Undergraduate history students can gain insight into the historical process from a short exercise using copies of documents that give conflicting interpretations of the same event. Explains how to lead class discussions based on two letters about lawlessness in Arizona in the 1880s. (Author/AV)

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

The vast majority of people are most familiar with arithmetic in base ten. This article presents a follow-up on a problem with several divisibility tests valid in base ten which are related to Freitag's general test and which follow directly from it. Base 13 is also explored. (Author/MA)

The paper-and-pencil game "Tri" is described. The authors argue that students gain logical skills by playing the game, and that the game lends itself to the introduction of diverse mathematical ideas. (SD)

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

The meaning of problem solving and investigations, what investigations are intended to achieve, the teacher's role, and how to introduce investigations in the curriculum are discussed. (MNS)

Use of a checkbook can hook even the most reluctant mathematics students into learning mathematical and problem-solving skills. (CB)

Presents several examples of algebraic word problems and demonstrates how spreadsheets are used to solve the problems. Spreadsheet templates are included to illustrate how each problem is solved. (MBR)

Solutions to a problem on seating arrangements and one on a box-office situation are discussed; a statistical approach is used. Four computer programs are included. (MNS)

One view of mathematical thinking is described, followed by detailing of the characteristics of a problem-solving program necessary to develop this kind of thinking. (MNS)

Use of the computer to simulate or imitate probability problems that are difficult to analyze in any other way is discussed. How the Monte Carlo method works is clarified, with sample problems and programs. (MNS)

Two activities are presented. The first involves geometric concepts using the alphabet, while the second is a game to provide practice in finding factors of composite numbers. (MNS)

Using data about companies with which children have first-hand experience (such as McDonald's or Mattel Toys) piques interest in graphing activities. How the project is developed, with group and individual activities, is described. (MNS)

Presents a problem-solving activity in which students first guess and then check their answer. Also presents an activity to help students develop skill in understanding the question in a problem and a suggestion to help develop a classroom climate conducive to problem-solving. (JN)

Discusses the nature of and the steps involved in a mathematical investigation, suggesting that a mathematical investigation can be used as a tool for developing mathematical processes in learners. Several examples of investigations suitable for secondary levels are included. (JN)