# Teaching

• ### A cooperative learning activity on methods of selecting a sample

This article describes a classroom activity designed to stimulate students to think creatively about methods of selecting a representative sample from a population. Students are presented with a data set consisting of gender, SAT verbal score, SAT mathematics score, and high school grade point average for 317 freshmen from North Carolina State University. The students, who have not yet studied sampling, work in groups of three or four to generate three possible methods for selecting a representative sample of 20 freshmen from the population of 317. Each group uses its proposed methods to select three samples and computes various summary statistics and plots for the variables in each sample. The students are then given corresponding information for the entire population. After comparing sample statistics and population parameters, the groups evaluate the advantages and disadvantages of the proposed sampling methods. During the two semesters that I have used this activity in my Statistics 101 class, students have "invented" simple random sampling, systematic sampling, stratified sampling, and various combinations thereof.

• ### A radically different approach to introductory statistics

This paper describes a new approach to a one semester introductory statistics course. This approach has been used by three instructors, including the author, at Madison. My primary goal is to enable students to discover that statistics can be an important tool in daily life. This is achieved by showing students that they are scientists, in a broad sense, and that statistics is an essential tool for doing science. The focus through the course is on scientific questions and how statistical thinking can shed light on their solutions. In short, data are preeminent and methods achieve importance through their ability to illuminate data sets. This is the reversal of the common practice of methods being the focal point and data sets being reduced to illustrating methods. This paper also describes the author's successes with early (in the semester) use of student projects.

• ### The quantitative reasoning course at Mount Holyoke College

In 1982, at Mount Holyoke College, a group of faculty began to plan what was eventually to find its way into the course catalog as Interdepartmental 100 -- Case Studies in Quantitative Reasoning. This paper is about the QR course, given in five sections. First, I shall describe the structure of the QR course, emphasizing its mechanics and content: then I'll turn to a closer look at some of what makes the course distinctive for some of us who have taught it. I'll end with two sections on assessment and one on exportability, in the hope not only that our blueprints can help interested others avoid reinventing a wheel or two, but equally important, that our experience can also save others from reinventing some of our more spectacular flat tires.

• ### Probability and the short run illusion: Perceptions and misperceptions

In this article we have provided teachers with four examples of short run illustrations which students can analyze and reflect upon. The examples provided can be handled by high school students once they realize that with suitable assumptions, the binomial distribution provides a reasonable approximation to the operation of chance in reality.

• ### Developments in statistical education

This paper describes recent work carried out by the Schools Council Project on Statistical Education. The Project advocates a problem-solving approach towards the teaching of statistics in secondary schools (11-16 years of age range). It sees statistics as an interdisciplinary subject primarily concerned with data. The article illustrates these important aspects with teaching materials which have been developed and tested extensively in a variety of schools. Finally an evaluation and assessment of the project's work is presented.

• ### Proposal of curriculum for teaching probability and statistics

Described here is the project for the teaching of elements of Probability and Statistics at the ages of 11-14. It is the result of the work of the Didactic Research Group of Pavia (1); formed of 5 university researchers and about 20 in-service teachers.

• ### Computer simulations of probability challenges: From data to theory

In this paper we will briefly address the use of microcomputers in the classroom to enhance data collection and data analysis for stochastic experiments. The approach that we have in mind is appropriate for middle school (lower secondary) students, secondary school students, preservice teachers at the college and university level, and inservice teachers doing post-baccalaureate work.

• ### Teaching descriptive and inferential statistics using a classroom microcomputer

There is no doubt that statistics should be an important part of the secondary mathematics curriculum. A single classroom microcomputer can be valuable for work in both descriptive and inferential statistics. This article presents a framework for integrating a microcomputer into a statistics unit and includes descriptions of some programs suitable for the Apple microcomputer and ideas for lessons. Three functions that a microcomputer can perform within a statistics unit are illustrated: the easy generation of attractive graphs; the illustration of concepts; and the performing of tedious calculations. These three functions will frequently overlap within a specific program. Simulations are important but will not be discussed here.

• ### The ASA-NCTM quantitative literacy project: An overview

The NSF-funded Quantitative Literacy Project (QLP), a joint project of the American Statistical Association (ASA) and the National Council of Teachers of Mathematics (NCTM), served as the basis from which the strand in statistics was developed for the NCTM Standards. The QLP provides curriculum materials in certain areas of data exploration, probability, and inference, in a style that makes the material accessible to teachers and students, and provides a model framework for in-service programmes to enhance the skills of teachers in the area of statistics and probability. More specific information on certain aspects of the QLP will be provided below.

• ### Data analysis in precalculus and calculus

Data analysis can play an important role in bridging the gap between the world of mathematics and the student's world experience. Students study functions in class, but seldom have the opportunity to see these functions and their interactions exhibited in the world around them. As the students study the behavior of functions in calculus and precalculus courses, they learn how things should happen in theory. Through data analysis, the theory can be motivated and realised in the actual. The principles of curve fitting, re-expression, and residual analysis, offer a very exciting and enlightening basis for the motivation and derivation of many of the functions and functional concepts taught in high school algebra and in calculus. The Mathematics Department at the North Carolina School of Science and Mathematics has created, tested, and published an innovative data-driven precalculus text and is presently writing a calculus course involving many laboratory experiences from which the examples in this article are taken.