Whether students are beginning their study of probability or are well into it, distinctions between complementary sets and mutually exclusive sets can be confusing. Cathy Schloemer writes in this article that for years she used typical classroom examples but was not happy with the student engagement or the level of understanding they produced.…

Mokken scale analysis (MSA) is a probabilistic-nonparametric approach to item response theory (IRT) that can be used to evaluate fundamental measurement properties with less strict assumptions than parametric IRT models. This instructional module provides an introduction to MSA as a probabilistic-nonparametric framework in which to explore…

There is extensive research pointing to the positive effects of education in the form of labour market outcomes. These outcomes are vital when evaluating education; there are however additional outcomes of education that might also be important for quality of life. From this point of view, education could affect non-market areas such as democracy,…

Hypothesis testing is one of the more difficult concepts for students to master in a basic, undergraduate statistics course. Students often are puzzled as to why statisticians simply don't calculate the probability that a hypothesis is true. This article presents an exercise that forces students to lay out on their own a procedure for testing a…

We introduce a design-based research framework, "learning axes and bridging tools," and demonstrate its application in the preparation and study of an implementation of a middle-school experimental computer-based unit on probability and statistics, "ProbLab" (Probability Laboratory, Abrahamson and Wilensky 2002 [Abrahamson, D., & Wilensky, U.…

A discussion on the use of group question on final exams is presented to approach work units on probability or counting. Where it is easy to find problems that are both nonroutine and will stretch students minds a bit. The group question is also the fist part of the exam, which involves preliminary discussion and planning, division of labor, and…

Investigates an interesting application of probability in the world of sports. Considers the role of permutations in the lottery system used by the National Basketball Association (NBA) in the United States to determine the order in which nonplayoff teams select players from the college ranks. Presents a lesson on this topic in which students work…

Examines the role of variation in statistics education. Describes a chance and data unit with a focus on variation that was conducted in three high school mathematics classes. (ASK)

In this issue's "Classroom Notes" section, the following papers are discussed: (1) "Constructing a line segment whose length is equal to the measure of a given angle" (W. Jacob and T. J. Osler); (2) "Generating functions for the powers of Fibonacci sequences" (D. Terrana and H. Chen); (3) "Evaluation of mean and variance integrals without…

A self-teaching module on queues, dealing with the use of random numbers in the simulation of realistic queueing or waiting-line situations, is described. Both mathematical content and teaching methods are considered. (MNS)

Described is a unit, SAMPLING, which focuses on developing student understanding of probability and data collection for junior high school students. Activities in SAMPLING incorporate physical materials, simple computer simulations, surveys of subjective data, computer simulations of complex situations, and a culminating activity requiring the…

Activities for a 10-day unit on probability and statistics are described, with preplanning ideas included. Spinners, dice, cards, wheels, and other materials are used in a variety of games. (MNS)

ProbLab is a probability-and-statistics unit developed at the Center for Connected Learning and Computer-Based Modeling, Northwestern University. Students analyze the combinatorial space of the 9-block, a 3-by-3 grid of squares, in which each square can be either green or blue. All 512 possible 9-blocks are constructed and assembled in a "bar…

The sport of Ultimate has grown from parking lot fun to international competition in its 35 year existence. As in many sports, the team that scores is subsequently on defense. Thus the probability that a team will score next is dependent on which team has scored most recently. Unlike in many other sports, teams switch ends after each score. Thus…

In 1995, rather than require seventh-grade computer literacy classes, Texas allowed school districts to integrate technology skills into curricula. This article, the first of three, describes technology integration for sixth grade. Includes unit ideas on nations; the Holocaust; Olympic diving; Christmas; probability; organisms; Antarctica;…