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)

An example of mathematizing a situation and mathematical model-building by means of using a finite geometry is presented. (DT)

A mathematics contest involving competition between high school remedial mathematics classes is described. (DT)

Worksheets for a dot-to-dot puzzle and a crossnumber puzzle are provided. (DT)

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

Classroom use of computers is briefly discussed. The role of hand calculators in the mathematics classroom is analyzed in general, and questions are raised concerning the effect of calculators on student skills. (DT)

The problem of determining the distance that an object fell is analyzed. (DT)

Using an incorrect conjecture as a learning activity in mathematics is discussed. The example used is from transformation geometry. (DT)

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

Achievement levels of geometry classes were compared following units of instruction employing analytic, synthetic, and combination strategies. For above-average and below-average achievement groups, instruction with different strategies was found to yield differences in MANOVA - identified achievement composite scores. (Author/DT)

This article shows that the recognition of the dualities in equality (operator-equivalent) of the minus sign (unary-binary) and the zero (nullity-totality) during the transitional process from arithmetic to algebra by 12-13 year-old students constitutes a possible way to achieve the extension of the natural number domain to the integers. (Contains…

This book's activities probe rational and irrational numbers and investigate properties of integers and complex numbers. They explore numbers and operations embedded in physical objects and show how simple problems can lead to sophisticated considerations. Students examine the usefulness of irrational numbers in designing musical scales and of…