Although traditional textbooks may not guide students through explorations or encourage group work, as many standards-based curricula do, virtually all textbooks contain mathematically accurate information and problems that, with adjustment, can be leveraged to support mathematical curiosity, reasoning, and discussion. Teachers who recognize rich…

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…

This article describes the connection between a novel puzzle and uses of algebra to generalize the fewest moves to solve it.

Addresses a problem originally published in the September 1994 issue in an article entitled "Creative Teaching Will Produce Creative Students" by Krulik and Rudnick. Problem stated: "Find all rectangles with integral dimensions whose area A and perimeter P are numerically equal." Presents solution to a rectangular solid,…

Highlights the argument that states that problem solving is much more than just solving problems, by focusing on problem-solving history, George Polya's view of problem solving, Asians' successful use of multiple intuitive solutions, and other examples. (ASK)

Brief mystery stories such as the three presented here can be used to help students develop critical reading and thinking skills, as well as to introduce the notion of indirect proof. (SD)

Students, playing the game described, develop strategies for guessing the four-digit number chosen by the opponent. The rules of the game are easily understood by low achievers, yet strategy development is challenging to advanced students. The game can be extended to numbers having more digits. (SD)

Domino games are used to illustrate problem-solving techniques in a college principles-of-mathematics course. Students develop tables and use Pascal's triangle to find the total number of pips and the sum of numbers on the pieces. (DC)

Reviews of the courseware "Discovery! Experiences with Scientific Reasoning" and "Guess My Rule" are given. Discusses the accompanying manuals, the relative ease of use, and content of the programs. (PK)