Presents recently developed generalizations to the sieve of Eratosthenes, showing the principles underlying these improvements, which increase its efficiency without changing too much of its simplicity. Offers several possibilities to propose good investigations for students to explore, find patterns, and make generalizations. (JRH)

Discusses the behavior of functions under reciprocal mappings, focusing on the horizontal reciprocal transformation. Offers suggestions for using the graphing calculator, for extending the concepts, and for teaching about reciprocal mappings. (JRH)

Describes inviting fourth-graders to use their own language to describe mathematical ideas, postponing the use of technical vocabulary so students can explain the significant concepts and ideas in their own way first. Discusses how this use of metaphorical language to teach math concepts can enliven student interest and understanding, and infuse…

Shows how the children's book "How Big Is a Foot?" can motivate measurement explorations with nonstandard units and lead to the development of standard units. (MKR)

Presents an elementary physics problem, the solution of which illuminates physical meaning and its relation to real, imaginary, and complex mathematical quantities. (JRH)

Holistic math focuses on problem solving with numbers and concepts. Whole math activities for adults include shopping for groceries, eating in restaurants, buying gas, taking medicine, measuring a room, estimating servings, and compiling a family cookbook. (SK)

Shows how mathematical concepts can be displayed on World Wide Web pages. Discusses HTML; embedding mathematical formulae into text as pictures; the use of word-processing tools; MathML, a version of HTML for math; IBM Techexplorer, a browser plug-in; and Java applets. (Author/LRW)

Notes that quantity and measurement estimation for young children is a difficult mathematical idea for teachers to convey effectively. Explores the problem and alternative teaching methods. Suggests using referents, chunking, and unitizing as optional ways to present estimation. Includes sample activities that develop estimating skills in young…

Introduces two methods of introducing trigonometry: ratio method and unit circle method. Presents a teaching experiment with two groups of students, half of whom were taught with ratio method and the other half with unit circle method. Concludes that ratio method students were better able to master the skills required and made greater improvements…

Four experiments examined children's understanding of the inverse relationship between the number of parts into which a quantity is divided and the size of each part. Found that children tended to judge that bigger shares resulted from sharing with more recipients. Seven-year olds performed correctly on a simplified equal-sharing task. Five-year…

Explores secondary school students' conceptions of division by zero. A substantial number of the participating secondary school students argued that division by zero results in a number, and concrete arguments were generally regarded as valid for justifying the impossibility of division by zero. (Contains 30 references.) (Author/ASK)

Generally, when recursion is introduced to students the concept is illustrated with a toy (Towers of Hanoi) and some abstract mathematical functions (factorial, power, Fibonacci). These illustrate recursion in the same sense that counting to 10 can be used to illustrate a for loop. These are all good illustrations, but do not represent serious…

Since the game SET[R] was first introduced to the public in 1993, it has stimulated some interesting studies. While the game itself is rather straightforward, a plethora of decent mathematical questions lies beneath the surface. It is perhaps because the game ties in so closely with such an underlying mathematical term that its implications can be…

This article presents a number of the mathematics and computer integration teaching opportunities related to the exploration of palindromes. (Contains 6 figures and 1 table.)

This article examines the classroom value of assigning good mathematical problems and especially of encouraging many different approaches to their solutions. (Contains 6 figures.)