Understanding rational numbers is often an elusive goal in mathematics. Presented is an approach for teaching rational numbers that has been used with many preservice and elementary school teachers. With some adaptation, the approach could be used with secondary school students. (RH)

This paper describes a design research study with ten second-grade students who are part of the Measure Up (MU) research and development project underway at the University of Hawai'i. Students were asked how they counted in multiple bases, specifically how they knew when to go to a new place value and why it was necessary to do so. All ten…

Theorems concerning the probability of the appearance of certain digits in a numeral are stated and proved. (DT)

The relationship of the harmonic mean of two positive real numbers to the geometric mean and to the arithmetic mean is discussed; two geometric constructions for the harmonic mean are given. (DT)

Investigates the differences between students' and instructors' perceptions of similarities among basic computation-related rational number skills. Results indicate that college students in developmental mathematics do see some relationships among rational number computation skills, although not necessarily the ones seen by instructors. (AIM)

In a course on proofs, a number of problems deal with identities for Fibonacci numbers. Some general strategies with examples are used to help discover, prove, and generalize these identities.

Technology and mathematics. manipulatives have been brought together in a new format. This joining has resulted in virtual manipulatives that are available on the Internet for students. Virtual manipulatives have been defined as computer based renditions of common mathematics manipulatives and tools. Just as a physical object can be flipped,…

A theoretical analysis of the development of numerical representations indicated that playing linear number board games should enhance preschoolers' numerical knowledge and ability to acquire new numerical knowledge. The effect on knowledge of numerical magnitudes was predicted to be larger when the game was played with a linear board than with a…