The "magic" paradigm was devised to assess conservation of number in young children. Subjects were 32 three- to four-year-old children. (MP)

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)

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)

An argument is made against the use of the metric system as the sole system of measurement since computers use a hexadecimal system. (MP)

Considerations of the history of similar techniques and the structure of the method itself are used to discuss this question. (MP)

A discussion is given of a method of finger reckoning in which the numbers one through ten are represented by one's fingers. (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)