Topics discussed are: triangular numbers; three proofs of the surface area of a sphere; reverse notation; highest common factors; square roots from a graph; and clock geometry. (MP)

Activities are suggested for setting up a mathematics center for a week or more at a time. The activities relate to weight, counting, puzzles, length, graphing, and ordering. (MP)

An activity is described that is designed to give students a chance to learn about speed by calculating their own running or walking speed and the speed of cars. (MP)

This paper discusses the process of investigating a mathematical situation, making conjectures, formulating an equation, then using mathematical induction to show the result is valid. Several examples appropriate for secondary school level are given. (DT)

A procedure for recording the prime factors of a composite number is explained. (DT)

Activities are described in which the calculator is used for extending students' knowledge of place value and of basic arithmetic operations. (DT)

Conjectures about triangular arrangements of nine digits are stated and proved. (DT)

A method is given for determining what months will have a Friday the thirteenth for any given year. (DT)

Investigates the problem-posing abilities of third-grade children who displayed different profiles of achievement in number sense and novel problem solving. Concludes that children had difficulties in posing a range of problems in formal contexts in contrast to informal contexts, and children of different achievement profiles displayed different…

How can a chain with 63 links be cut in 3 places so that you could hand a person any number of links from 1 to 63? Considers variations on the problem and derives a general formula. (TO)

Describes five basic understandings involved in rational counting: (1) groupings of same or different items may be counted; (2) there is a stable order of the counting numbers; (3) one-to-one correspondence; (4) it does not matter which item is counted first; and (5) the cardinal principle. Discusses the importance of rational counting ability and…

Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…

A familiar procedure for generating magic squares is reviewed. A surprising pattern is noted. (MNS)

The study compared two methods of teaching an initial place value skill: a concrete, semiconcrete, abstract teaching sequence and an abstract-only presentation. Learning-disabled elementary and middle school students (N=24) using the concrete to abstract teaching sequence performed significantly better on three posttests than students taught the…