Relationships between both the elements and the overall characteristics of Pascal's triangle are explored. (DT)

A number problem is presented and analyzed. (DT)

This article formalizes activities using a pool table into a related mathematical system complete with definitions, axioms, and theorems. (DT)

An algorithm is given for computing the cube root of any real number on a calculator. (DT)

The fundamental role of the theorems of Pappus and Desargues in the construction of nomograms is explained. (DT)

A card trick is explained and generalized using modular arithmetic. (DT)

The construction of a nomograph for the harmonic mean is explained, and several problems involving the harmonic mean are stated and proved. (DT)

First graders at three different schools were individually interviewed to determine their understanding of missing addend problems. Details of the interview are provided. Behaviors separating successful from unsuccessful students, students' number conservation ability, and the abstractness of missing-number problems are discussed. (DT)

The teaching of different number bases to elementary school children is questioned. (DT)

An ant city is used as the basis for counting and other numerical activities. (DT)

The objective of preschool teachers should be to determine the mathematical ability of preschool children and improve their skills using meaningful teaching methods through pictorial demonstration and manipulative models. Children who receive number concept instruction through hands-on play models, activities, and discussion show greater…

Fractions and division are two topics that receive considerable attention in elementary school mathematics, particularly in grade three and beyond. Despite this attention, fraction and division concepts and skills prove difficult for many middle school students to learn and for teachers to teach. This paper reports on part of a larger study…

The rationale of this study is based on the premise that the outcomes of children's learning are specifically shaped by the interaction of their individual cognitive structures with the presentations of curricular content in the classroom. Therefore, since the interpretive tools that children apply to instructional content may vary substantially,…