Solution of, and commentary on, a problem suitable for use in the secondary school mathematics classroom. Topics from arithmetic, algebra, and number theory appear in a unified way. (FL)

The problem of placing stamps on a grid is presented, with variable forms of the problem and various levels of the solution described. (MNS)

Problems which can be solved or partially solved by the Gregory Interpolation Formula are presented. The formula is explained and applied to three problems. (MNS)

A history of perfect numbers is presented, which briefly covers the 27 values known at this time. (MP)

Interrelationships between problem solving and number sense are discussed. Suggestions are given on helping children to search for a solution process and to reject unreasonable answers. The teacher's role in developing number-sense skills with problem-solving tasks is also discussed. (MNS)

Shares some explorations of Fibonacci sequences with a special focus on problem-solving and posing processes. (ASK)

Analyzes a didactical sequence for the teaching of addition and subtraction procedures and algorithms. Uses didactical procedures by children in problem solving activities in order to gain a better understanding of the interaction between numbers, numeration, and operations knowledge which are involved in the construction of addition and…

A classic problem involving the "misuse" of mathematical induction is presented. The error in the "proof" is then exposed. The generalization of this problem is presented as a false theorem which should serve to highlight the error. (LS)

Elucidated is the relationship among three threads of mathematical investigations: Kirkman's schoolgirl problems, finite geometries, and Euler's n-square officer problems. (JP)

Provided is an introduction to the properties of continued fractions for the intellectually curious high school student. Among the topics included are (1) Expansion of Rational Numbers into Simple Continued Fractions, (2) Convergents, (3) Continued Fractions and Linear Diophantine Equations of the Type am + bn = c, (4) Continued Fractions and…

The author gives a method for involving students in developing and verifying elementary number theory hypotheses by studying areas and perimeters of primitive pythagorean triangles. (MN)

The focus is on multi-step problems, with suggestions on helping students understand the mathematical relations, decide which computational procedures to use, and identify the sequence in which computations should be performed. An activity to aid understanding of variables is also included. (MNS)

Research on college students' ability to estimate means and variances for sets of data showed that they were more able to estimate means, and that various characteristics of the data (e.g. magnitude of numbers) influenced the accuracy of estimates. (SD)