Suggests scales as alternative representations of numerical concepts and operations that can be used as arithmetic-mean machines, adding machines, multiplication machines, and geometric-mean machines. (ASK)

Presents solutions for a problem concerning doubling a recipe from a previous article on number concepts in the October 1997 issue. (ASK)

Presents research on students' use and understanding of algorithms in Poland. Concludes that there are detrimental side effects that stem from the teaching and learning of standard written algorithms. (ASK)

Discusses the role of play in the learning of mathematics. Describes a play for the third grade mathematics classroom that focuses on negative numbers and number concepts, and revisits Vygotsky from this point of view. Concludes that mathematically imaginative play can contribute greatly to mathematics learning in elementary school. (Contains 20…

Giving children time and encouragement to explain methods of calculation is a useful strategy. Uses this strategy with a group of children and discovers surprising thinking by one child on number facts. (ASK)

Discusses ways to improve the understanding of problems involving combination and complementation. Analyzes three children's initial mental representations, procedures, and reflections when presented with four different situations. Concludes with the impacts of the logico-mathematical relation of inclusion in these processes. Contains 31…

Presents a lesson that provides students in the early primary grades with the opportunity to explore counting techniques and develop an informal sense of permutations and combinations. (Author/CCM)

Discovers and analyzes the proportions of the Golden Section in the rare stone tablet, Tablet of Sippar, representing the four main feats of the god Marduk. (ASK)

Introduces data collated by Glendon Lean on nearly 900 counting systems in Papua New Guinea, Oceania, and Irian Jaya (West Papua) which came from a questionnaire completed by students and talks with village elders. Lean's thesis on the spontaneous developments of these ancient cultures challenged traditional theories describing the spread of…

For the last several years teachers have been using counters and connected cube "trains" and creating base-10 block models to help students develop number sense and understand number concepts. It is described how ten-frame tiles could be more useful tool for building number understanding for many students.

This article presents a brief biography of Johann Carl Friedrich Gauss. Gauss was born on April 30, 1777, in the German city of Braunschweig (Brunswick). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze. Neither of Gauss's parents had much education, his father could read and write, but earned his living doing menial jobs such as…

A teacher shares his successful experience in helping students understand the relationship between exponents and logarithms in high school and college courses. He presents the procedure that he used for teaching using a graphing calculator that shows previous calculations made.

Linguistic descriptions of sign languages are important to the recognition of their linguistic status. These languages are an essential part of the cultural heritage of the communities that create and use them and vital in the education of deaf children. They are also the reference point in language acquisition studies. Ours is exploratory…

Within the set of points in the plane with integer coordinates, one point is said to be visible from another if no other point in the set lies between them. This study of visibility draws in topics from a wide variety of mathematical areas, including geometry, number theory, probability, and combinatorics.

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…