A problem concerned with a ball on a billiard table is discussed. A theorem and corollaries regarding the path of the ball are formulated and proved. (MK)

The author argues that the idea of canonical elements provides a coherent relationship between equivalence relations, the basis of modern approaches to too many mathematical topics, and the traditional aspect of computation. Examples of equivalent relations, canonical elements, and their calculations are given. (MK)

The historical development of the integers, the rationals, the reals, and the complex numbers is traced. (MK)

An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

A number of activities are suggested that provide motivation and increases the confidence of students involved in practicing numerical skills. (MP)

Some of the most important types of arguments used in mathematical proofs are pointed out, with examples drawn entirely from work with numbers. (MP)

A method of multiplying using fingers is described and an explanation given. The method is then generalized to other number bases. (MP)

A method is described for teaching secondary school mathematics students about the harmonic mean. (DT)

A method is discussed for justifying to students the fact that the product of two negative integers is positive. (DT)

A method is given for generalizing Pascal's triangle to three dimensions. (DT)

Investigates possible relations between the methods of quantification available to children and their performance on certain tasks requiring an understanding of number invariance. (Author/RK)

Cardinal-ordinal abilities and attentional preferences of kindergarten nonconservers, kindergarten conservers, and third grade conservers of number were compared by employing standarized versions of Piagetian cardinal-ordinal tasks and a triad preference task. (Author/JMB)

Investigates the extent to which children's number sense and novel problem-solving skills govern their problem-posing abilities in routine and nonroutine situations. Children who participated in the program appeared to show substantial developments in each of the program components in contrast to those who did not participate. Contains 66…

Examines 199 middle school students' understanding of percent, focusing on number sense. Reports that students performed better interpreting a quantity expressed as a percent given a pictorial continuous region than when a pictorial discrete set of circles was given. Students had difficulty interpreting a quantity expressed as a percent of a…