not the same as mathematics. But an appropriate level of mathematics is needed to understand any statistical topic, and understanding statistics can contribute to an understanding of mathematics. Statistics is not the same as the scientific method. Yet statistics helps solve problems in science, engineering, medicine, business, and many other fields. Using statistics is inherently interdisciplinary. While using statistics demands that one understand the problem, the reason that statistics is so powerful is that key statistical concepts, methods and ideas are applicable in so many different problem contexts. This paper discusses the key concepts in statistics that students must learn in the K-12 curriculum so that all high school graduates can become productive citizens and use quantitative information effectively. The topics are organized and discussed in terms of number sense, planning studies, data analysis, probability, and statistical or inferential reasoning.

• Teaching introductory statistical methods for understanding: Techniques, assessment, and affect

This paper presentation contains a variety of useful materials for introductory statistics instructors. Kenney discusses the tool box metaphor that she often uses in her class, and she also shares activites and thoughts about issues such as metacognition and portfolio assessment. She includes a survey that she gives to her students in order to gather feedback about study strategies and teaching techniques that seemed to be most helpful to the students. Finally, she includes an anecdotal report from one of the students in her class.

• Using humor to teach statistics: Must they be orthogonal?

The purpose of this paper is to aquaint individuals in the use of humor to develop conceptual understanding in statistics. Many statistics instructors are not as aware as they could be of the statistical humor available to them or how to use it as a conceptual development and assessment device in their instruction. The main objective, then, is to inform individuals of these many sources as well as how they can be used in the classroom to foster deeper conceptual understanding.