For centuries, the basic operations of school mathematics have been identified as addition, subtraction, multiplication, and division. Notably, these operations are "basic," not because they are foundational to mathematics knowledge, but because they were vital to a newly industrialized and market-driven economy several hundred years…

Most future teachers are familiar with number patterns that represent an arithmetic sequence, and most are able to determine the general representation of the "n"th number in the pattern. However, when they are given a visual representation instead of the numbers in the pattern, it is not always easy for them to make the connection between the…

Using the structure of a metacognitive journal, this article describes the author's discovery of an unusual method for adding fractions after carefully considering a student's response. (Contains 3 figures.)

Teachers must be prepared to recognize valid alternative representations of arithmetic problems. Challenging examples involving mixed fractions and division are presented along with teacher's discussion from a professional development workshop. (Contains 6 figures and 1 table.)

This article describes one way to introduce fraction, decimal, and percent equivalents by linking student-created Op Art with examples of twentieth-century abstract painting. (Contains 7 figures.)

During the twentieth century, major changes occurred in conception of arithmetic as a school subject. These changes resulted from both the study of arithmetic itself and from influences from movements and developments outside the subject matter; and they have affected both the content of arithmetic and the methodology of presenting that content to…