This paper summarizes the thinking of 84 middle school mathematics students' about variability in three stochastics tasks that involve repeated trial. Differences in students' acknowledgment of variability were found, depending on whether the task was from a sampling environment, or a probability environment. Students tended to neglect variability…

This teacher resource manual is designed to help teachers implement the Mathematics Preparation 10 course. This manual is a support document that provides helpful information to classroom teachers. The general and specific outcomes of the program of studies for Mathematics Preparation 10 are discussed. These outcomes have been shared to show that…

This document is concerned with developing an understanding of problem solving by providing tasks to help students with their problem solving strategies. These tasks were used by Vermont teachers during the pilot years of the High School Mathematics Assessment and were selected by attendees of the June, 1995 Research Scoring meeting. Tasks are…

Mathematics has become increasingly important in this technological age. That is why it is even more important for children to learn mathematics at home as well as in school. This second edition of "Helping Your Children Learn Math" is for parents of children in kindergarten through fifth grade. It has been revised to include a variety of…

Mathematics has become increasingly important in this technological age. That is why it is even more important for children to learn mathematics at home as well as in school. This second edition of Helping Your Children Learn Math is for parents of children in kindergarten through fifth grade. It has been revised to include a variety of activities…

Two experiments reproduced in a simulated computerized test-taking situation the effect of two of the main determinants in answering an item in a test: the difficulty of the item and the time available to answer it. A model is proposed for the time to respond or abandon an item and for the probability of abandoning it or answering it correctly. In…

When studies are conducted over a period of time, the sample size typically decreases. In a study of the effects of exercise therapy and education with recovering congestive heart failure (CHF) patients (Brubaker, Witta, & Angelopoulus, 2003), the sample size decreased from over 40 to 9 participants after an 18-month time span. Although the…

Reviews the principles of Monte Carlo calculation and random number generation in an attempt to introduce the direct and the rejection method of sampling techniques as well as the variance-reduction procedures. Indicates that the increasing availability of computers makes it possible for a wider audience to learn about these powerful methods. (CC)

Five models which perform search tasks of the Data Base Access and Search Environment (DBASE) are presented and used for comparison with subject search performance--unconstrained (rule-based, decision theoretic) and constrained (optimal rule-based, rule-based, probabilistic rule-based). Previous experiments and the modeling approach are briefly…

Brief articles on a linguistic approach to learning mathematics vocabulary, designing cross-figure puzzles, an activity with probability, and a problem with an erroneous solution are included in this section. (MNS)

A lesson for a sixth grade class that came out of an article in a Sunday newspaper is described. The instruction centered around an experiment in probability that was seen to provide an opportunity to add to pupil intuitive understanding of some basic notions. The lesson was viewed as worthwhile. (Author/MP)

Three probability problems designed to challenge students are presented: Liars and Diamonds, Heads Wins, and Random Walks. Other statistic problems are suggested that could involve computer simulations. (MNS)

Until recently, norms of experimental reasoning have lacked systematic theoretical development. Thus, it has been easy for psychologists like Tversky and Kahneman to misclassify certain human reasoning processes as being Pascalian and invalid, rather than as being Baconian and valid. (CP)

Some activities designed around the Monte Carlo method of solving probability problems are described. The instructional applications of this method involve physical models or simple BASIC computer programs. (MP)

Several BASIC computer programs designed to illustrate concepts in probability are presented. The programs are geared for the Apple II computer, but most samples are adaptable to other systems. (MP)