An interesting class of purely pandiagonal, i.e. non-magic, whole number (integer) squares of orders (row/column dimension) of the powers of two which are related to Gray codes and square Karnaugh maps has been identified. Treated as matrices these squares possess just two non-zero eigenvalues. The construction of these squares has been automated…

The educational background of students termed "limited English proficient" (LEP) is discussed, with consideration of how that background might affect the LEP student's learning of arithmetic. Reasons why knowledge of background is important are first noted. Then examples of different ways to read and write numerals and differing subtraction and…

The purpose of this paper is to identify how the theory and techniques of research in cognitive development can be applied to the study of learning and instruction in mathematics. Five basic research paradigms are characterized; major directions of research on number, measurement, geometry, and adolescent reasoning are identified. Most of the…

Nomadism is a worldwide phenomenon and its practitioners fall into three categories: (1) hunter/food gatherers, such as the Hadzabe in the United Republic of Tanzania; (2) itinerant workers, including the gypsies in North America; and (3) pastoralists, such as the Masai and Shuaw Arabs in Africa, the Sami in Finland, Norway, and Sweden, and the…

This paper describes the current debate over developmentally appropriate teaching practice. The paper presents the perspective of multicultural educators, who argue that developmentally appropriate practice is biased toward white, middle-class values, and the perspective of special educators, who argue that modification of developmentally…