An imaginary journey to Planet Seven is used to introduce the concept of number systems not based on ten. Activities include making a base 7 chart, performing base 7 addition and subtraction, designing Planet Seven currency, and developing other base systems for other planets. (MT)

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…

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.

Authors use combinatorical analysis to prove some interesting facts about the Fibonacci sequence.

The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

The paper presents reasons for teaching topics from number theory to elementary school students: (1) it can help reveal why numbers "act" in a certain way when added, multiplied, etc., (2) it offers drill material in new areas of mathematics, (3) it can develop interest - as mathematical enrichment, (4) it offers opportunities for students to…

A brief survey of the elementary number systems is provided. The natural numbers, integers, rational numbers, real numbers, and complex numbers are discussed; numerals and the use of numbers in measuring are also covered. (DT)

This is the first volume of a series produced by the State Education Department of the University of the State of New York. Mathematics objectives and sample items included were originally developed by four local school districts and are not intended to be official or comprehensive, but an aid to teachers in constructing curricula and making…

It is shown that a unit segment can be constructed from a given line segment of length the square root of x if x is a surd. (MP)

The examination by students of the associative property of a binary operation is used to illustrate how students can be involved in mathematical discovery. (MP)

A theory on the origin of Roman numerals proposes that the principal numbers can be stylized in terms of a square. It is speculated that the abacus or its equivalents, such as the counter or chequer-board, was used to count before the alphabet became common. (SW)