Fifteen trainable mentally retarded students (four-six years old) were generally capable of rule-governed and other counting skills, and some could mentally compare numbers and choose the larger. Some Ss demonstrated a basic form of problem solving: they used the addition identity and commutativity principles to shortcut computational effort.…

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

A number problem is presented and analyzed. (DT)

When asked to report the first digit that comes to mind, a predominant number (28.4 percent) of the respondents choose 7. Three further experiments sought to establish whether this predominance is due to an automatic activation process or to a deliberate choice. (Editor)

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)

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)

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)

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 paper provides some guidance as to what to listen for to help students make sense of expressions in ways that connect to their ideas and honestly address the mathematics of rational numbers. It offers a reasonable initial answer to the question, "Where do students' ideas about fractions and ratios come from, and how can we work productively…