Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

Diagnostic assessment is currently an active research area in educational measurement. Literature related to diagnostic modeling has been in existence for several decades, but a great deal of research has been conducted within the last decade or so, especially within the last five years. The author summarizes the key components in the application…

Some uncomplicated illustrations of how probability yields results that seem in conflict with traditional intuition are given. (MNS)

This document is designed to assist teachers by providing practical examples of real world applications of high school mathematics. Fifteen problems are presented that individuals in industry and business solve using mathematics. Each problem provides the contributor's name, suggested skills required to solve the problem, background information…

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…

This book is intended for middle-grade mathematics teachers who are searching for a wide variety of appropriately challenging and motivating problems with which to supplement regular textbook offerings. The 125 problems presented were found in the "Arithmetic Teacher" from 1975 to 1990. References are given both to the articles that contain these…

This book presents 129 problems selected from the calendar problem section of the "Mathematics Teacher" to supplement regular mathematics textbook offerings for middle grade teachers and students. The problems are categorized by six topics: (1) Numbers; (2) Computation; (3) "Oldies but Goodies"; (4) Offbeat and Unusual; (5)…

"Gedankensimulation" is a term adapted from Einstein's "thought experiments" to indicate mentally created simulations that can help conceptualize ideas. Presents seven examples of simulations that can be utilized to solve problems or illustrate concepts in probability and statistics. Problem contexts include games of chance,…

The information in this supplementary notebook is intended to provide teachers with additional materials, ideas and suggestions, and activities to help in implementing the first 21 units of the Applied Mathematics modules that help develop and refine job-related mathematics skills. An introduction lists the 36 units of the complete Applied…

The probability of selecting two matching socks is discussed. (MNS)

Methods of determining probabilities of various outcomes of the game Yahtzee are described. (SD)

Presents an educational game on probability that can be the starting point for an open-ended statistical project. (ASK)

A sequence of numbers from combinatorial theory called the Bell numbers is discussed, along with several problems and examples that demonstrate their usefulness. (MN)

A realistic problem is presented, computing the probability of winning a sports playoff series if the probability if winning a single game is known. Only simple permutation formulas and some basic logic are required to solve the problem. Two computer programs and a discussion of solution methods are included. (MNS)

Suggestions for five activities are presented. They include: ideas for several student problem-solving projects; preparing a flowsheet and program for 10 coin and dice games; using word processor formatting commands to create word designs; creating sounds; and writing a program to print out sums indefinitely. (JN)